Lloyd Nicholas TrefethenFRS^[1] (born 30 August 1955) is an American mathematician, professor ofnumerical analysis and until 2023 head of the Numerical Analysis Group at theMathematical Institute, University of Oxford.^[6][7][8][9] He was elected a Member of theNational Academy of Sciences in 2025.^[10]

Trefethen was born 30 August 1955 inBoston, Massachusetts,^[11] the son of mechanical engineerLloyd M. Trefethen and codebreaker, poet, teacher and editorFlorence Newman Trefethen.^[3] Trefethen attendedPhillips Exeter Academy.

He obtained his bachelor's degree fromHarvard College in 1977 and his master's fromStanford University in 1980. His PhD was onWave Propagation and Stability for Finite Difference Schemes supervised byJoseph E. Oliger atStanford University.^[2][12][13]

Following his PhD, Trefethen went on to work at theCourant Institute of Mathematical Sciences in New York,Massachusetts Institute of Technology, andCornell University, before being appointed to a chair at theUniversity of Oxford and a Fellowship ofBalliol College, Oxford.^[14]

His publications span a wide range of areas within numerical analysis and applied mathematics, including non-normaleigenvalue problems and applications, spectral methods for differential equations,numerical linear algebra,fluid mechanics, computationalcomplex analysis, and approximation theory.^[15] He is perhaps best known for his work onpseudospectra ofnon-normal matrices and operators. This work covers theoretical aspects as well as numerical algorithms, and applications including fluid mechanics, numerical solution of partial differential equations, numerical linear algebra, shuffling of cards, random matrices, differential equations andlasers. Trefethen is currently anISI highly cited researcher.^[16]

Trefethen has written a number of books on numerical analysis includingNumerical Linear Algebra^[17] with David Bau,Spectral Methods in MATLAB,Schwarz–Christoffel Mapping with Tobin Driscoll, andSpectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators^[18] withMark Embree.^[5] He is the leader of theMATLAB-basedChebfun software project.

In 2013 he proposed a new formula to calculate theBMI of a person:^[19][20]

${\displaystyle \text{BMI}=1.3\times \frac{\text{weight}}{{\text{height}}^{2.5}}}$

(International System of Units)

• Numerical Linear Algebra (SIAM, 1997) with David Bau
• Spectral Methods in Matlab (SIAM, 2000)
• Schwarz-Christoffel Mapping (Cambridge, 2002) with T. A. Driscoll
• Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators (Princeton, 2005) with Mark Embree
• Trefethen's Index Cards (World Scientific 2011)
• Approximation Theory and Approximation Practice (SIAM, 2013 and 2020)
• Exploring ODEs (SIAM, 2018) with Á. Birkisson and T. A. Driscoll
• An Applied Mathematician’s Apology (SIAM, 2022)

Trefethen was the first winner of theLeslie Fox Prize for Numerical Analysis. In 1998 he was an Invited Speaker of theInternational Congress of Mathematicians in Berlin.^[21] He is a fellow of theAmerican Mathematical Society,^[22] and a member of theNational Academy of Engineering in the United States. Trefethen was elected aFellow of the Royal Society (FRS) in 2005,^[1] and his certificate of election reads:

Nick Trefethen is distinguished for his many seminal contributions to Numerical Analysis and its applications in Applied Mathematics and in Engineering Science. His research spans theory, algorithms, software and physical applications, particularly involving eigenvalues, pseudospectra – a concept which he introduced – and dynamics. He has an international reputation for his work on nonnormal matrices and operators. He has also made major contributions to finite difference and spectral methods for partial differential equations, numerical linear algebra, and complex analysis. His monograph Numerical Linear Algebra (SIAM, 1997) is one of the SIAM's best selling books and has already been through five printings.^[1]

In 2010 Trefethen was awarded theGold Medal of theInstitute of Mathematics and its Applications in recognition of his "outstanding contributions to mathematics and its applications over a period of years".^[23]In 2013 Trefethen was awarded theNaylor Prize and lectureship in Applied Mathematics from theLondon Mathematical Society.^[24] He was awarded the George Pólya Prize for Mathematical Exposition in 2017 and the John von NeumannPrize in 2020 by SIAM.

Trefethen has one son and one daughter from his first marriage toAnne Elizabeth Trefethen (née Daman).^[3] He is currently married to Kate McLoughlin, a professor of English Literature at Oxford.

• Personal website at Oxford University
• Chebfun project website
• Nick Trefethen at theMathematics Genealogy Project
• Publications by Nick Trefethen atResearchGate
• Trefethen onGitHub

• Numerical analysts
• 20th-century American mathematicians
• 21st-century American mathematicians
• Living people
• Harvard University alumni
• Stanford University alumni
• 1955 births
• Fellows of the American Mathematical Society
• Fellows of Balliol College, Oxford
• Fellows of the Society for Industrial and Applied Mathematics
• Members of the United States National Academy of Engineering
• Presidents of the Society for Industrial and Applied Mathematics
• Courant Institute of Mathematical Sciences faculty
• Trefethen family
• Members of the United States National Academy of Sciences
• American fellows of the Royal Society

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