Abraham Fraenkel ( he, אברהם הלוי (אדולף) פרנקל; February 17, 1891 – October 15, 1965) was a German-born

Israel Israel (; he, יִשְׂרָאֵל, ; ar, إِسْرَائِيل, ), officially the State of Israel ( he, מְדִינַת יִשְׂרָאֵל, label=none, translit=Medīnat Yīsrāʾēl; ), is a country in Western Asia. It is situated ...

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, structure, space, models, and change. History On ...

. He was an early

Zionist Zionism ( he, צִיּוֹנוּת ''Tsiyyonut'' after ''Zion'') is a nationalist movement that espouses the establishment of, and support for a homeland for the Jewish people centered in the area roughly corresponding to what is known in Je ...

and the first Dean of Mathematics at the

Hebrew University of Jerusalem The Hebrew University of Jerusalem (HUJI; he, הַאוּנִיבֶרְסִיטָה הַעִבְרִית בִּירוּשָׁלַיִם) is a public research university based in Jerusalem, Israel. Co-founded by Albert Einstein and Dr. Chaim Weiz ...

. 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 mathematics, ...

, 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 axiomatic se ...

'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 such as ...

Biography

Abraham Adolf Halevi Fraenkel studied mathematics at the Universities of

Munich Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the States of Germany, German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the List of cities in Germany by popu ...

Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...

Marburg Marburg ( or ) is a university town in the German federal state (''Bundesland'') of Hesse, capital of the Marburg-Biedenkopf district (''Landkreis''). The town area spreads along the valley of the river Lahn and has a population of approximate ...

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 post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who pr ...

in 1922. In 1919 he married Wilhelmina Malka A. Prins (1892–1983). Due to the severe housing shortage in post-war Germany, for a few years the couple lived as subtenants at professor Hensel's place. After leaving Marburg in 1928, Fraenkel taught at the University of Kiel for a year. He then made the fateful 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. Fraenkel was a fervent

and as such was a member of

Jewish National Council The Jewish National Council (JNC; he, ועד לאומי, ''Va'ad Le'umi''), also known as the Jewish People's Council was the main national executive organ of the Assembly of Representatives of the Jewish community (Yishuv) within Mandatory Pale ...

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 rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be s ...

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'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 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 mathematics, is mostly conce ...

and

foundational mathematics Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathe ...

. Fraenkel also was interested in the history of

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, writing in 1920 and 1930 about Gauss's works in

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

, and he published a biography of

Georg Cantor Georg Ferdinand Ludwig Philipp Cantor ( , ; – January 6, 1918) was a German mathematician. He played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of ...

. 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 ( he, רָמַת גַּן or , ) is a city in the Tel Aviv District of Israel, located east of the municipality of Tel Aviv and part of the Tel Aviv metropolitan area. It is home to one of the world's major diamond exchanges, and many ...

(near

Tel Aviv Tel Aviv-Yafo ( he, תֵּל־אָבִיב-יָפוֹ, translit=Tēl-ʾĀvīv-Yāfō ; ar, تَلّ أَبِيب – يَافَا, translit=Tall ʾAbīb-Yāfā, links=no), often referred to as just Tel Aviv, is the most populous city in the G ...

Awards

* In 1956, Fraenkel was awarded the

Israel Prize The Israel Prize ( he, פרס ישראל; ''pras israél'') is an award bestowed by the State of Israel, and regarded as the state's highest cultural honor. History The Israel Prize is awarded annually, on Israeli Independence Day, in a state cer ...

, 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 Year 943 ( CMXLIII) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. Events By place Byzantine Empire * Spring – Allied with the Rus', a Hungarian army raids Moesia and Thrace. ...

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 (; ; ) is a Northwest Semitic language of the Afroasiatic language family. Historically, it is one of the spoken languages of the Israelites and their longest-surviving descendants, the Jews and Samaritans. It was largely preserved ...

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 (Latin for "British Encyclopædia") is a general knowledge English-language encyclopaedia. It is published by Encyclopædia Britannica, Inc.; the company has existed since the 18th century, although it has changed ownership various time ...

''. *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 The ''Encyclopaedia Hebraica'' ( he, האנציקלופדיה העברית) is a comprehensive encyclopedia in the Hebrew language that was published in the latter half of the 20th century.ha-Entsiklopediyah ha-ʻivrit (האנציקלופדיה ...

'', vol 26. *1973 (1958). (with

Yehoshua Bar-Hillel Yehoshua Bar-Hillel ( he, יהושע בר-הלל; 8 September 1915, in Vienna – 25 September 1975, in Jerusalem) was an Israeli philosopher, mathematician, and linguist. He was a pioneer in the fields of machine translation and formal linguisti ...

Azriel Levy Azriel, Asriel or Ezriel may refer to: People * Azriel of Gerona (c. 1160–c. 1238), Catalan kabbalist * Azriel Hildesheimer (1820–1899), German rabbi * Azriel Rabinowitz (1905–1941), Lithuanian rabbi and Holocaust victim * Azriel Rosenfeld ( ...

, and

Dirk van Dalen Dirk van Dalen (born 20 December 1932, Amsterdam) is a Dutch mathematician and historian of science. Van Dalen studied mathematics and physics and astronomy at the University of Amsterdam. Inspired by the work of Brouwer and Heyting, he received ...

) ''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