Adolf Abraham Halevi Fraenkel
Encyclopedia
Abraham Halevi Fraenkel ' onMouseout='HidePop("89860")' href="/topics/Munich">Munich
, Germany
– October 15, 1965, Jerusalem, Israel
), known as Abraham Fraenkel, was an Israel
i mathematician
born in Germany
. He was an early Zionist and the first Dean of Mathematics at the Hebrew University of Jerusalem
. He is known for his contributions to axiomatic set theory, especially his addition to Ernst Zermelo
's axioms which resulted in Zermelo–Fraenkel axioms.
in 1922.
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 Hebrew 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 as Rector of the University.
Fraenkel 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.
's p-adic number
s and on the theory
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") 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
and foundational mathematics
.
Fraenkel also was interested in the history of mathematics
, writing in 1920 and 1930 about Gauss
' works in algebra
, and he published a biography of Georg Cantor
. 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 (near Tel Aviv
).
Munich
Munich The city's motto is "" . Before 2006, it was "Weltstadt mit Herz" . Its native name, , is derived from the Old High German Munichen, meaning "by the monks' place". The city's name derives from the monks of the Benedictine order who founded the city; hence the monk depicted on the city's coat...
, Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
– October 15, 1965, Jerusalem, Israel
Israel
The State of Israel is a parliamentary republic located in the Middle East, along the eastern shore of the Mediterranean Sea...
), known as Abraham Fraenkel, was an Israel
Israel
The State of Israel is a parliamentary republic located in the Middle East, along the eastern shore of the Mediterranean Sea...
i mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
born in Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
. He was an early Zionist and the first Dean of Mathematics at the Hebrew University of Jerusalem
Hebrew University of Jerusalem
The Hebrew University of Jerusalem ; ; abbreviated HUJI) is Israel's second-oldest university, after the Technion – Israel Institute of Technology. The Hebrew University has three campuses in Jerusalem and one in Rehovot. The world's largest Jewish studies library is located on its Edmond J...
. He is known for his contributions to axiomatic set theory, especially his addition to Ernst Zermelo
Ernst Zermelo
Ernst Friedrich Ferdinand Zermelo was a German mathematician, whose work has major implications for the foundations of mathematics and hence on philosophy. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem.-Life:He graduated...
's axioms which resulted in Zermelo–Fraenkel axioms.
Life
Fraenkel studied mathematics at the University of Munich, University of Berlin, University of Marburg and University of Breslau; after graduating, he lectured at the University of Marburg from 1916, and was promoted to professorProfessor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
in 1922.
After leaving Marburg in 1928, Fraenkel taught at the University of Kiel
University of Kiel
The University of Kiel is a university in the city of Kiel, Germany. It was founded in 1665 as the Academia Holsatorum Chiloniensis by Christian Albert, Duke of Holstein-Gottorp and has approximately 23,000 students today...
for a year. He then made the fateful choice of accepting a position at the Hebrew University of Jerusalem
Hebrew University of Jerusalem
The Hebrew University of Jerusalem ; ; abbreviated HUJI) is Israel's second-oldest university, after the Technion – Israel Institute of Technology. The Hebrew University has three campuses in Jerusalem and one in Rehovot. The world's largest Jewish studies library is located on its Edmond J...
, 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 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
Mizrachi (Religious Zionism)
The Mizrachi is the name of the religious Zionist organization founded in 1902 in Vilnius at a world conference of religious Zionists called by Rabbi Yitzchak Yaacov Reines. Bnei Akiva, which was founded in 1929, is the youth movement associated with 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 first work was on Kurt HenselKurt Hensel
Kurt Wilhelm Sebastian Hensel was a German mathematician born in Königsberg, Prussia.He was the son of the landowner and entrepreneur Sebastian Hensel, brother of the philosopher Paul Hensel, grandson of the composer Fanny Mendelssohn and the painter Wilhelm Hensel, and a descendant of the...
's p-adic number
P-adic number
In mathematics, and chiefly number theory, the p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number systems...
s and on the theory
Ring theory
In abstract algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers...
of rings
Ring (mathematics)
In mathematics, a ring is an algebraic structure consisting of a set together with two binary operations usually called addition and multiplication, where the set is an abelian group under addition and a semigroup under multiplication such that multiplication distributes over addition...
. He is best known for his work on axiomatic set theory, publishing his first major work on the topic ("Einleitung in die Mengenlehre") 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
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
and foundational mathematics
Foundations of mathematics
Foundations of mathematics is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, type theory and recursion theory...
.
Fraenkel also was interested in the history of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, writing in 1920 and 1930 about Gauss
Carl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...
' works in algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
, and he published a biography of Georg Cantor
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets,...
. After retiring from the Hebrew University and being succeeded by his former student Abraham Robinson
Abraham Robinson
Abraham Robinson was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics....
, Fraenkel continued teaching at the Bar Ilan University in Ramat Gan (near Tel Aviv
Tel Aviv
Tel Aviv , officially Tel Aviv-Yafo , is the second most populous city in Israel, with a population of 404,400 on a land area of . The city is located on the Israeli Mediterranean coastline in west-central Israel. It is the largest and most populous city in the metropolitan area of Gush Dan, with...
).
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, 53. Jahrgang, Heft 11-12.
- 1910. "Die Berechnung des Osterfestes". Journal für die reine und angewandte Mathematik, vol 138.
- 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: Verlag von 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.
- 1922b. "The notion of 'definite' and the independence of the axiom of choice" in Jean van HeijenoortJean Van HeijenoortJean Louis Maxime van Heijenoort was a pioneer historian of mathematical logic. He was also a personal secretary to Leon Trotsky from 1932 to 1939, and from then until 1947, an American Trotskyist activist.-Life:Van Heijenoort was born in Creil, France...
, 1967. From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931. Harvard Univ. Press: 284–289. - 1922. "Zu den Grundlagen der Cantor-Zermeloschen Mengenlehre", Mathematische Annalen 86: 230-7.
- 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.
- 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.
- 1930-1 (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 HakirahHakirahḤakirah, The Flatbush Journal of Jewish Law and Thought is a peer-reviewed journal in the field of Jewish Law and Thought. The journal is currently published by Hakirah, Inc. from editorial offices in Brooklyn, NY, USA, with 2 annual issues....
vol 12. - 1930-1b. "Die heutigen Gegensätze in der Grundlegung der Mathematik." In ErkenntnisErkenntnisErkenntnis is a journal of philosophy that publishes papers in analytic philosophy. Its name is derived from the German word for knowledge recognition. The journal was founded by Hans Reichenbach and Rudolf Carnap in 1930. The journal was "refounded" by Wilhelm K. Essler, Carl G...
1 Bd. - 1935. "Zum Diagonalverfahren Cantors," Fundamenta MathematicaeFundamenta MathematicaeFundamenta Mathematicae is a scientific journal of mathematics with a special focus on the foundations of mathematics. At present, it concentrates on papers devoted to set theory, mathematical logic, topology and its interactions with algebra, and dynamical systems...
25, 45-50. - 1935. "Concerning the Method of Number Pairs." Philosophy of Science 2 (1).
- 1938. "Alfred Loewy (1873-1935)". In Scripta MathematicaScripta MathematicaScripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics...
. Vol V(1). - 1939. "Natural Numbers as Cardinals." In Scripta MathematicaScripta MathematicaScripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics...
VI (2). - 1940. "Natural Numbers as Ordinals." In Scripta MathematicaScripta MathematicaScripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics...
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 [1943]. ירושלים : חברה להוצאת ספרים על-יד האוניברסיטה העברית
- 1943c. "Problems and Methods in Modern Mathematics - 1. In Scripta MathematicaScripta MathematicaScripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics...
IX (1). - 1943d. "Problems and Methods in Modern Mathematics - 2." In Scripta MathematicaScripta MathematicaScripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics...
IX (2). - 1943e. "Problems and Methods in Modern Mathematics - 3." In Scripta MathematicaScripta MathematicaScripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics...
IX (3). - 1943c. "Problems and Methods in Modern Mathematics - 4." In Scripta MathematicaScripta MathematicaScripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics...
IX (4). - 1944. "Problems and Methods in Modern Mathematics - 5." In Scripta MathematicaScripta MathematicaScripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics...
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 MathematicaScripta MathematicaScripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics...
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 MathematicaScripta MathematicaScripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics...
XIII, pp 17-36. - 1951. "On the Crisis of the Principle of Excluded Middle." In Scripta MathematicaScripta MathematicaScripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics...
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" 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 MathematicaScripta MathematicaScripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics...
XXV, pp 33-47. (Appeared in Hebrew in Tekhnika Umada, Tel Aviv, 1947. Footnote 12 of the Scripta MathematicaScripta MathematicaScripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics...
version claims that the essay was written in the 1930's.) - 1960. "Epistemology and logic" in SyntheseSyntheseSynthese is a scholarly periodical edited by Johan van Benthem, Vincent F. Hendricks and John Symons specializing in papers in epistemology, methodology and philosophy of science...
12, pp 333-337. - 1960. "Theory of Sets" in Encyclopedia Britannica.
- 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-HillelYehoshua Bar-HillelYehoshua Bar-Hillel was an Israeli philosopher, mathematician, and linguist at the Hebrew University of Jerusalem, best known for his pioneering work in machine translation and formal linguistics.- Biography :...
, Azriel LevyAzriel LevyAzriel Levy is an Israeli mathematician, logician, and a professor emeritus at the Hebrew University of Jerusalem....
, and Dirk van DalenDirk van DalenDirk van Dalen 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 LEJ Brouwer and Arend Heyting, he received his Ph.D...
) Foundations of Set Theory. North Holland.