Abraham Adolf Halevi Fraenkel studied mathematics at the Universities ofMunich,Berlin,Marburg andBreslau. After graduating, he lectured at the University of Marburg from 1916, and was promoted toprofessor in 1922.
In 1919, he married Wilhelmina Malka A. Prins (1892–1983). Due to the severe housing shortage in post-First World war Germany, for a few years the couple lived with fellow professorKurt Hensel as subtenants.
After leaving Marburg in 1928, Fraenkel taught at theUniversity of Kiel for a year. He then made the choice of accepting a position at theHebrew University of Jerusalem, which had been founded four years earlier, where he spent the rest of his career. He became the first dean of the faculty of mathematics, and for a while served asrector of the university.
On moving to Palestine, Fraenkel changed his name from Adolf to Abraham.[1] He was a ferventZionist and as such was a member ofJewish National Council and the JewishAssembly of Representatives under theBritish mandate. He also belonged to theMizrachi religious wing of Zionism, which promoted Jewish religious education and schools, and which advocated giving the Chief Rabbinate authority over marriage and divorce.
Fraenkel was also interested in the history of mathematics, writing in 1920 and 1930 aboutGauss's works inalgebra, and he published a biography ofGeorg Cantor. After retiring from the Hebrew University and being succeeded by his former studentAbraham Robinson, Fraenkel continued teaching at theBar Ilan University inRamat Gan (nearTel Aviv).
1908. "Bestimmung des Datums des jüdischen Osterfestes für die Zeitrechnung der Mohammedaner". InZeitschrift für Mathematik und naturwissenschaft Unterricht (39).
1909. "Eine Formel zur Verwandlung jüdischer Daten in mohammedanische". InMonatsschrift für Geschichte und Wissenschaft des Judentums, vol. 53, issue 11–12.
1910. "Die Berechnung des Osterfestes".Journal für die reine und angewandte Mathematik, vol 138.
1914. "Über die Teiler der Null und die Zerlegung von Ringen". J. Reine Angew. Math. 145: 139–176.
1918. "Praktisches zur Universitätsgründung in Jerusalem".Der Jude 3:404–414.
1918b. "Mathematik und Apologie".Jeschurun, 5:112–126.
1919.Einleitung in die Mengenlehre. Berlin: Julius Springer.[3]
1920.Materialien für eine wissenschaftliche Biographie von Gauss.
1921. "Die neueren Ideen zur Grundlagung der Analysis und Mengenlehre". InJahresbericht der Deutschen Mathematiker-Vereinigung.
1922b. "The notion of 'definite' and the independence of the axiom of choice". InJean van Heijenoort, 1967.From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Harvard University Press: 284–289.
1927.Zehn Vorlesungen über die Grundlegung der Mengenlehre. B. G. Teubner.[4]
1930. "Georg Cantor". InJahresbericht der Deutschen Mathematiker-Vereinigung 39, 189–266. Also appeared separately asGeorg Cantor Leipzig: B. G. Teubner and is abridged in Cantor'sGesammelte Abhandlungen.
1930–1931 (5691). "אמונות ודעות לאור מדעי הטבע". Part 1 inההד VI(8) 16–19, part 2 inההד VI(9). Reprinted together as a monograph byההד in 1931 Reprinted in 1987–8. Translated by Mark Zelcer inHakirah vol. 12.
1930–1931b. "Die heutigen Gegensätze in der Grundlegung der Mathematik." InErkenntnis vol. 1.
1943.הילודה בישוב ובעיותיה. Jerusalem: D. B. Aaronson.
1943b. יצחק ניוטון 1642–1942: דברים שנאמרו על-ידי ד"ר י.ל. מאגנס, ... , א.ה. פרנקל ... י.רקח ... בחגיגת ניוטון שנערכה באוניברסיטה העברית בירושלים, ביום ג' אדר תש"ג [1943]. ירושלים : חברה להוצאת ספרים על-יד האוניברסיטה העברית
1943c. "Problems and Methods in Modern Mathematics – 1". InScripta Mathematica IX (1).
1943d. "Problems and Methods in Modern Mathematics – 2". InScripta Mathematica IX (2).
1943e. "Problems and Methods in Modern Mathematics – 3". InScripta Mathematica IX (3).
1943c. "Problems and Methods in Modern Mathematics – 4". InScripta Mathematica IX (4).
1944. "Problems and Methods in Modern Mathematics – 5". InScripta Mathematica X (3–4).
1945. "על נימוקיהם של דחיית אד"ו ושל הסדר גו"ח אדז"ט לשנים המעוברות". In Y. L. Fishman (ed.)זכרון לנשמת הרב אברהם יצחק הכהן קוק למלאות עשר שנים לפטירתו, קובץ תורני-מדעי. Jerusalem Mossad HaRav Kook.
1946. "Address by Abraham A. Fraenkel". InFounder's Day: The Dropsie College for Hebrew and Cognate learning. Addresses: The Honorable Herbert H. Lehman, Professor Abraham Fraenkel. Philadelphia: Dropsie College.
1946. "The Recent Controversies about the Foundations of Mathematics". InScripta Mathematica XII(4).
1947. "The Hebrew University and the Regulation of Secondary Education in Palestine". InJewish Education 18:2.
1947. "The recent controversies about the foundation of mathematics". InScripta Mathematica XIII, pp 17–36.
1951. "On the Crisis of the Principle of Excluded Middle". InScripta Mathematica XV (1–2).
1953.מבוא למתמטיקה: בעיות ושיטות מן המתמטיקה החדישה. Ramat Gan: Masada Publishing.
1953b.Abstract Set theory. Amsterdam: North Holland Publishing Co.
1955.Integers and the Theory of Numbers. New York:[Scripta Mathematica], Yeshiva University.
1955b. ."על סדר התפילות בקיבוץ הדתי" Inשי לישעיה: ספר יובל לר' ישעיהו וולפסברג בן הששים. Y. Tirosh (ed.). Tel Aviv: Merkaz LeTarbut Shel HaPoel Mizrahi; 193–194.
1958. "משום ירקיא – משום מתיא". In Shimon Braunstein and Gershon Chorgon (eds.)ספר יובל לכבוד שמואל קלמן מירסקי. New York: Vaad HaYovel; 248–250.
1960. "Jewish mathematics and astronomy". InScripta Mathematica XXV, pp 33–47. (Appeared inHebrew inTekhnika Umada, Tel Aviv, 1947. Footnote 12 of theScripta Mathematica version claims that the essay was written in the 1930s.)
1960. "Epistemology and logic". InSynthese 12, pp. 333–337.
1961.Essays on the foundations of mathematics, dedicated to A. A. Fraenkel on his seventieth anniversary. Y. Bar-Hillel, E. I. J. Poznanski, M. O. Rabin and A. Robinson, eds. Jerusalem, the Hebrew University: Magnes Press.
1966 (1953).Abstract Set Theory. North Holland.
1966.Set Theory and Logic. Addison-Wesley.
1966. "עיבור שנים וקידוש החודש". Inאמונה, דת ומדע. Jerusalem: Misrad HaChinuch VeHaTarbut.
1967.Lebenskreise: Aus den Erinnerungen eines jüdischen Mathematikers. Deutsche Verlags-Anstalt.
