Firstsage of Greece,he founded classical geometry and natural philosophy. Alchemists have claimed him as one of their own. Thetheorem of Thales (one oftwo) is about two triangles with parallel sides: The pyramid's shadow is to the pyramid what a man's shadow is to the man [wow].
Anaximander of Miletus (610-546 BC)
First Greek scholar to write about Nature. A student and/or friend of Thales, he succeeded him ashead of hisMilesian school. Anaximander founded astronomy and cosmology (cf. apeiron). He introduced into Greece thegnomon, thesundial andcartography. Pythagoras was one of his pupils.
He founded metaphysics and argued that nothing remains still, which led him to aMach-like principle of Relativity. Dubbed the weeping philosopher (while Democritus is thelaughing philosopher). He called Pythagoras a fraud.
Parmenides of Elea (c. 515-450 BC)
Existence is timeless; change is impossible.
Parmenides upheld the extreme view ofstaticmonism. He spent some time as a member of thePythagorean community at Croton. Zeno was hiseromenos. At age 65, Parmenides went to Athens and met a youthful Socrates (469-399 BC).
Inventor of rhetoric and borderline charlatan. His arbitrary explanation of reality with 4 elements (Earth, Air, Fire and Water) and 2 forces (Love and Strife) dominated Western thought for over two millenia. Several of his intuitions were correct, though, including the finiteness of the speed of light.
Zeno of Elea (c. 490-425 BC)
In the most famous of his provocative paradoxes, Zeno asks how swift-footedAchilles could overcome a tortoise, since Achilles must first reach the initialposition of the tortoise... By the time he gets there, the animal is elsewhere andAchilles is left with a similar challenge, ad infinitum.
Philolaus of Croton (c.470 - c.385 BC)
He put Pythagoreanism in writing (including numerology). He is credited with the first astronomical system where the Earth wasn't at the center of the Universe. After a second fire destroyed the Pythagorean campus at Croton (c. 454 BC) Philolaus fledto Lucania and Thebes. He taught Archytas.
Hippias of Elis (c. 460 - fl. 399 BC)
A sophist whom Plato despised (he portrays him as vain and arrogant, with a wide but shallow knowledge). Hippias devised the first transcendental curve, known as quadratrix or trisectrix because the quadrature of the circle and the trisection of an angle would be trivial if its use was allowed.
Democritus of Abdera (c. 460-370 BC)
The atomists' school in Abdera was founded by his teacher Leucippus, himself a student ofZeno and a proponent of the law of causality. Democritus argued that all was made of indivisible atoms moving in the void. One of his followers, the alchemist Bolus of Mendes, also signed "Democritus".
Hippocrates of Cos, physician (c. 450-377 BC)
Revolutionary founder of Western medicine. An asclepiad, said to be a direct descendant (17 or 19 generations) of the legendaryAesclepius, Hippocrates studied philosophy underDemocritus and learned rudiments of medicinefrom his father, Heraclides, and from Herodicus of Selymbria.
Archytas of Tarentum (428-347 BC)
Mathematician, statesman, staunchPythagorean. Student of Philolaus and teacher of Eudoxus. Invented the pulley and the screw. Archytas considered surfaces generated by rotating curves and coulddouble the cubeby intersecting three of those (defining theArchytas curve in the process).
Plato (427-347 BC)
To develop ideal laws behind appearances, he createdhe created the first institution of higher learning, in 387 BC. In agardennear an olive grove dedicated toAkademos; Northwest of Athens (between the city walls and the Cephissus River). It lasted 915 years. (Justinian closed it in 529). Initiation to Geometry was anentrance requirement.
Eudoxus of Cnidus (408-355 BC)
His definition of the comparison between ratios of (possibly irrational) numbersappears in the fifth book ofEuclid. It inspired Dedekind's definition of real numbers (1872). Eudoxus invented the methodof exhaustion built upon by Archimedes. He was the first Greek scholar to map the stars.
In 338 BC, he was (narrowly) elected third rector of the Academia (suceedingPlato's nephewSpeusippus of Athens). Unlike otheratomists, heenvisioned the ultimate constituents of matter as lines; not corpuscules. Xenocrates may thus be construed as the firststring theorist...
Aristotle of Stagira, logician (384-322 BC)
He shunned mathematics entirely in his natural philosophy which was lightly based on crude observations. The lack of discussionof his dogma for two millenia greatly hinderedthe development of natural Science, especiallywhen some Aristotelian misconceptions became part of Church doctrine.
Epicurus of Samos, materialist (341-270 BC)
FollowingDemocritus, he believed only matter existed, consisting of atoms and void. Unlike Pythagoras or Plato he didn't believe in an immortal soul and argued that death shouldn't be feared. His philosophy and physics (causality and conservation laws) inspired Lucretius and Newton.
Euclid of Alexandria (c. 325-265 BC)
Father of axiomatic geometry and author of The Elements (the most enduring textbook in the history of mathematics). His presentation of the mathematics of his timeswould become the centerpiece of mathematical teaching for more than 2000 years. Euclid shunned neusis constructions.
Aristarchus of Samos (c. 310-230 BC)
Copernicus credited him for the idea that Earth rotates on its own axisand revolves around the Sun. From rough angular measurements, he estimated the distance to the Sun. As he couldn't detect the parallax of stars, he declared them to be extremely distant (whichArchimedes wouldn't accept).
Ctesibius of Alexandria (c. 310-222 BC)
Starting out as a barber, he became an engineer and founded the schoolof mathematics at the Library of Alexandria (he may have served as its first head librarian). He invented a suction pump, a compressed-air catapult,awater organ and the regulated water-clock (fed by an overflowing vessel).
Philo of Byzantium, engineer (c. 280-220 BC)
Also known as Philo Mechanicus, he was an engineerwho journeyed to Rhodes and Alexandria. He is credited for inventing the escapement, the water mill and the gimbal suspension (described by Cardano).Philon constructed theDelian constantby intersecting a circle and an hyperbola.
Archimedes of Syracuse (c. 287-212 BC)
A native and resident ofSyracuse,Archimedes studied inAlexandria and maintainedrelations with Alexandrian scholars. Although he became famous for designing warmachines, this early physicist was, above all, an outstanding mathematician. The 14Archimedean solidsare uniform.
Apollonius named and studied theconic sections. He found that a circle consists of allpoints M whose distances to two foci (I,J) are in a fixed ratio (e.g., 2/3). He said that planets revolve around the Sun and that the Earth itself mightas well be thought of as moving, like planets do.
The only extant work of Lucretius is the didactic poem De rerum natura (On the Nature of Things) where the basic Epicurean tenets are expressed in a surprisingly modern way. It's especially so about atomism,randomnessandfree-will. Rutherford's motto is a quote from Lucretius.
Seneca, stoic philosopher (c.4 BC-65 AD)
Lucius Annaeus Seneca the Younger served asNero's tutor and an advisor early in hisreign. He retired from public life in 62. He reflected on comets, meteors, meteorological optics, thunder and the colors produced byglass corners. Forced to commit suicide as a suspect in aplot against Nero.
Hero of Alexandria, physicist (c. AD 10-75)
Influenced byCtesibius. Some of his works were meant to be lecture notes: Pneumatica (fluids &steam) Metrica (methods andformulas for areas and volumes, lost until 1896) Mechanica (statics & simple machines) Catoptrica (mirrors). Hero still thought light-rays came from the eyes.
Pliny the Elder, encyclopedist (AD 23-79)
Gaius Plinius Secundus was a public official who wrote a lot. The 37 books of Historia Naturalis (AD 77) present, in an anthropocentric way, everything the Romans knew about the natural world. In this, Pliny cites nearly 4000 authors (his "Ostanes" need not bethe one who cited Miriam).
Earliest female experimentalist on record (signing Miriam the prophetess, sister of Moses). The tribikosstill and the eponymous balneum Mariae may be due to her. F. Hoefer credits her for muriatic acid. The oldest extant alchemical texts (byZosimos ofPanopolis) quote her as a past master.
Dioscorides, pharmacologist (c. AD 40-90)
Pedanius Dioscorides was the Greek author of the first major pharmacopeia (which never went out of print and remained authoritative for over 1500 years). The 5 volumes of De Materia Medica (AD 70) present about 600 plants.
A leading member of the late Pythagorean School. His Introduction to Arithmetic(Arithmetike eisagoge, c. AD 100) was the standard arithmetic text for more than 1000 years but itcontains noproofs and has several elementary mistakes in it. He knew only 4 perfect numbers (6, 28, 496 and 8128).
Menelaus of Alexandria (c. AD 70-135)
A resident of Rome who spent his youth in Alexandria, he recognized geodesics on a curved surfaceas analogs to straight lines on a plane. Shunning arcs of parallels, he definedspherical triangles as consisting of arcs of great circles. This was a turning point inspherical trigonometry.
Ptolemy of Alexandria (c. AD 87-165)
Claudius Ptolemaeus was a Roman citizen who wrote in Greek (his first name may have been Tiberius). His Almagest dominated astronomy for centuries. Ptolemy's theorem says that a tetragon is cyclic iff the product of its diagonalsis the sum of the pairwise products of facing sides.
Galen of Pergamos, physician (AD 129-217)
A Roman citizen of Greek ethnicity, he started out as physician to the gladiators. He was so prolific (10 million words) that his surviving works (30%) representnearly half of the extant literature from ancient Greece. His thinking dominated medicine for more than a thousand years.
Leading commentator ofAristotle, he revived Aristotelian ideas. Appointed to an endowed chair in Athensduring the co-reign of Septimius Severus and Caracalla (AD 198-209). He first described the dark band,named after him, between the brignt primary rainbow and the dim secondary rainbow.
Diophantus of Alexandria (c. AD 200-284)
A Diophantine problem is to find aninteger satisfying apolynomial equationwith integer coefficients, or several such equations simultaneously. Diophantus himself never considered irrational numbers or nonpositive ones. His age at death was reportedly x = x/6 + x/12 + x/7 + 5 + x/2 + 4.
Liu Hui, Chinese mathematician (AD 225-295)
Possibly the best mathematician of ancient China, he was a descendant ofLiu Yi, Marquis of Zixiang,and lived in the state ofCao Wei (one of the feudingThree Kingdoms). He expanded theJiuzhang Suanshu with his owncommentaries and an appendix which became an official surveying manual.
Pappus of Alexandria (c. AD 290-350)
The theorem of Pappus (generalized byPascal in 1639) is a fundamental theorem of projective geometry. The name is also used for the twocentroid theoremspublished byPaul Guldin (1577-1643) in Centrobaryca (1635) pertaining tothe surface area and the volume of a solid of revolution.
Daughter of the mathematician Theon (c. 335-405) last librarian of Alexandria, who raised her like a boy. Her teaching of science was seen as pagan. She was ambushed and skinned alive by a mob of Christian fanatics. Hypatia's murder marks the beginning of the Dark Ages in the West.
Ioannis Grammaticus was one of the last to hold the chair of philosophy inAlexandria. Controversial in his time, he was the only writer in late antiquity to point out that the duration of a body's free fall doesn't depend on its weight (contra Aristotelem ). Galileo would give him credit for that.
Brahmagupta Bhillamalacarya (AD 598-668)
Brahmagupta (the "teacher fromBhillamal") was the first to treat 0 like any other number. LikeDiophantus before him,he pioneered the use of symbols in equations. He failed to specify that his celebratedformulafor the area of a quadrilateral is only validfor cyclic quadrilaterals.
Geber, experimental chemist (c. AD 721-815)
Abu MusaJabir ibn Hayyan al Azdi was born in Tus (Persia) but theArabs claim himas one of their own. Geber (orJabir) made remarkable scientific advances inpractical chemistry but also producedeponymous gibberish on occult alchemy.
Al-Khwarizmi, Algorismus (c. AD 783, fl.847)
Al-jabr (transposition from one side of an equation to the other) is the techniquewhich gave algebra its name. The term is from thetitleof the masterpiece published around 810 by Abu Abdallah Muhammed bin Musaal Khwarizmi. The quadratic formula is due to Al Kwarizmi.
Sanad ibn Ali (d. c. 864)
Ahmad al-Fhargani, Alfraganus (798-865)
Born in the Cuba City of Transoxiana (Ferghana region of far-eastern Uzbekistan). Worked in Baghdad and died in Egypt. Alfraganus summarized and perfectedptolemaic astronomy in The book of 30 chapters (c. 833). Messed-up the al-Ja'fari branch of theNahrawan Canal near Samarra.
Al-Sabi Thabit ibn Qurra al-Harrani (836-901)
A Sabian, not a Muslim, he's best known as Thabit or Thebit. All later editions ofEuclid's Elements were based on his revision. He was a founder ofstatics. Hisremark that there are as many integers as even oneshelpedDedekind characterize infinite sets (as equipollent to aproper subset).
Mohammad Abu'l-Wafa al-Buzjani (940-998)
Abu'l-Wafa was the first to build a wall quadrant to observe the stars. Whenever possible, he determined quantities by giving arulerand compass construction for them. He was an expert inAl-Khwarizmi's "Indian reckoning", but still wrote out all numbers in arabic letters, for the sake of his audience.
IbnSahl (c. 940-1000)
Precursor of Alhazen largely ignored before1993 (Roshdi Rashed). First Muslim known to have studiedPtolemy's Optics. In Burning Mirrors and Lenses (c.984) he first stated theproportionality of sines in a refracted ray (Snell's law) andworked out the exact shapes of anaclastic lenses.
Al-Karaji / al-Karkhi, engineer (953-1029)
Abu Bekr ibn Muhammad ibn al-Husayn Al-Karaji was probably born inKarajalthough his alternative name would imply a connection withKarkh,the west part of Baghdad, where he worked most of his life. He devised the notion of mathematical induction and used it on the binomial triangle.
Alhazen, "First Scientist" (965-1039)
Abu Ali Muhammed ibnal-Hasn ibn al-Haytham al-Basriwas hired byAl-Hakimand had to feign madness to avoid impossible duties,until the "Mad Caliph" died (1021). Early proponent of thescientific method,Alhazen pioneeredoptics and anticipatedthe first law of Newton (who quoted him).
Abu Rayhan al-Biruni, Alberonius (973-1048)
Celebrated polymath who was first exposed to mathematics by associating withAbu Nasr Mansur (970-1036)ofsine law fame. Al-Biruni pioneered scientific methods in astronomy and geology. First mathematician to state the limitation ofBrahmagupta's simplified formula for areas of quadrilaterals.
Ibn Sina, Avicenna, polymath (980-1037)
Abu Al al-Hosain ibn Abdall h ibn S na is also known as Pur Sina, the Prince of physicians. He was a child prodigy born on 980-08-23 in the Persian city of Afshaneh,nearBukhara. 7 centuries before Newton, he held that motion in a vacuum would be self-sustaining (first law of dynamics).
Last and greatest mathematician in the Golden Age of Indian mathematics. He developed trigonometry for its own sake, including spherical trigonometry,and introduced the addition formula: sin (x+y) = sin x cos y + cos x sin y He conceived derivatives and statedRolle's theorem.
Robert Grosseteste (1168-1253)
Educated atOxford University,of which he became Chancellor in 1215 (until 1221). Grosseteste introduced the earliest teaching of thescientific method in Oxford (comparing theories with observations). After holding other ecclesiastical posts, he becameBishop of Lincoln in 1235.
Leonardo Pisano Fibonacci (1170-1250)
He ended a mathematical lull of eight centuries in the West. As a teenager in Algeria, Fibonacci learned the Hindu-Arabicdecimal systemthat he would advocate in Europe. In Liber Abaci (1202) he discussed manycomputational puzzles,including one about theFibonacci sequence...
Roger Bacon, Franciscan (1214-1292)
Nicknamed Doctor Mirabilis. He went to the University of Paris to take a degree(1241) and he started lecturing onAristotle there (1234-1247) before returningto Oxford. Influenced byGrosseteste, Roger Bacon became themost active early proponent of thescientific method in Europe.
He was born and raised on the Island of Mallorca, off the coast of Catalonia. He was brought up in the Royal Court and would become the dominant figure in Medieval Catalan literature. In 1272, he conceived of reducing all knowledge to first principles. His work greatly influenced Leibniz.
William of Ockham, friar (c.1288-1348)
Arguably, the foremost Medieval logician. His enduring contribution to natural philosophy is the "principleof parsimony" known as Occam's Razor (the simplest explanation compatible with observations is preferred).
In 1327 and 1340,Joannes Buridanus was rector of Paris where he had studied underOckham (whom he condemned in 1340). Buridan seededCopernican ideas. He contributed toprobabilities and optics. His concept of impetus (c.1340)anticipated momentum. Excommunicated for nominalism.
Nicole Oresme, bishop (1323-1382)
Star student ofJean Buridan, Nicolas Oresme is credited with the introduction offractional exponents and the graphing of functions. He also established thedivergence of the harmonic series. Oresme anticipated analytic geometry, the lawof free fall and chemical structures...
Madhava of Sangamagrama (1350-1425)
Madhava gave the first examples of power series (besidesgeometric series) as expansions of trigonometric functions (sin, cos, arctg). Madhava's knowledge was perpetuated and expanded by the school he founded in Kerala and may have influenced similar developments later, in the West.
Regiomontanus, publisher (1436-1476)
Mathematical prodigy, earliest publisher of printed scientific works. Johannes Müller vonKönigsberg signed Joannes de Monte Regio. ( "Regiomontanus" was coined in 1534, by Melanchthon). Cardano scorned him for publishingJabir ibn Aflah'sspherical trigonometry without proper credit.
Luca Pacioli, Franciscan friar (1445-1517)
Artist and full professor of mathematics, Pacioli invented modern Venitian double-entry accounting in 1494. He shared living quarters in Milan (1494-1499) with Leonardo da Vinci, who illustrated Pacioli's second masterpiece "De divina proportione"(with iconicpolyhedral frames).
Leonardo da Vinci (1452-1519)
A stellar Renaissance painter, he left 13000 pages of illustrated notes on science and engineering (in mirror-image cursive). He was taught mathematics by Luca Pacioli with whom he lived in Milan, whilepaintingThe Last Supper.(c. 1495) and illustrating Pacioli's"De divina proportione".
Scipione del Ferro (1465-1526)
Lecturer in arithmetic and geometry since 1496 atBologna, Pacioli visited in 1501-02 and somehow inspiredthe private solution of the cubic equation in depressed form (quadratic term suitably removed) passed by Ferro to his son-in-law and successor (1526) Hannibal della Nave.
Philippus Aureolus Theophrastus Bombastus von Hohenheim chose the pseudonym Paracelsus in honor of the encyclopedistCelsus. He is the first systematic botanist. He namedzinc (1526) and revolutonized medicine (without freeing it from superstition) by usingmineral chemicals.
Niccolò Fontana Tartaglia (1499-1557)
Son of a mounted postman who was murdered when he was only six. The nickname Tartaglia (stutterer) came from an infirmity due to the larynx injury he suffered in theSack of Brescia(Feb. 1512). He became a military engineer and founded ballistics (1531). Solved the cubic on 1535-02-13.
First scholar to use negative numbers routinely. In 1545, he revealed the solution of cubic equations obtained by del Ferro (1465-1526) in 1516 and rediscovered (1535-02-13) byTartaglia (1499-1557). It had been extended to quartics, in 1540, by his own assistantLodovico Ferrari(1522-1565).
Bernardino Telesio (1509-1588)
Born into a nobleCalabrian family,he studied in Milan, Rome andPadua. He left the universities in 1535, without a doctorate. Once married (1553) he went back home toCosenzaand reorganized what became theCosentian Academy. He revolted against Aristotelian doctrines.
Ambroise Paré, surgeon (1510-1590)
Ambroise Paré was a royal military surgeon. On one occasion on the battlefield, he had to use a makeshift ointment. He observed that the soldiers so treated recovered much better than thosewho underwent the formerly "recommended" treatment (i.e., burning wounds with oil).
Andries Wijtinck van Wesele (1514-1564)
Breaking with the precepts ofGalen, Andreas Vesalius Bruxellensis revolutionized medicine in 1543with the first modern book onhuman anatomy, based on the detailed observations he made duringthe dissections that he carried out in front of medical studentsat the University of Padua.
François Viète (1540-1603)
His name is also spelled Viette (latin: Franciscus Vieta). Viète pioneered modern algebraic notations,where known constants and unknown quantities are represented by letters. The trigonometric law of tangents (c. 1580) is due to him. In 1593, he gave an expression of as aninfinite product.
Tycho Brahe, astronomer (1546-1601)
Tyge Ottesen Brahe was from the high Danish nobility. HisUraniborg observatory,onHven island,cost 1% of the state budget but allowed precise (naked-eye)observations of planetary positions which made possible the work ofKepler.
Simon Stevin, Stevinus (1548-1620)
Flemish engineer who introduced decimal fractions (1583) shortly afterViète (1579). Stevin wrote in Dutch and coined many Dutch scientific terms(without the Latin/Greek roots used in other languages). He found that the pressure exerted by a liquid at rest in a vessel depends only on depth (1586).
John Napier of Merchiston (1550-1617)
Known as Neper to the French, he invented an early version of logarithmswhich he spent years tabulating. This improved uponprosthaphaeresis (multiplication using trigonometry). Common (decimal) logarithms are due to his younger contemporary Henry Briggs (1561-1630).
Thomas Harriot (1560-1621)
Harriotre-discoveredthelaw of refraction in July 1601 (before Snell andDescartes). He made the first telescopic drawing of the moon (1609-07-26). and was first to record sunspots (1610-12-08). He worked out the Sun's rotation. His research waned after 1613, as he battled skin cancer.
Using his own pulse as a timer,Galileo discovered thependulum isochronism in 1581. He found that all bodies fall with the same acceleration anddeclared mechanical laws valid for all observers in uniform motion. He made the first telescopic observations of celestial bodies (1609).
Johannes Kepler (1571-1630)
He found vision comes from inverted images formimg on the retina. His calculations helped establish heliocentric astronomy. In 1609 and 1619,he published his famous 3 laws of planetary motion. He studiedoptics,polyhedra,logarithms, etc. Arguably,he paved the road to Calculus.
William Oughtred (1574-1660)
Inventor of the slide rule (1630). The symbols × for multiplication and :: for proportionality are due to him. Ordained in 1603, vicar of Shalford in 1604, rector of Albury (1610-1660). For half a century, he mentored many mathematicians, includingJohn Wallis (1616-1703).
Jan Baptist Van Helmont (1577-1644)
Founder of pneumatic chemistry and biochemistry, who coined the word gas (1632). He famously proved that plant bulk doesn't come from soil by weighing a potted willow tree after 5 years. His chemical work was published in 1640 by his son, FranciscusVan Helmont (1614-1698).
William Harvey, physician (1578-1657)
William Harvey started modern experimental medicine with his discoveryof thecirculation of the blood. He had been a student atPadua,where the Flemish anatomistAndreas Vesalius (1514-1564)had started encouraging students to observe rather than conform to the precepts ofGalen.
Marin Mersenne, Minim friar (1588-1648)
Of modest origins, Mersenne attended the newly-created Jesuit college of La Flèche (1604-1609) then studied in Paris until July 1611, when he joinedthe Order of Minims (founded in 1436). He was ordained one year later. His informal Academia Parisiensis (1635) had 140 members.
Gérard Desargues (1591-1661)
Building on the fundamental results ofPappus, Desargues invented projective geometry in 1639. That innovation was largely ignored, except by the likes ofPascalandLa Hire,until a key manuscript rediscovered in 1845 was published in 1864,following a remarkable rebirth of the subject.
Descartes attended the famous Jesuit college of La Flèchefrom 1607 to 1615. He met his scientific mentorIsaac Beeckman (1588-1637)in 1618. He introduced cartesian geometry in one of the three appendicesto Discourssur la méthode (1637). Proponent of substancedualism (1641).
Bonaventura Cavalieri, Jesuit (1598-1647)
In Pisa, Cavalieri was mentored byBenedetto Castelli (1578-1643)who put him in touch withGalileo. Cavalieri's principles can be construed as the preliminary conceptual foundations for integral calculus, stating (in modern terms) that theintegrals of equal functions are equal...
Orphan. Assistant to Castelli, thenGalileo. Torricelli invented the barometer in 1644: Hefigured out that the rarefied mercury vapor above the mercury is nearly a vacuum. What pushes the liquid up the tubeis the (variable) atmospheric pressure. Gabriel's horn (1643).
John Wallis (1616-1703)
Appointed to theSavilianChair of Geometry at Oxford by Oliver Cromwell in 1649, John Wallis held that position for more than 50 years. In 1655, he published his great Arithmetica Infinitorum, which helped pave the way for the introduction of modernCalculusbyNewton andLeibniz.
Francesco Maria Grimaldi (1618-1663)
The Jesuit (1632) who discovered light diffraction and named it so. His posthumous book sparkedNewton's interest in optics. Huygens also owned a copy, which may have inspired hisformulation of Huygens' principle in 1678 (whichFresnel only applied to diffraction patterns in 1816).
Blaise Pascal (1623-1662)
At 16, hegeneralizedthe theorem ofPappus. At 19, he built a celebratedmechanical calculator. In 1647, Pascal thought of using aTorricelli barometer asan altimeter, which established experimentally (1648) the origin of atmospheric pressure. The SI unit of pressure (Pa) is named after him.
In 1660 (as assistant ofRobert Boyle) his law of elasticity affirmed the notion of force. After theGreat Fire (1666) he surveyed half of London and designed many new buildings. For 40 years, he produced new experiments weekly for theRoyal Society. He was a microscopic & telescopic observer.
The JapaneseNewton. Second son of a Samurai warrior. Adopted by a technocrat (Gorozaemon SEKI ) whose name he took. Some of his findings predate their Western discoveries: Determinants (1683) Bernoulli numbers, etc. He was the teacher of Katahiro (1664-1739).
Also known as Lucrezia Piscopia, Elena Lucrezia Cornaro-Piscopia was from theVenetian nobility. She was anOblateof the Order of St. Benedict (1665) and a mathematician... On 25 June 1678, she became the first woman to beawarded a doctorate (fromPadua). 54 years before Laura Bassi.
In 1691, he proved a statement ofBháscara: If a polynomial has equal values at two points, then its derivative vanishes somewhere between those points. The result was generalized beyond polynomials byCauchy (1823). It was first called "Rolle's theorem" byDrobisch (1834)andBellavitis (1846).
Earliest mathematician in afamily that would produce many (but none among his descendants). With his younger brotherJohann, Jacob pioneered the calculus of variations (whichEuler would tackle in 1744). He found Bernoulli numbers (independently ofSeki) and formalized probability theory.
Stephen Gray (1667-1736)
Chemist, astronomer and electrician. In 1729 (well before Du Fay) he realized that electricity could flow through conductors but not insulators (both names were coined by Desaguliers in 1742). Gray was the first recipient of theCopley Medal (1731). He died a pauper.
FrenchHuguenot, tutored by Jacques Ozanam (1640-1718) in 1684-85. He fled to England shortly after 1685, eking out a living as a tutor and actuary. He befriended the likes of Halley and Newton and entered all major mathematical societies: London (1697), Berlin(1735) and...Paris (1754).
Johann Bernoulli (1667-1748)
Father ofDaniel and main teacher of Leonhard Euler. Initiated by his older brotherJacob, he collaborated with himon early topics in the calculus of variations.Hired to teachGuillaume de l'Hôpital, Johann had toname after his student the famous rule he discovered during that work-for-hire.
Scottish mathematician (, 1726). In his first publication Lineae Tertii Ordinis Neutonianae (1717) he extended to 76 the number of types of planar cubiccurves (Newton had identified 72). The Stirling series is a classic example of a divergentasymptotic series.
James Bradley (1693-1762;1718)
Attempting to detectstellar parallax(whichBessel observed in 1838) he discoveredthe aberration of light and obtained a good estimate of the speed of light (1728). Bradley later found the nutation of the Earth's axis (1742). He was bothSavilian Professor (1721-) and Astronomer Royal (1742-).
Colin Maclaurin, mathematician (1698-1746)
Having entered the University ofGlasgow at age 11, he was granted an MA three years later for a thesis entitled The Power of Gravity. He then read divinity until elected professor of mathematics at 19, in Marischal College, after a 10-day competition. (That record would hold until2008.)
Maupertuis (1698-1759)
Pierre-Louis Moreau de Maupertuis used his principle of least action (1744) to reformulate Newtonian mechanics. This paved the way for Lagrangian and Hamiltonian mechanics and provided an elegant key foranhistorical derivation of Schrödinger's equation, published in 1928.
Independently ofWatson (1746) Franklin discovered theconservationof charge by positing opposite signs for what Du Fay(1733) had called resinous (-) and vitreous (+) electricity.
Emilie du Châtelet (1706-1749)
At 19,Gabrielle-Emilie de Breteuil married the Marquis Florent-Claude du Chastellet. She was the lover ofVoltaire whom sheand her husband protected in their château. She was tutored byMaupertuis (1733) andClairaut (1735). Shepopularizedthe concept of energy introduced by Leibniz.
Leonhard Euler (1707-1783)
He solved the Basel Problem in 1735. Themost prolific mathematician of all times,Euler became totally blind in 1771. He still produced nearly half of his 866 works after 1766(inSt. Petersburg)with the help of several assistants, includingNicolaus Fuss(1755-1826) who joined in 1773.
Laura Bassi, physicist (1711-1778)
Gabriele Manfredi(1681-1761) initiated her to higher mathematics and newtonian physics. In 1732 (at age 21) Laura Bassi became thesecond womanto earn a doctorate and the first to teach at a European university (Bologna). She was finally named professor of physics there, in 1776.
Alexis Clairaut (1713-1765)
At age 16, he introduced the study ofspace curves. He was the youngest member ever of theAcadémie des Sciences (July 1731). Clairaut's theorem(1740) says that, provided it'scontinuous,a partial derivative with respect to several variables doesn't depend on the order of the differentiations.
Child prodigy and author of the first mathematical book by a woman (1748). In 1750, she was appointed to the chair of mathematics at Bologna byPope Benedict XIV but she never went there (the first woman to hold a chair in Europe was thus Laura Bassi, in 1776).
JohnMichell, polymath (1724-1793; 1760)
CambridgeDon. He invented thetorsion balance (before Coulomb) andfound the inverse square law for magnetic poles (1750). Pioneered seismology (1760). Detected radiation pressure. Conceived, before Laplace, of dark stars with escape velocities exceeding thespeed of light.
Jean-Etienne Montucla (1725-1799)
Etienne Montucla was a mathematician and a historian. He authored the first book on the history of mathematics: Histoire des mathématiques(1758, 1798). The third volume (1799) was completed and published byLalande (1732-1807)who also wrote the fourth and final one (1802).
JohannHeinrich Lambert (1728-1777)
Johann Heinrich Lambert (French: Jean-Henri Lambert) was born inMulhouse,which was then in Switzerland (it's now in France).
His 6-volume mathematical textbook (1770-1782) was once standard for studentswishing to enter Polytechnique (this was also used atHarvardforcalculus). His theory (1779) of algebraic equations led to algebraic geometry. Bézout'slittle theorem says (x-a) divides the polynomial P(x)-P(a).
Jan Ingenhousz, early biochemist (1730-1799)
Dutch-born British physician who discovered the principles of photosynthesis. Building on the work of Joseph Priestley (1771) Ingenhousz showed that green plants do require sunlight to produce oxygen (1779). He was honored by a Google Doodle on his 287-th Birthday (2017-12-08).
Né Friedrich Wilhelm Herschel in Hanover, where he followed his father as a military musician, before emigrating to England (1757). He built his first large telescope in 1774. He discovered the planet Uranus on 1781-03-13.
Antoine-Laurent de Lavoisier (1743-1794)
Antoine Lavoisier founded quantitative chemistry by establishing thatmass is conserved in any chemical transformation. He was infamously executed during the French Revolution because of hisrôle as a tax collector.
Nicolas de Condorcet (1743-1794)
Marie, Jean, Antoine, Nicolas de Caritat, Marquis de Condorcet founded Social Choice Theory in 1785 with his Essay on the Application of Analysis to the Probabilityof Majority Decisions (introducing Condorcet's paradox). He was a moderate leader during the French revolution.
Alessandro Volta (1745-1827)
Correctly interpreting the 1791 observation byLuigi Galvani (1737-1798) of muscle contractionsin a dead frog, Volta reasoned that electricity is generated upon contact of two different metals. Replacing living tissue by paper soaked with saline electrolyte, he built the first battery in 1799.
Gaspard Monge (1746-1818)
In 1768, he succeeded his mentorCharlesBossut to the chair of mathematics at theEcolede Mézières. Monge would use that school as a model for Ecole Polytechnique, founded in 1794 with himself as Director andinstructor in descriptivegeometry (his 1765 drafting method).
Pierre Simon Laplace (1749-1827)
Initiated to mathematics, inCaen, by ChristopheGadbled and Pierre Le Canu, Laplace was mentored byd'Alembert (in Paris) and became one of the most influential scientists ever (Laplacian,Laplace transform). WithLavoisier, he proved respiration to be a form of combustion (1783).
Edward Jenner, immunologist (1749-1823)
Before Jenner, risky variolation and other inocculations were believed to induce immunity to dangerous diseases (20% of human deaths were due to smallpox). Putting some human lives at risk, Jenner proved that innoculation withharmless cowpox did protect against the dreaded smallpox.
Caroline Herschel, astronomer (1750-1848)
Because oftyphus,she only grew to be 4'3'' (1.295 m) and wasn't expected to marry. She was denied an education until she joinedthe household of herbrother (1772) with whose helpshe became an award-winning astronomer; the first woman to receive an official salaryas a scientist (1787).
Adrien-Marie Legendre (1752-1833)
A student ofl'abbé Marie (1738-1801) Legendre grew to be one of the greatest contributors to the mathematics of his times. Many concepts are named after him. At left is what seems to behis only extant portrait (it was found among 73 caricatures of members of the French academy of Sciences).
Jean-Baptiste Meusnier (1754-1793)
In 1776, under Monge, Meusnier read to the Académie two papers about surface curvature and the helicoid (both published in 1785). With Lavoisier, he mass-produced hydrogenbyoxydizing600°C iron with water vapor (1777). Meusnier fought as ageneraland died in battle nearMainz.
Nicéphore Niépce, engineer (1765-1833)
Joseph Nicéphore Niépce invented photography (1826). He built the first internal combustion engine (Pyréolophore, 1807) with his brotherClaude (1763-1828). His cousinAbel Niépce de Saint-Victor(1805-1870) photographed radioactivityin 1857 (39 years beforeHenri Becquerel did).
John Dalton (1766-1844; 1822)
Quaker schoolteacher. His first paper was on thegeneticred-green color blindness (Daltonism) which affected him and 8% of European boys but only 0.64% of the girls. Studying meteorology, he found the law of partial pressures (1801)which supported his celebrated atomistic views ofchemistry.
Joseph Fourier (1768-1830)
In January 1795, Jean-Baptiste Joseph Fourier was the star trainee in the new Ecole normale de l'an III (the forerunner ofENS) simultaneously teaching at Polytechnique. He is the founder of Harmonic Analysis (cf.Fourier transform).
Thomas Young, polymath (1773-1829)
Notorious for histwo-slit experimentdemonstrating the wavelike nature of light(1802) and forYoung's modulus of elasticity (1807). Young's rule gives the posology for an n-year old child as n/(n+12) of the adult dose. Young paved the way for the decoding of hieroglyphics by Champollion.
Andre-Marie Ampère (1775-1836)
Appointed professor of mathematics at Polytechnique in 1809. In september 1820, he discovered thatlike currents attract each other whereas opposite currents repel. The effect is now used to define the SI unit of current, which is named after him.
Etienne Louis Malus (1775-1812; X1794)
Expelled from Mezières for shady reasons (1793) he became a student at Ecole Polytechnique upon its creation (1794). Malus discovered the polarization of light by reflection off non-metallic surfaces (1809) and by double-refraction (1810) which brought him multiple honors.
Sophie Germain (1776-1831)
At 13, she was inspired by Montucla's tale of thedeathof Archimedes. She was 18 when Polytechnique opened (it was male-only until1972) and made available Lagrange's lecture notes. This gave her a start to correspond with him and others (signing Monsieur LeBlanc at first).
Amedeo Avogadro (1776-1856)
Lorenzo Romano Amedeo Carlo Avogadro, Conte de Quaregna e di Cerreto was born in Turin to a noble family of Savoy-Sardinia. In 1820, he accepted the first chair of mathematical physics at theUniversity of Turin, whichhad to close in 1822. Avogadro got the chair back in Nov. 1834.
Carl Friedrich Gauss (1777-1855)
At the age of 7, the Prince of Mathematics found instantly the sum (5050) of all integersfrom 1 to 100 (as the sum of 50 pairs, each adding up to 101). At 19, his breakthrough aboutconstructible polygons helped him choosea mathematical career. Honored by a Doodle on2018-04-30.
Joseph Louis Gay-Lussac (1778-1850; X1797)
Perfecting the ideal gas law, Gay-Lussac formulatedthe isochoric law in 1802. WithHumboldt (1805) he figuredthat water is evolved from one volume of oxygen and two volumes of hydrogen. His generalizations to other gaseous reactants (1809) prompted Avogadro's law (1811).
NéeFairfax. Twosonsfrom first marriage (1804) to Samuel Greig (1778-1807). 4 children from second marriage (1812) toWilliam Somerville (1771-1860). Her study of Uranus (1836) paved the way for thediscovery of Neptune (1846). She andCaroline Herschel,were the first women in theRAS.
Siméon Poisson (1781-1840; X1798)
Among his many mathematical contributions is a very abstract construct in analytical mechanics (PoissonBrackets, 1809) which helpedDiracformulate a precise correspondence between classical and quantummechanics (Sunday, Sept. 20, 1925).
Friedrich Bessel (1784-1846)
In 1799, he left school at the age of 14 to become an import-export apprentice, studying various subjects on his own time. His first astronomical paper (1804)eventually led to academic appointments and an honorary doctorate (1810). He found the first distances to stars using parallax (1838).
François Arago (1786-1853; X1803)
He taught analysis and geometry at Polytechnique from 1810 to 1830,at the peak of his creativity (electromagnet, 1820). A popular left-wing deputy elected in 1830, Arago became Minister of Marine and War in 1848 and was instrumental in abolishing slavery in the French Colonies (1848).
Joseph von Fraunhofer (1787-1826)
In 1814, his observation of the Sun's dark-line spectrum (Fraunhofer lines) marked thebeginning of astrophysics. Fraunhofer is also remembered for related studies of diffraction in optical systems with smallFresnel numbers (Fraunhofer diffraction). Knighted in 1824 (Bavaria).
Augustin Fresnel (1788-1827; X1804)
Trained inCaen (1801-1804) then at Polytechnique. Poor physicist at first... In 1821,Augustin Fresnel established (withArago) that light is a transverse wavewhose two polarizations don't interfere with each other. He inventedFresnel lenses for use in lighthouses.
Jean-Victor Poncelet (1788-1867; X1807)
POW in Russia for 15 months (1812-1814) he brought backfromSaratovthe7 notebooks in which he had inventedmodern projective geometry. Promoted to Colonel in 1845 and General in 1848, Poncelet headed Polytechnique from 1848 to 1850.
Augustin Cauchy (1789-1857; X1805)
A devout royalist, Cauchy wrote 789 papers in all areas of the mathematics andtheoretical physics of his time. In 1821, his Cours d'analyse at Polytechnique madeanalysis rigorous. He originated the calculus of residues (1826) andcomplex analysis (1829).
In 1831, Faraday discovered the Law of Electromagnetic Induction, whichmade the electric era possible. He is widely regarded as one of the greatestexperimentalists who ever lived. Yet, he had little or no grasp of higher mathematics.
Charles Babbage (1791-1871)
He wasLucasian Professor(1828-1839) at Cambridge but never taught. He designed two computing machines: The Difference Engine (funded in 1822) was never completed. The more advanced Analytical Engine would have been the first true computer (Ada Lovelace wrote programs for it).
Gaspard de Coriolis (1792-1843; X1808)
He gave the terms work (travail) and kinetic energy their precise mechanical meanings. At Ponts-et-Chaussées since 1832, Coriolis inherited the chair of Mechanics there, in 1836, upon the death ofNavier,and became director of studies at Polytechnique.
Green worked in his father's bakery and mill. He entered Cambridge at the age of 40 (in 1833) 5 years after self-publishing his best work (extending the work of Poisson in electricity and magnetism) using self-taught mathematical physics. Green coined the word potential.
Michel Chasles (1793-1880; X1812)
Professeur of geodesy at Polytechnique from 1841 to 1851,he inaugurated the Sorbonne chair ofprojective geometry,then called higher geometry (1846-1867). His reputation as a science historian was all but ruined when hebought forged manuscripts (1861-1869) fromDenis Vrain-Lucas.
He found the law of induction independently ofFaraday (mutual inductance) and discovered self-inductance (1832). The SI unit of inductancewas named after him in1960. His relay (1835) made practical the electrical telegraph devised by Schilling (1832) and patented by Morse (1847).
Mary Anning, paleontologist (1799-1847)
Born in Lyme Regis, she first collected fossils fortourists from the nearby cliffs during winter storms, before the Sea could reclaim them. At age 12 (1811) she found the skull of the first properly idenfifiedIchthyosaur (Blainville, 1835). She later helped promote the notion of extinction.
Julius Plücker, scientist (1801-1868)
In 1858, using the handiwork ofHeinrich Geissler (1814-1879)he paved the way for the inventionof the CRT (byCrookes, c. 1875). He was the doctoral advisor ofKlein. In 1866. Plücker received theCopley Medalfor his work in analytical geometry, magnetism and spectral analysis.
Niels Henrik Abel (1802-1829)
Niels Abel produced many brilliant results during a short life spent in poverty: Non-solvability of quintic equations by radicals,double periodicity of the elliptic functions, etc. An offer for his first professorship (at Berlin) arrived two days after he had succombed to tuberculosis.
Charles-François Sturm, analyst (1803-1855)
A pupil of Lhuilier in Geneva, he earned a top prize with Colladon for measuring the speed of sound in water (1826-27). They both moved to Paris. Teacher at Rollin (1830). French citizen (1833). He succeeded Ampère at Académie des sciences (1836) and Poisson at Polytechnique (1840).
Carl Gustav Jacob Jacobi (1804-1851)
An inspiring teacher, he was an outstanding and prolific creator of mathematicswho has been likened toEuler. He introduced and Jacobians in 1841. Jacobi admired Poisson brackets and proved that they satisfy what's now calledJacobi's identity.
Peter Gustav Lejeune Dirichlet (1805-1859)
Johann Peter Gustav Lejeune-Dirichlet. signed Gustav Lejeune Dirichlet, (no hyphen) published as P.G.L. Dirichlet and was quoted as Lejeune-Dirichlet. He contributed tonumber theory, mechanics andanalysis. He was the first to consider unrestrictedfunctions.
Sir William Rowan Hamilton (1805-1865)
A calculating prodigy who lost toZerah Colburnat age 8, Hamilton started to teach himself higher mathematics at 13. In 1833, he devised a version of rational mechanics(based on conjugate momenta) which would help clarifyquantum mechanics later. He inventedquaternions in 1843.
Charles Robert Darwin (1809-1882)
Against strong religious animosity (which lasts to this day in the US) Darwin established that the mechanism of natural selection was powerful enough to explain the evolution of the humblest ancient lifeformsinto the most advanced modern ones, featuring very sophisticated organs.
Joseph Liouville (1809-1882; X1825)
Many of Liouville's 400+ papers include key contributions, like hisconservationof Hamiltonian phase-measure. In 1836, he founded the Journal de mathématiques pures et appliquées and promotedthe work of others, including the late Evariste Galois.
Hermann Grassmann (1809-1877)
Around1832,he pioneered the modern approach tovectorsand went on to invent exterior algebra (the correct basisfor Cartan'sdifferential formsand/or Bourbaki's"Stokes' theorem"). Grassmann had little mathematical influence during his own lifetime (he became successful as a linguist).
Galois theory is aboutsymmetries of polynomials onfields. Galois "didn't have time" toextend that to transcendental functions (nobody else has done so). He died in a stupid duel at the age of 20 and hisfundamental work might have been lost ifLiouville hadn'trevived it in 1843.
Ludwig Schläfli, Swiss geometer (1814-1895)
He introduced the notion of higher-dimensional vectors (between 1850 and 1852, full treatise published in 1901). He pioneered multi-dimensionalRiemannian manifolds by considering the3D-hypersurface of a 4D-hypersphere. Schläfli also classified allregular polytopes.
Eugène Catalan (1814-1894; X1833)
In 1838, he founded the preparatory school at Sainte-Barbe with Sturm andLiouville. His left-wing activism damaged his academic career. He was elected to the French National Assembly. Catalan's conjecture (1843) saying that the only solution of 1+xm = yn is 1+23 = 32, was proved in 2002.
Julius Robert Mayer was ennobled on 1867-11-05 (inWürttemberg) for his founding rôle in thermodynamics: In 1841, he gave a preliminary version of the first law (energy is conserved). He identified oxidation as the main source of energy for living organisms (1842).
Karl Weierstrass, analyst (1815-1897)
The father of analysis spent 15 years teaching secondary school before one paperearned him an honorary doctorate and a professorship. He gave the rigorousmetric definition of limits and invented theconcept ofanalytic continuation.
Daughter and heiress of Lord Byron (the poet) whom she never knew. Ada was introduced by Mary Somerville to Charles Babbage on June 5, 1833. She then developped an intense interest in the mathematics of computation and is now regarded as the first computer programmer. [ Video ]
James Prescott Joule (1818-1889)
By measuring the mechanical equivalentof heat, his paddlewheel experiment (1845) established the first law of thermodynamics, whereby the total energy (heat and mechanical energy) is conserved. The SI unit of energy was called joule (J) in his honor in 1889, shortly before he died.
He could only gain access to books (and a self-education) by becoming a janitor at the museum of theAndersonian Institute in Glasgow (1859-67). Once amended for Northern dominance by Milankovic, hisproposed astronomical causes for climate variations would be vindicated in 1976.
Home-schooled Russian aristocrat. His mathematics tutor was the textbook author Platon Nikolaevich Pogorelski (1800-1852). Chebyshev contributed to number theory, algebra, analysis, mechanics, etc. In 1850, he derivedBertrand's postulatefrom thetotient function's asymptotics.
Arthur Cayley (1821-1895;1852)
He wrote 996 papers on many mathematical subjects(200 of these while praticing law, for 14 years). In 1858, Cayley established (without a formalproof) the Cayley-Hamilton theorem: A matrix is a zero of its characteristic polynomial.
Hermann von Helmholtz (1821-1894)
We use his initial (H) forenthalpy, not for the Helmholtz free energy (F). Helmholtz is primarily known for his work in physics (thermodynamics, acoustics,elasticity, etc.) but the fundamental theorem of vector calculus (3D only) is also named in his honor (Helmholtz decomposition).
Rudolf Clausius, thermodynamicist (1822-1888)
Clausius formulated the second law of thermodynamics. He coined the word entropy (1865) for which he introducedthe deprecated clausius unit (1 Cl = 1 cal/°C = 4.184 J/K). His only doctoral student was Carl von Linde (1842-1934) of gas liquefaction fame.
Father of genetics. Mendel communicated his results toKarl von Nägeli (1817-1891)who expressed contempt for them and was instrumental in burrying them for three decades. Mendel's laws of heredity were rediscovered in the 1890s byHugo de Vries (1848-1935).
After one year at Polytechnique, the military managementdismissed him because of a congenitally deformed right leg. Returning as a teacher, five years later, he contributed to number theory,orthogonal polynomials and elliptic functions. He proved e transcendental in 1873.
Louis Pasteur, microbiologist (1822-1895)
A chemist by training, he separated chiral isomersby sorting the different crystals they produce. He proved the germ theory of infectious diseasesand invented pasteurization. Motto: Fortune favors the prepared mind.
Gotthold Eisenstein (1823-1852)
His impoverished family had converted from Judaism to Protestantism before he was born. Gauss named Eisensteinone of the top three epoch-making mathematicians in history (alongArchimedes andNewton) and Weil considered his approachparamount to modern mathematics. He died at 29.
Leopold Kronecker, algebraist (1823-1891)
Famous for his credo "God made thenatural numbers;all else is the work of man", Kroneckerchampioned constructivism. He strongly opposed his formerstudentGeorg Cantor and theemerging nonconstructiveSet Theory.
Born William Thomson, Lord Kelvin was knightedin 1866 and raised to the peerage in 1892 (Baron Kelvin of Largs). The SI unit of temperature is named after thismathematician noted for his engineering work (e.g., transatlantic telegraph).
ApplyingPasteur's ideas, he introduced antiseptic surgery while workingat theGlasgow Royal Infirmary. Lister used carbolic acid (phenol) to sterilize instruments and clean wounds. This reduced post-operative infections and made surgery safer. Baronet in 1883, he became a Baron in 1897.
Marcellin Berthelot, chemist (1827-1907)
Pioneer of synthetic organic chemistry. He was opposed to atomist notations. He signed his papers P.E.M Berthelot. Collège de France (1865). Académie des sciences (1873). Senator (1881). French Minister of education (1886-87) and foreign affairs (1895-96). Académie française (1901).
August Kekulé von Stradonitz (1829-96)
In 1865, Kekulé had a revelation of the cyclic structure of benzene in a daydream where he saw snakes biting their own tails. He first proposed a planar molecule of trigonal symmetry,with alternating single and double bonds (instead of the currently accepted perfecthexagonal symmetry).
James Clerk Maxwell (1831-1879)
In1864, his equations unified electricity and magnetism, by describing electromagnetic fields traveling at thespeed of light. In 1866, he proposed (independently ofBoltzmann) the Maxwell-Boltzmann kinetic theory ofgases. In 1867, Maxwell's Demon helped equate entropy and information.
Richard Dedekind, mathematician (1831-1916)
Julius Wilhelm Richard Dedekind wasthe last doctoral student ofGauss(1852)but he also learned much fromDirichletafter his doctorate. In 1858, he defined every real number as aDedekind cut of rationals (asBertrand has done in 1849). In 1871, he introduced algebraicideals.
Dmitri Mendeleev, chemist (1834-1907)
In1869,he presented a classification ofchemical elements(based mostly on atomic masses) which showed periodic patterns in their chemical properties. He predicted the properties of 3 unknown elements which were discovered shortly thereafter: Ga (1871), Sc (1879) and Ge (1886).
Born in Canada. In 1861, he received a commission in the corps of professors of mathematics in the US Navy. He reached the mandatory retirement age for captains in 1897, but was promoted to rear-admiral so he could remain in the service.
Eugenio Beltrami, Italian geometer (1835-1900)
Bringing to a great conclusion the works of Gauss, Bolyai,Lobachevsky andRiemannon non-Euclidean geometry, he showed that geodesics matched straight lines on the plane onlyfor surfaces of constantcurvature. His pseudosphere (generated by rotating atractrix) is the key example (1868).
Johannes van der Waals (1837-1923)
Johannes Diderik van der Waals obtained a doctorate in his native town of Leiden only when classical languages requirements were lifted in Science (he was 36). At a time when the very existence of molecules was doubted, his thesisshowed how molecular interactions explaingas liquefaction.
M.E. Camille Jordan (1838-1922; X1855)
A universal mathematician and one of the greatest teachers of the 19-th century, he inspired Lie, Klein, Borel and Lebesgue. He invented the topological concept ofhomotopy (1866). Camille Jordan was appointed professor of Analysis at Polytechnique in 1876.
Ernst Mach, physicist (1838-1916)
Mach would only consider relative motion between objects, irrespective ofabsoluteNewtonian space. He studied the shockwaves produced by fast projectiles (the Mach number of a projectile is the ratio of its speedto the speed of sound in the surrounding fluid). Mach wasPauli's godfather.
Josiah Willard Gibbs, Jr. (1839-1903)
Son of aphilology professor at Yale, Gibbs earned the first American doctorate in Engineering (1863). His work instatistical mechanics andthermodynamics transformedmuch of chemistry into a deductive science. The great importance of his contributions was only acknowledged after his death.
Ernst Abbe, optician (1840-1905)
Founder of modern optics. His industrial commitments to the instrument-makerCarl Zeiss (1816-1888) andthe glassmakerOtto Schott (1851-1935)prevented Abbe from accepting a professorship atBerlin (offered byHelmholtz).
Gaston Darboux, geometer (1842-1917)
He tiedhis definition of integrals (1870)to that ofRiemann in 1875. The Darboux formulas define the normaland geodesic curvatures as well as the geodesic torsion for a curve drawn on a surface. He was a biographer ofPoincaré.Darboux was elected to the Académie des Sciences in 1884.
John Strutt, Lord Rayleigh (1842-1919)
He's the man who explained why the sky is blue (Rayleigh scattering). He described surface acoustic waves (SAWor Rayleigh waves, 1885) before they were observed in earthquakes. He earned the Nobel prize (1904) for his1892discovery ofArgon. Rayleigh wasJ.J. Thomson's advisor.
Robert Koch, bacteriologist (1843-1910)
Founder of modern bacteriology. He identified theetiologic agents of anthrax (1876), tuberculosis (1882) and cholera (1884). HisGoogle Doodle(2017-12-10) shows the potato slices he first used for bacterial growth and the Petri dish invented by his assistant Julius Petri (1852-1921).
Sophus Lie, mathematician (1842-1899)
With Felix Klein, Sophus Lie originated the investigation of the continuousgroups of symmetry now named after him. The study of Lie groups and the related Lie algebras would become a major branch of20-th century mathematics, with applications to quantum mechanics.
Ludwig Boltzmann, physicist (1844-1906)
A proponent of atomic theory and the father of statistical physics. We call Boltzmann's constant the coefficient of proportionality between entropy (in J/K) and the natural logarithm ofthe number of allowed physical states.
Georg Cantor, mathematician (1845-1918)
Cantor'sdiagonal argument shows thatthe points of a line are not countable. More generally,Cantor's Theorem states that no function from a set to its powerset can possibly be surjective, which establishes an infinite sequence of increasing infinities.
Wilhelm Röntgen, physicist (1845-1923)
He received the first Nobel prize in physics (1901) for his discovery of X-Rays, on1895-11-08. In his honor, element 111 was named Roentgenium (Rg) in 2004.
Swedish mathematician who founded Acta Mathematica in 1882 and served as chief editor for 45 years. His own research specialized in what was then called the theory of finctions (complex analysis). A major theorem in the fieldis due to him, so is a keyfunction for fractional calculus.
GeorgeWestinghouse, inventor (1846-1914)
With two early railway patents (frog andcar replacer, 1867) he financed a major one: air brakes (1869) which he'd make failsafe (1873) and responsive (1876). He distributed natural gas and AC electricity (with transformers)prevailing overEdison's DC.He made Saturday a half-holiday (1881).
ThomasEdison, inventor (1847-1931)
The most successfullinventor ever. His 1093 US patents cover thephonograph,light-bulb, motion picture camera... In 1876, he created the first industrial research laboratory atMenlo Park, NJ. He favored DC current, which lost out toTesla'sAC generation and distribution of electric power.
Wilhelm Killing (1847-1923)
Investigating Lie groups independently ofLie andKlein,he fully classified simple Lie groups in 1887 (as confirmed byCartan in 1894): 5exceptional Lie groups (E6 , E7 , E8 , G2 , F4 ) and threeregular families: special linear groups SL(n), orthogonal groups O(n), symplectic groups Sp(2n).
C. FelixKlein, mathematician (1849-1925)
Born on 1849-4-25 (432, 22, 52) to a Prussian government official, he married the granddaughterofHegel in 1875. Thenoncyclic group of order 4 bears his name. As first president of theICMI (1908) he was instrumental in bringingCalculus (back) to secondary schools worldwide.
Sofia Vasilyevna Kovalevskaya was born Sonya Korvin-Krukovskaya. Weierstrass tutored her privately (1870-1874) and helped herbecome the first female professor at a European university (Stockholm, 1889) since the days ofLaura Bassi (1776) orMaria-Gaëtana Agnesi.
In 1884, he started the investigations of quadratic differential forms which led himto invent tensor calculus (1884-1894). The text he published about that with Tullio Levi-Civitain 1900 would enableEinstein to formulateGeneral Relativity in 1915.
Hendrik A. Lorentz, physicist (1853-1928)
Among the many contributions of H.A. Lorentz isthecoordinate transformationwhich is the cornerstone of Special Relativity. In 1892, Lorentz proposed atheory of the electron (discovered byPerrin in 1895 andJ.J. Thomson in 1897, who measured the mass-to-charge ratio).
J. Henri Poincaré (1854-1912;X1873)
Doctoral student ofHermite (1879) and last universal genius. Quintessentialabsent-minded professor (cf. Savant Cosinuscomic strip). Poincaré conceivedSpecial Relativitybefore Einstein did. His mathematical legacy includeschaos theory and contributions totopology.
Nikola Tesla (1856-1943)
He was originally trained as a mechanical engineer. At least 272patentswere awarded to Tesla in 25 countries. His work is the basis of modern alternating current (AC) electric power distribution. In 1960, theSI unit of magnetic induction (magnetic flux density) was named after him.
Emile Picard, mathematician (1856-1941)
Picard's little theorem (1879) says that any nonconstant entire function takes any value infinitely often, with at most one exception (dubbed lacunary). His great theorem says that, about an essential singularity, ananalytic function takes every value infinitely often, with one possible exception.
In 1887, Heinrich Rudolf Hertz discovered the photoelectric effect, whoseexplanation byEinstein, in 1905, would establish the existenceof photons. In 1888, he made the first transmission of a signal by radio waves. The SI unit of frequency (symbol Hz) was named after him, in 1960.
Max Planck, physicist (1858-1947)
Planck combined the formulas ofWien (UV) andRayleigh (IR) intoa unified expression for theblackbody spectrum. OnDec. 14, 1900,he justified it by proposing that exchanges ofenergy only occur in discretelumps,dubbed quanta.
Giuseppe Peano, logician (1858-1932)
In1880,Peano joined the staff atTurinwhere he succeeded Angelo Genocchi(1817-1889) to the chair of Calculus, in 1890. Peano defined the integers axiomatically (1889) and found a space-filling curve (1890). He invented symboliclogic (1895) anddevised a new natural language (1903).
Otto Ludwig Hölder (1859-1937)
Like his mentor Paul du Bois-Reymond (a student ofKummer) Otto Hölder argued against formalism in foundational mathematics, aschampioned byCantor,Hilbertor Robert Grassmann, of whom he was most critical(1892). His intuitionism resembledPoincaré's (notBrouwer's).
David Hilbert, mathematician (1862-1943)
One of the most powerful mathematicians ever, David Hilbert gave a famouslist of 23 unsolved problems in 1900. Quantum Theory is based on the complex normedvector spaceswhich are named after him. In 1931, Gödelshattered the dream Hilbert had voiced in 1930 ("we will know").
Agnes Pockels, physicist (1862-1935)
Barred from higher education as a woman, she accessedscientific litterature through her younger brother Friedrich (PhD 1889) and was helped by Rayleigh once she senthim her research on surface tension. Her homemade apparatus paved the way for the Langmuir-Blodgett trough.
Maurice d'Ocagne (1862-1938)
Polytechnicien (X1880). He held the chair of Professor of Geometry (1912-1937) at Polytechnique, preceeding Gaston Julia. Credited for the (lost) science of nomography (1884) in spite of the key rôles of Charles Lallemand (1857-1938; X1874) and Rodolphe Soreau (1865-1935; X1885).
Hermann Minkowski (1864-1909)
Pioneeringconvex geometry, he provedan early version of the separation theorem (of Hahn-Banach)and called A+B the set of all sums with oneaddend in A and the other in B. His name was given to the Lptriangular inequality (1896) and to the relativisticscalar product in spacetime (1908).
Jacques Hadamard, analyst (1865-1963)
In 1892, he obtained his doctorate and was awarded the French Academy's Grand Prix for completing the work ofRiemann on the Zeta function. He authored one of the first two proofs of thePrime number theorem in 1896. He gavefunctional analysis its name in 1910. Deeply influential.
Marie Curie, physical chemist (1867-1934)
Madame Curie (née Maria Salomea Sklodowska ) was the first woman to earn a Nobel prize and the first person to earn two. In 1898, she isolated two new elements (polonium and radium)by tracking their ionizing radiation, using the electrometerof Jacques andPierre Curie (her husband).
Henrietta S. Leavitt, astronomer (1868-1921)
In 1908, Henrietta Swan Leavitt published the period-luminosity relationship for Cepheid variable stars, which reveals their actual distances,even whenparallax is undetectable. This paved the way for the first measurement of the expansion of the Universe byEdwin Hubble (1929).
Felix Hausdorff, topologist (1868-1942)
In aHausdorff space (1914) two distinct pointsare alwaysdisconnected. In 1919, he introducedfractional dimensionsand defined d-dimensional measures. Hausdorff published literary work as Paul Mongré. Unable to escape the Nazis, he committed suicide with his wife and sister-in-law.
In 1913, Cartan established, from a purely geometrical standpoint, the relations thatlead to the quantization ofspin. He developedexterior calculusand published his Theory of Spinors as a textbookin 1935. Godfather of Bourbaki and father ofkey Bourbakist Henri Cartan(1904-2008).
A Sainte-Barbe bursar, he placed first in the top threeFrench academic competitions of 1889: Concours Général,Polytechnique, Ecole Normale. He chose the latter school. Borel developedpoint-set topology andfoundedMeasure theory. Elected to the Académie des Sciences in 1921.
Ernest Rutherford (1871-1937)
British physicist born in Nelson, New Zealand. His investigations of alpha and beta decay (which he so named) earned hima Nobel prize before he moved toManchester, where hesupervised theGeiger-Marsdenexperiment (1909) and inferred the planetary model of the atom (1911).
Willem de Sitter, cosmologist (1872-1934)
His papers on the astronomical consequences of Einstein's general relativity (1916-17) stirred early interest. De Sitter argued for an expanding Universe well before Hubble found any evidence for it. He also gave an acceleratingsolutionfor early and late regimes where matter isnegligible.
Building on the work of Jordan (whocriticized him) and Borel (his advisor) he laid the goundwork of measure theory in 1901 and revolutionized the notion ofdefinite integration in his doctoral dissertation (1902). Lebesgue was elected to the Académie des Sciences on 29 May 1922.
G.H. Hardy, pure mathematician (1877-1947)
Known only by his initials G.H. (for Godfrey Harold) Hardy was asexual, entirely devoted to mathematics and cricket (a nonpractising homosexual, saidLittlewood). His collaboration with Littlewood is legendary. So is the way Hardyrecognized and guidedRamanujan's raw genius.
Last student of Ludwig Boltzmann, she collaborated with Otto Hahn who was awarded aNobel prize (1944)for their joint work. With Otto Frisch (her nephew) Lise Meitner gave nuclear fission its name (Kernspaltung in German). She correctly explained the related mass defect (1938).
He improved upon the forgotten climate model of James Croll using new geological data and a better mathematical insight that thekey to climate change is the Summer melting of the Northern ice cap over land masses, rather than the growing of either ice cap over water in the cold season.
A student of Ludwig Boltzmann in Vienna. In 1901, he was sent for 18 months to Göttingen where he met Tatyana, the Russian studenthe'd marry after getting his doctorate, back in Vienna (1904). He mentored many rising stars, fromGregory Breit (in 1921)toJan Tinbergen (Nobel 1969).
L.E.J. Brouwer, mathematician (1881-1966)
Early in his career, Bertus Brouwer founded moderntopology. He later championed the incompatible philosophy of intuitionism which considers only sets whose elements can be shown to belong in finitely many steps. As topology isn't intuitionistic, he wouldn't teach it at all!
Theodore von Kármán, engineer (1881-1963)
Born in Budapest. Visiting Paris in March 1908, he saw early aviation flights and decided he'd apply mathematics to aeronautics. He became director of the Aeronautical Institute at Aachen in 1912. He emmigrated to the US in 1930 and received the firstNational Medal of Science, in 1963.
Waclaw Sierpinski (1882-1969)
Sierpinski was the first person to lecture on set theory (1908). After WWI, he organized mathematics in Poland around set theory & logic, topology and real analysis. He wrote about 600 papers on those topics. Later in life,he produced about 100 more papers onnumber theory.
Emmy Noether, mathematician (1882-1935)
Emmy Noether discovered the remarkable equivalence between symmetries in physical lawsand conserved physical quantities (Noether's theorem, 1915). Her considerable legacy also includesNoetherian ringsand threeIsomorphismtheorems named after her (1927). [EmmyNoether.com ]
Max Born, mathematical physicist (1882-1970)
He coined the term quantum mechanics%nbsp; in 1924. Born's probabilistic interpretation of Schrödinger's wave function ended determinism in physics but provided a firm ground for quantum theory. Irene Born, the eldest of his 3 children, is the mother ofOlivia Newton-John. Doodledon 2007-12-11.
John E. Littlewood, analyst (1885-1977)
Littlewood had22 doctoral studentsbut, likeHardy, never bothered to take a doctoral degree himself. In 1910 or 1911, he started a prolific collaboration withG.H. Hardy which spanned 35 years. He was so discreet that rumors once circulated that he was just afigment of Hardy's imagination.
Niels Bohr, physicist (1885-1962)
In 1913, Bohr started thequantum revolutionwith amodel wherethe orbital angular momentum of an electron only has discrete values. He later spearheaded the Copenhagen interpretation (i.e., probabilistic measurements cause the collapse of otherwiselinearly-evolving quantum states).
In 1926, Schrödinger matched observed quantum behavior with the properties ofa continuous nonrelativistic wave obeying theSchrödinger Equation. In 1935, he challengedBohr's Copenhagen Interpretation, with the famous tale ofSchrödinger's cat. He lived inDublin from 1939 to 1955.
Ramanujan lacked a formal mathematical education but, in 1913, a few of his early resultsmanaged to startle G.H. Hardy (1877-1947) and J.E. Littlewood (1885-1977) who invited him toCambridge in 1914. Ramanujan has left an unusual legacy of brilliant unconventional results.
Louis J. Mordell (1888-1972)
Born inPhiladelphiatoLithuanian parents, he was inspired by second-hand textbooks andconceived the mad project of competingfor aCambridgescholarship. Against all odds, Mordell placed first (1906). His results would set the tone for modern views of number theory (cf.elliptic curves).
Edwin Hubble, astronomer (1889-1953)
In 1929, with sketchy observational data, he saw that galaxiesrecede at speeds proportionalto their distances from us. The coefficient of proportionality H (Hubble's constant) varies inversely as the age of the Universe (thus proved to be expanding, by the cosmological principle).
In 1923, he proposed that any particle could behavelike a wave ofwavelength inversely proportional to its momentum (this helpsjustify Schrödinger's equation). He predicted interferences for an electron beam hitting a crystal.
Normalien (1911). He lost his nose in combat (1915). His 199-page memo on the iteration of rational functions (1918)won a Grand prix which made him famous (groundwork of Mandelbrot'sfractals). In 1937, Julia suceeded Maurice d'Ocagne to lead mathematics at Polytechnique, withLévy.
Georges Lemaitre, cosmologist (1894-1966)
Jesuit Catholic priest (1923). Father of the Big Bang theory (1927) which he called the primeval atom. First proponent of Hubble's law. Lemaître passed away on June 20, 1966, shortly after his theory had been vindicated experimentally by the discovery of the CMB in 1964 (Penzias & Wilson).
TheHasse-Minkowski theorem (1921)transfers arithmetical questions tolocal fields. The Hasse invariant of a non-singular algebraic curve over a finite field is therank of itsHasse-Witt matrix. In 1937, Hasse's application to the Nazi party was denied becausehe had a Jewish great-grandmother.
Before Grothendieckintroduced schemes (c. 1960),the Zariski topology was a non-Hausdorff topology defined on any algebraic variety by equating closed setsandprime ideals. The underlying field (usually C) needn't even be a topological field.
Wolfgang [Ernst] Pauli, physicist (1900-1958)
In 1925, Wolfgang Pauli formulated the exclusion principle which explains the entiretable of elements. His Godfather wasErnst Mach. Pauli's sharp tongue was legendary; he once said about a bad paper: "This isn't right;this isn't even wrong."
Cecilla Payne-Gaposchkin, (1900-1979)
She was the first to propose (1925) that stars consist mostly of hydrogen and helium, the twomost abundant elements in the Universe. She married her colleague Sergei Gaposchkin (1889-1984) in 1934 and had three children with him. They met in Germany and she helped him join the Harvard faculty.
She obtained her Ph.D. from Oxford in 1930, underG.H. Hardy and Ted Titchmarsh. She first metJ.E. Littlewood as he was sitting in her jury. With him, she would pioneer the use of chaos theory in radio engineering (1945). First female mathematician elected to the Royal Society (1947).
Enrico Fermi, physicist (1901-1954)
In 1926, Fermi helped formulate theFermi-Dirac statisticsobeyed by what we now call fermions. He identified the neutrino in beta-decay. He discovered slow neutrons and the radioactivity they induce. On December 2, 1942, Fermi produced the first self-sustainingnuclearchain reaction.
Werner Heisenberg, physicist (1901-1976)
In 1925, Werner Heisenberg replaced Bohr's semi-classical orbitsby a new quantum logic which became known asmatrix mechanics (withthe help ofBorn andJordan). A consequence of the noncommutativity so entailed is Heisenberg's uncertainty principle.
He constructed functions whoseFourier series divergealmost everywhere (1922)or everywhere (1926). In 1933, he laid the foundations of axiomatic probability theory. Based on his 1954 work, thelong-term stability of thesolar system can almost be established (KAM theorem).
He is credited with the stored program architecture (1946) whereby a computer usesits primary memory space to store both the data it operates on and the codes for the programs it executes. Von Neumann pioneered game theory, decision analysis, automata theory. fault-tolerant systems, etc.
Son ofElie Cartan, son-in-law of Pierre Weiss. Key founder, withWeil, ofBourbaki (1935) which consumeda large part of his research activities. Leading professor at ENS for several decades. Henri Cartan was instrumental in reconciling French and German mathematics after WWII.
In 1944,Thomas Harold Flowers built the first large-scale electroniccomputer (Colossus) at Bletchley Park. As the accomplishment remained classified for decades, Flowers was deprivedof the glory which went instead toMauchly andEckert for theENIAC (Philadelphia, 1946).
The completeness theorem in his dissertation (1929) states that a statement true in everymodel of an axiomaticsystem is provable in it. His more famous incompleteness theorem (1931) says that, in any model of a set of axioms covering arithmetic,some true statements are not provable.
Brother of the philosopherSimoneWeil (1909-1943) but unrelated to the politicianSimone Veil (1927-2017). He was the leading founder of Bourbaki. Weil established the field of algebraic geometry and, arguably, charted the course of much abstract mathematics in the twentieth century.
Hans Bethe, physicist (1906-2005)
He fled Germany in 1933, after losing his post at Tübingen because of his Jewish ancestry. In 1935, he got a position atCornell,which he never left except for wartime work atMIT andLos Alamos (as head of the theoretical division). Nobel prize for his work on nuclear fusion in stars of all sizes.
Arguably the most brilliant of a dozenVia Panisperna boysselected byFermi (including the likes ofWick andSegrè). Majorana published only 9 scientific papers but left a huge 10,000-page legacyof notebooks written between 1927 and 1932. He organized his own disappearance in March 1938.
He conceived electronic television in 1922 (at the age of 14) applied for a patent in 1927and first tested it on 1927-09-07. His wife Elma Gardner "Pem" Farnsworth(1908-2006) was the first person to be televised. He demonstrated nuclearfusion on a tabletop and held about 300 patents.
Donald Coxeter, geometer (1907-2003)
Harold Scott MacDonald Coxeter was a British-born Canadian mathematicianteaching atToronto. He put forth reflection groups. He wrote Introduction to Geometry (1961) and Regular Polytopes (1963). A correspondant ofMartin Gardner, he inspiredBucky Fuller andM.C. Escher.
He died (in a mountaineering accident) before Bourbaki was formed. His close friend Chevalley (who, like him, became normalien at a very young age) made sure they took his views on logic into account.
Astrophysicist. Chandra was the nephew of Raman(1888-1970; Nobel1930). On Chandra's 107th birthday, Google's home page in 28 countries featured an animation illustrating the Chandrasekhar limit (1.44 solar masses) beyond which a star's death can only yield a neutron star or a black hole.
Top code-breaker of Bletchley Park (WWII). A Turing Machine is a finite automaton endowed with an infiniteread/write tape on which it can move back and forth, one step at a time. Turing showed that such a machine is capableof computing anything that any other machine could.
Paul Erdős, mathematician (1913-1996)
Paul Erdös wrote over 1500 papers with 511 collaborators. He contributed many conjectures and proved some great ones. Faced with antisemitism, he left Hungary in 1934 and spent therest of his frugal life on the road, touring mathematical centers.
Son-in-law of Paul Lévy. "One night in 1944", he figured out that the distributions used in physics (includingDirac'sdelta) were continuous linear forms over a restricted set ofsmooth test functions. He found the Fourier transform to be a linear automorphism among tempered distributions.
Got hisPhD (1942) underWheeler. In 1949, he introduced Feynman diagrams for the relativistic quantum theory of electromagnetism (Quantumelectrodynamics = QED) using perturbation theory. This has helped visualize all other types of fundamental interactions ever since.
Abraham Robinson (1918-1974)
Robinson's non-standard analysis (1961) gave a rigorous footing to the infinitesimals introduced byLeibniz (1675) thus providing an alternative basis for analysis (competing with the approach made standard by Cauchy in1821). This was an early application of Model theory.
Franklin Chen-Ning Yang, physicist (1922-)
With Robert Mills (1927-1999) in 1954, Frank Yang generalized the gauge theories of Weyl (1919). Yang-Mills theory, is now the paradigm for the modern description of all interactions. With T.D. Lee and Chien-Shiung Wu (1912-1997) Yang found beta-decay to violate parity (1956).
Raised in England, Dyson went toCornell as a student(1947) and went onto replaceFeynman there, without ever getting a doctorate. In 1949, he showed Feynman's QEDdiagrams to be equivalent,to the methods ofSchwinger orTomonaga.He joined Princeton'sIAS in 1953 and never left.
A Bourbakist noted for broad contributions in fields liketopology, group theory and number theory (particularly Galois representations and modular forms). First prize for mathematics inConcours Général (1944). Youngest Fields medalist (in 1954) and first Abel prize laureate (2003).
Father of modern cosmology. Last doctoral student ofDirac (before he moved to Florida) with a thesis entitled"On the Origin of Inertia". He served as thesis advisor toStephen Hawking in 1966.
Joe Kruskal obtained his Ph.D. from Princeton in 1954, underLyndon andErdös. He was the younger brother of the statisticianWilliam H. Kruskal (1919-2005)and the physicistMartin D.Kruskal (1925-2006) who is known for theKruskal principle,used in magic.
In his 1950 thesis about non-cooperative games, the notion of a Nash equilibrium made game theory relevant to many real-life situations. Nash battledschizophrenia for decades,but willed it off before receivingthe Nobel prizein economics, at 66 (1994) and theAbel prize, at 86 (2015).
John Stewart Bell earned his Ph.D. in nuclear physics atBirmingham in 1956. In 1960, he and his wife(Mary Ross)gave up tenured positions to work atCERN for the rest of their careers. After a year-long sabbatical from CERN, John published his masterpiece: "On the EPR paradox" (1964).
Inalgebraic geometry, the index theorem (1963) equates the topological index of an elliptic differential operator, on acompact manifold, to its algebraic index (pertaining to the dimension of the space of solutions). This very general theorem has many specializations and applications.
An early proponent of the chirality of weak interactions (1958) he dubbed strangeness one flavor they don't conserve. Gell-Mann gave "quarks" their name andcalled color what they trade. The same scheme was independently proposed by George Zweig (1937-) using the word aces.
His father,Lionel,was a geneticist. His mother, Margaret, was a physician. His older brother,Oliver,was a professor of mathematics. His younger brother,Jonathan,was 10 times British Chess Champion. Roger penrose put forth twistors in 1967andspin networks in 1971. Nobel 2020.
Normalien at 18 (Ulm, 1951). Founding father of soft matter physics (French: matière molle) including liquid crystals and polymers, where the dominant phenomena occurat an energy scale comparable to thermal energy at room temperature (where quantum aspects are negligible).
In 1967, he formulated the electroweak unification of theweak nuclear force and electromagnetism,predicting a massive neutral messengerparticle (the Z boson) which was first observed in 1979. Steven Weinberg gave the Standard Model its name. ["To Explain the World", 2015.]
Paul Cohen, logician (1934-2007)
His invention of the technique of forcing revolutionized logicand allowed him to prove, in 1963, the undecidability ofCantor's continuum hypothesis (CH): Gödel had shown CH to be compatible with the axioms of set theory and Cohen proved the same for the negation of CH...
Robert P. Langlands, mathematician (1936-)
Langlands is now a professor emeritus at the IAS,where he occupiesAlbert Einstein's former office. The Langlands program, oulined in a letter to Weil (1967)seeks to connect algebraic number theory (Galois groups) with automorphic forms and representationsover local fields and adele rings.
In 1970, Conway found the simple rules of a cellular automaton (the Game of Life) capable of self-replication and universal computation. His other original discoveries includethe ultimate extension of the ordered number line (surreal numbers, 1973) and the free-will theorem (2006).
Don Knuth, computer scientist (1938-)
Donald Ervin Knuth made therigorous analysis of algorithms a key aspect of computer science. Complexitytheory studies the best possible asymptotic performance of all procedures that can solve a given problem (running time and/or memory-space used, as functions of input data size).
Diagnosed with ALSat age 21, he wasn't expected to reach his 25th birthday, but went on to establishthe pointlike nature of the Universe's origin. Communicating only viaone cheek muscle, he achieved a legendary status in the public eye. Hawking's fame in physicsis second only to Einstein's.
Susan Jocelyn Bell, astrophysicist (1943-)
Dame Jocelyn Bell Burnell discovered the first pulsar (neutron star) in July 1967 and thenext three shortly thereafter. She was then a Ph.D. student supervised by Antony Hewish (who would be awarded a Nobel prize in physics,in1974,for their subsequent joint work).
Alan Guth (MIT) came up with the idea of cosmic inflation in 1979 to explain the extremely even distribution of the contents of the Universe at the beginningof the Big Bang. For this, he shared the 2002ICTP Dirac Medal withAndrei Linde(Stanford) and Paul Steinhardt (Princeton).
Alain Connes, mathematician (1947-)
Classifying the noncommutative structures underlaying anyforeseeable quantum theory (1973) he found an unavoidable evolution indicator (moduloinner automorphisms) looking like emergent time. That paves the way for a quantum theory of spacetime, unifying gravity with all other forces.
He was awarded a Fields Medal (1990) for his mathematical contributions toa physical theory (String Theory) which captured the hearts of generationsof physicists without any empirical support. In 1995, Witten unified the 5 or 6 flavors of that theory under a single umbrellahe called M-Theory.
Andrew Wiles, number theorist (1953-)
He worked secretly on a proof of Fermat's last theorem for seven years before offering it for publication in 1993. A flaw discovered byNick Katzrequired new insights and the collaboration ofRichard Taylor. By resolving the issue on 1994-09-19, Andrew Wiles achieved worldwide fame!
Grisha Perelman, topologist (1966-)
Grigori Yakovlevich Perelman turned down the Fields Medal (2006)and a million-dollar Clay prize (2010) for his 2002 proof of Thurston's geometrization conjecture, implying the legendary Poincaré conjecture (1904). Since 2005, Perelman has been living as a recluse in Saint-Petersburg.
Ctesibius of Alexandria (c. 310-222 BC)
Diophantus of Alexandria (c. AD 200-284)
Pappus of Alexandria (c. AD 290-350)
.jpg "Evangelista Torricelli (c. 1647)")
Ada Byron, Lady Lovelace (1815-
Dmitri Mendeleev, chemist (1834-1907)
