Abraham Fraenkel (; 17 February, 1891 – 15 October, 1965) was a German-born Israeli
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
. He was an early
Zionist and the first Dean of Mathematics at the
Hebrew University of Jerusalem
The Hebrew University of Jerusalem (HUJI; ) is an Israeli public university, public research university based in Jerusalem. Co-founded by Albert Einstein and Chaim Weizmann in July 1918, the public university officially opened on 1 April 1925. ...
. He is known for his contributions to
axiomatic set theory, especially his additions to
Ernst Zermelo's axioms, which resulted in the
Zermelo–Fraenkel set theory.
Biography
Abraham Adolf Halevi Fraenkel studied mathematics at the Universities of
Munich
Munich is the capital and most populous city of Bavaria, Germany. As of 30 November 2024, its population was 1,604,384, making it the third-largest city in Germany after Berlin and Hamburg. Munich is the largest city in Germany that is no ...
,
Berlin
Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...
,
Marburg and
Breslau. After graduating, he lectured at the University of Marburg from 1916, and was promoted to
professor
Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...
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 professor
Kurt Hensel as subtenants.
After leaving Marburg in 1928, Fraenkel taught at the
University of Kiel for a year. He then made the choice of accepting a position at the
Hebrew University of Jerusalem
The Hebrew University of Jerusalem (HUJI; ) is an Israeli public university, public research university based in Jerusalem. Co-founded by Albert Einstein and Chaim Weizmann in July 1918, the public university officially opened on 1 April 1925. ...
, 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 as
rector of the university.
On moving to Palestine, Fraenkel changed his name from Adolf to Abraham. He was a fervent
Zionist and as such was a member of
Jewish National Council and the Jewish
Assembly of Representatives under the
British mandate. He also belonged to the
Mizrachi religious wing of Zionism, which promoted Jewish religious education and schools, and which advocated giving the Chief Rabbinate authority over marriage and divorce.
Mathematician
Fraenkel's early work was on
Kurt Hensel's
p-adic numbers and on the
theory
A theory is a systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, ...
of
rings. He is best known for his work on
axiomatic set theory, publishing his first major work on the topic ''Einleitung in die Mengenlehre'' (Introduction to set theory) in 1919. In 1922 and 1925, he published two papers that sought to improve
Zermelo's axiomatic system; the result is the
Zermelo–Fraenkel axioms. Fraenkel worked in
set theory
Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...
and
foundational mathematics.
Fraenkel was also interested in the history of mathematics, writing in 1920 and 1930 about
Gauss's works in
algebra
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...
, and he published a biography of
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor ( ; ; – 6 January 1918) was a mathematician who played a pivotal role in the creation of set theory, which has become a foundations of mathematics, fundamental theory in mathematics. Cantor establi ...
. After retiring from the Hebrew University and being succeeded by his former student
Abraham Robinson, Fraenkel continued teaching at the
Bar Ilan University in
Ramat Gan
Ramat Gan (, ) is a city in the Tel Aviv District of Israel, located east of the municipality of Tel Aviv, and is part of the Gush Dan, Gush Dan metropolitan area. It is home to a Diamond Exchange District (one of the world's major diamond exch ...
(near
Tel Aviv
Tel Aviv-Yafo ( or , ; ), sometimes rendered as Tel Aviv-Jaffa, and usually referred to as just Tel Aviv, is the most populous city in the Gush Dan metropolitan area of Israel. Located on the Israeli Mediterranean coastline and with a popula ...
).
Awards
* In 1956, Fraenkel was awarded the
Israel Prize, for exact sciences.
Published works
*1908. "Bestimmung des Datums des jüdischen Osterfestes für die Zeitrechnung der Mohammedaner". In ''Zeitschrift für Mathematik und naturwissenschaft Unterricht'' (39).
*1909. "Eine Formel zur Verwandlung jüdischer Daten in mohammedanische". In ''Monatsschrift 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.
*1920. ''Materialien für eine wissenschaftliche Biographie von Gauss''.
*1921. "Die neueren Ideen zur Grundlagung der Analysis und Mengenlehre". In ''Jahresbericht der Deutschen Mathematiker-Vereinigung''.
*1922.
*1922b. "The notion of 'definite' and the independence of the axiom of choice". In
Jean van Heijenoort, 1967. ''From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931''. Harvard University Press: 284–289.
*1922c.
*1924. "Die neueren Ideen zur Grundlegung der Analysis und Mengenlehre". In ''Jahrsebericht Der Deutschen Mathematiker-Vereinigung'', Vol 33, 97–103.
*1924. "The Jewish University in Jerusalem (From the Viewpoint of Orthodoxy)". ''Jewish Forum'', January: VII (1), 27–31.
*1924b "The Jewish University in Jerusalem (From the Viewpoint of Orthodoxy)". ''Jewish Forum'', May: VII (5), 299–302.
*1925. "Leben, Natur, Religion". ''Jeschurun'' 12:337–348.
*1927. ''Zehn Vorlesungen über die Grundlegung der Mengenlehre''. B. G. Teubner.
*1930. "Georg Cantor". In ''Jahresbericht der Deutschen Mathematiker-Vereinigung'' 39, 189–266. Also appeared separately as ''Georg Cantor'' Leipzig: B. G. Teubner and is abridged in Cantor's ''Gesammelte Abhandlungen''.
*1930–1931 (5691). "אמונות ודעות לאור מדעי הטבע". Part 1 in ''ההד'' VI(8) 16–19, part 2 in ''ההד'' VI(9). Reprinted together as a monograph by ''ההד'' in 1931 Reprinted in 1987–8. Translated by Mark Zelcer in ''
Hakirah'' vol. 12.
*1930–1931b. "Die heutigen Gegensätze in der Grundlegung der Mathematik." In ''
Erkenntnis'' vol. 1.
*1935. "Zum Diagonalverfahren Cantors". ''
Fundamenta Mathematicae'' 25, 45–50.
*1935. "Concerning the Method of Number Pairs". ''Philosophy of Science'' 2 (1).
*1938. "Alfred Loewy (1873–1935)". In ''
Scripta Mathematica'' vol. V(1).
*1939. "Natural Numbers as Cardinals". In ''
Scripta Mathematica'' VI (2).
*1940. "Natural Numbers as Ordinals". In ''
Scripta Mathematica'' VII (1–4).
*1941. "מכתב למערכת". In ''הצופה'' September 12, p8.
*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
943 ירושלים : חברה להוצאת ספרים על-יד האוניברסיטה העברית
*1943c. "Problems and Methods in Modern Mathematics – 1". In ''
Scripta Mathematica'' IX (1).
*1943d. "Problems and Methods in Modern Mathematics – 2". In ''
Scripta Mathematica'' IX (2).
*1943e. "Problems and Methods in Modern Mathematics – 3". In ''
Scripta Mathematica'' IX (3).
*1943c. "Problems and Methods in Modern Mathematics – 4". In ''
Scripta Mathematica'' IX (4).
*1944. "Problems and Methods in Modern Mathematics – 5". In ''
Scripta 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". In ''Founder'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". In ''
Scripta Mathematica'' XII(4).
*1947. "The Hebrew University and the Regulation of Secondary Education in Palestine". In ''Jewish Education'' 18:2.
*1947. "The recent controversies about the foundation of mathematics". In ''
Scripta Mathematica'' XIII, pp 17–36.
*1951. "On the Crisis of the Principle of Excluded Middle". In ''
Scripta 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: ''
cripta Mathematica', Yeshiva University.
*1955b. ."על סדר התפילות בקיבוץ הדתי" In ''שי 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". In ''
Scripta Mathematica'' XXV, pp 33–47. (Appeared in
Hebrew
Hebrew (; ''ʿÎbrit'') is a Northwest Semitic languages, Northwest Semitic language within the Afroasiatic languages, Afroasiatic language family. A regional dialect of the Canaanite languages, it was natively spoken by the Israelites and ...
in ''Tekhnika Umada'', Tel Aviv, 1947. Footnote 12 of the ''
Scripta Mathematica'' version claims that the essay was written in the 1930s.)
*1960. "Epistemology and logic". In ''
Synthese'' 12, pp. 333–337.
*1960. "Theory of Sets". In ''
Encyclopædia Britannica
The is a general knowledge, general-knowledge English-language encyclopaedia. It has been published by Encyclopædia Britannica, Inc. since 1768, although the company has changed ownership seven times. The 2010 version of the 15th edition, ...
''.
*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". In ''אמונה, דת ומדע''. Jerusalem: Misrad HaChinuch VeHaTarbut.
*1967. ''Lebenskreise: Aus den Erinnerungen eines jüdischen Mathematikers''. Deutsche Verlags-Anstalt.
*1969. "הלוח העברי". ''
Encyclopedia Hebraica'', vol 26.
*1973 (1958). (with
Yehoshua Bar-Hillel,
Azriel Levy, and
Dirk van Dalen) ''Foundations of Set Theory''. North Holland.
*2016
Recollections of a Jewish Mathematician in Germany'' Translated from the German 1967 edition by Allison Brown. Edited by Jiska Cohen-Mansfield. Basel: Springer Birkhäuser History of Science.
See also
*
List of Israel Prize recipients
*
Fränkel
References
External links
*
{{DEFAULTSORT:Fraenkel, Abraham
1891 births
1965 deaths
20th-century Israeli mathematicians
Academic staff of Bar-Ilan University
German emigrants to Mandatory Palestine
20th-century German Jews
Academic staff of the Hebrew University of Jerusalem
Humboldt University of Berlin alumni
Ludwig Maximilian University of Munich alumni
Israeli Jews
Israel Prize in exact science recipients who were mathematicians
Members of the Assembly of Representatives (Mandatory Palestine)
Members of the Israel Academy of Sciences and Humanities
Scientists from Munich
Set theorists
University of Breslau alumni
Academic staff of the University of Kiel
University of Marburg alumni
Burials at Har HaMenuchot
German Zionists