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 Zionism is an Ethnic nationalism, ethnocultural nationalist movement that emerged in History of Europe#From revolution to imperialism (1789–1914), Europe in the late 19th century that aimed to establish and maintain a national home for the ...

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 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 ...

, especially his additions to

Ernst Zermelo Ernst Friedrich Ferdinand Zermelo (; ; 27 July 187121 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel set theory, Z ...

's axioms, which resulted in the

Zermelo–Fraenkel set theory In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes suc ...

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 Marburg (; ) is a college town, university town in the States of Germany, German federal state () of Hesse, capital of the Marburg-Biedenkopf Districts of Germany, district (). The town area spreads along the valley of the river Lahn and has ...

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 Kurt Wilhelm Sebastian Hensel (29 December 1861 – 1 June 1941) was a German mathematician born in Königsberg. Life and career Hensel was born in Königsberg, Province of Prussia (today Kaliningrad, Russia), the son of Julia (née von Adelson ...

as subtenants. After leaving Marburg in 1928, Fraenkel taught at the

University of Kiel Kiel University, officially the Christian Albrecht University of Kiel, (, abbreviated CAU, known informally as Christiana Albertina) is a public research university in the city of Kiel, Germany. It was founded in 1665 as the ''Academia Holsator ...

for a year. He then made the choice of accepting a position at the

, 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

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

p-adic number In number theory, given a prime number , the -adic numbers form an extension of the rational numbers which is distinct from the real numbers, though with some similar properties; -adic numbers can be written in a form similar to (possibly infin ...

s 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

, 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 Ernst Friedrich Ferdinand Zermelo (; ; 27 July 187121 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel axiomatic se ...

'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 Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observat ...

'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 Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorp ...

, Fraenkel continued teaching at the

Bar Ilan University Bar-Ilan University (BIU, , ''Universitat Bar-Ilan'') is a public research university in the Tel Aviv District city of Ramat Gan, Israel. Established in 1955, Bar Ilan is Israel's second-largest academic university institution. It has 20,000 ...

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 The Israel Prize (; ''pras israél'') is an award bestowed by the State of Israel, and regarded as the state's highest cultural honor. History Prior to the Israel Prize, the most significant award in the arts was the Dizengoff Prize and in Israel ...

, 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 Jean Louis Maxime van Heijenoort ( ; ; ; July 23, 1912 – March 29, 1986) was a historian of mathematical logic. He was also a personal secretary to Leon Trotsky from 1932 to 1939, and an American Trotskyist until 1947. Life Van Heijenoort wa ...

, 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 ''Erkenntnis'' is a journal of philosophy that publishes papers in analytic philosophy. Its name is derived from the German word " Erkenntnis", meaning "knowledge, recognition". The journal was also linked to organisation of conferences, such as th ...

'' vol. 1. *1935. "Zum Diagonalverfahren Cantors". ''

Fundamenta Mathematicae ''Fundamenta Mathematicae'' is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic, topology and its interactions with algebra, and dynamical sys ...

'' 25, 45–50. *1935. "Concerning the Method of Number Pairs". ''Philosophy of Science'' 2 (1). *1938. "Alfred Loewy (1873–1935)". In ''

Scripta Mathematica ''Scripta Mathematica'' was a quarterly journal published by Yeshiva University devoted to the Philosophy, history, and expository treatment of mathematics. It was said to be, at its time, "the only mathematical magazine in the world edited by spe ...

'' vol. V(1). *1939. "Natural Numbers as Cardinals". In ''

'' VI (2). *1940. "Natural Numbers as Ordinals". In ''

'' 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 ''

'' IX (1). *1943d. "Problems and Methods in Modern Mathematics – 2". In ''

'' IX (2). *1943e. "Problems and Methods in Modern Mathematics – 3". In ''

'' IX (3). *1943c. "Problems and Methods in Modern Mathematics – 4". In ''

'' IX (4). *1944. "Problems and Methods in Modern Mathematics – 5". In ''

'' 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 ''

'' 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 ''

'' XIII, pp 17–36. *1951. "On the Crisis of the Principle of Excluded Middle". In ''

'' 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 ''

'' 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 ''

'' version claims that the essay was written in the 1930s.) *1960. "Epistemology and logic". In ''

Synthese ''Synthese'' () is a monthly peer-reviewed academic journal covering the epistemology, methodology, and philosophy of science, and related issues. The name ''Synthese'' (from the Dutch for '' synthesis'') finds its origin in the intentions of its f ...

'' 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 Yehoshua Bar-Hillel (; 8 September 1915 – 25 September 1975) was an Israeli philosopher, mathematician, and linguist. He was a pioneer in the fields of machine translation and formal linguistics. Early life and education Born Oscar Westreich ...

Azriel Levy Azriel or Ezriel may refer to: People *Azriel the father of Seraiah in the Bible, see Jeremiah 36#Verse 26 * Azriel of Gerona (c. 1160–c. 1238), Catalan kabbalist * Azriel Graeber (born 1948), Talmudic Scholar and founder of the Jewish Scholars ...

, 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.

References

External links