Abstract
It is as if my life unfolded in 19-year cycles. After the first such period as a child and teenager in my parents’ home, I spent the next 19 years (1910–1929) as a student, and then as a professor at German universities, admittedly also including 4 years as a soldier in the First World War. During the next 19 years (1929–1948), I was a professor at the Hebrew University in Jerusalem, in the land of Israel/Palestine under the British Mandate. Although I continued as professor after 1948, and as emeritus professor from 1959, the fourth 19-year period focused more on activities for the benefit of the State of Israel rather than strictly on my academic career.
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Notes
- 1.
The normal Jewish calendar year consisting of 12 lunar months is roughly 11 days shorter than the solar year of 365 days (except in a solar leap year, which has an extra day). The leap month Adar Rishon (The First Adar) is added in seven years (the 3rd, 6th, 8th, 11th, 14th, 17th, and 19th) of each 19-year cycle of Jewish years so that the seasons in the lunar year keep pace with the solar ones. In leap years, the Jewish holidays occurring after the leap month fall relatively late in the Gregorian solar calendar. In the eighth year of each 19-year cycle, they fall on the latest Gregorian date, since the largest number (5) of leap months have been added in the preceding 11 years.**
- 2.
My “official” name was Adolf and my “Jewish” name, Abraham Halevi. In the 1930s I dropped the “Adolf” for understandable reasons and replaced it with my Jewish name when I became naturalized in Palestine/Land of Israel.
- 3.
Rudolf Fuchs, Die Thora und die Sprache (complete text with German translation on corresponding lines) (Vienna: k.-k. Schulbücher Verlag, 1878–1899; early editions of the five books of the Pentateuch).**
- 4.
Benzion means “son of Zion.”**
- 5.
Franz Ferdinand was killed on June 29, 1914. Germany declared war on France on August 3, 1914.**
- 6.
Alcoholic cardiomyopathy, a disease associated with alcohol abuse, is characterized by enlargement of the heart and low cardiac output. Mosby’s Medical Dictionary, 8th ed. (Amsterdam: Elsevier, 2009).**
- 7.
This refers to the Classical-Romantic period.**
- 8.
מברך השנים The prayer that blesses the years: “Bless on our behalf, O Lord our God, this year and all its kinds of crops for the best, and give dew and rain for a blessing on the face of the earth, and satisfy us from Your bounty, and bless our year like the best years. Blessed are You, God, Who blesses the years. …” ; adapted from The Complete ArtScroll Siddur. A new translation by Rabbi Nosson Scherman, co-edited by Rabbi Meir Zlotowitz (Brooklyn, NY: Mesorah Publications, 2007), 105.**
- 9.
The original quotation in Proverbs 16:1 is: לאדם מערכי לב; ומיהוה, מענה לשון,
“The reflections of the heart belong to man, but the tongue in which to express it is from the LORD.” [The original text is obscure and can be interpreted in various ways. This seems to be Fraenkel’s understanding of the verse]. The prayer to which Fraenkel refers is אוחילה לאל אחלה פניו, which appears in the musaf prayer on Rosh Hashanah, the Jewish New Year, and on Yom Kippur, the Day of Atonement.
,אוחילה לאל אחלה פניו
.אשאלה ממנו מענה לשון ,אשר בקהל עם אשיר עזו
אביעה רננות בעד מפעליו. .לאדם מערכי לב, ומה' מענה .לשון .ה' שפתי תפתח, ופי יגיד תהלתך
I shall put my hope in God, I shall beseech His presence,
I shall request of Him eloquent speech.
So that I can sing of His strength in the people’s congregation,
That I can express glad songs for the sake of His human creations.
It is for man to arrange his feelings,
But eloquent speech is a Godly gift.
My Lord, open my lips, that my mouth may declare Your praise.
Translation from The Complete Artscroll Machzor. Rosh Hashana. A new translation by Rabbi Nosson. Scherman, co-edited by Rabbi Meir Zlotowitz and Rabbi Avie Gold (Brooklyn, NY: Mesorah Publications, 1997), 505. Fraenkel is claiming that in the conventional view of prayer, pertaining to will and aspiration, the content comes from God, and the mode of expression from man. By contrast, Fraenkel’s view is that the ability to express oneself, and the voice, i.e., the means of the prayer, are given by God, but human will determines whether they are used to raise prayers to a meaningful level. Thus, while the means come from God, providing content and essence is the role of human beings. He found support for his interpretation in the verse from Proverbs in the אוחילה לאל prayer.**
- 10.
The siddur is the prayer book for every day and the Sabbath, not including services for the holidays.**
- 11.
This is an abbreviated form for יוב, משלי, תהיליםℵ **
- 12.
The Onkelos translation is the main translation of the Torah into Aramaic. This translation is attributed to Onkelos, a convert to Judaism around 35–120 ad.**
- 13.
Hebräisches und Aramäisches Handwörterbuch über das Alte Testament; English: Wilhelm Gesenius’s Hebrew Lexicon of the Old Testament, including the Biblical Chaldee, trans. Edward Robinson (1836; 5th edition, with corrections and additions, 1854).**
- 14.
Regarding the different styles of learning: see chap. 3, pp. 90–91, and chap. 5, p. 156.**
- 15.
The chaver title is conferred by a community rabbi on a community member for special service to the community.**
- 16.
The Tetzaveh portion is from Exodus 27:20 to Exodus 30:10.**
- 17.
This refers to an exception to the general rule that women are exempt from time-limited mitzvot (commandments). The exemption pertains to mitzvot relating to historical events in which women were involved. Note that women are obligated to follow regular non-time-limited mitzvot. The text says: “Women are exempt from time-limited precepts (mitzvot), but are obligated to [observe some others, pertaining to lighting Hanukkah candles, reading the Scroll of Esther on Purim, and drinking four cups of wine during the Passover Seder] because they too had been saved by those miracles.”**
- 18.
See the Prins family tree.**
- 19.
In commemoration of the last of the ten plagues, God’s killing of the Egyptian first-born, it is customary for Jewish first-born to fast on the day preceding Passover. As a child, Fraenkel fasted only half a day.**
- 20.
This is part of Homer’s description of Odysseus making love to the beautiful nymph Calypso just before parting from her (quotation set in italics): “So he spoke, and the sun set and darkness came on. And the two went into the innermost recess of the hollow cave, and took their joy of love, abiding each by the other’s side.” (Homer, The Odyssey, trans. A. T. Murray, 2 vols. (Cambridge, MA: Harvard University Press; London: William Heinemann, 1919), book 5, lines 225–227.**
- 21.
The Obersalzberg, the Eagle’s Nest, was Hitler’s mountain retreat.**
- 22.
A heller was a German coin of low value worth half a pfennig.**
- 23.
Heinrich Steinitzer, Sport und Kultur (Munich: Deutsche Alpenzeitung publishers, 1910).
- 24.
I briefly sketched his scientific significance in an article published in English in Scripta Mathematica 5, no. 1 (New York, January 1938): 17–22.
- 25.
Of course, all these formulas only have theoretical significance. In practice, data can be compared more rapidly by using tables.
- 26.
See the annual report of the Deutsche Mathematikervereinigung (German Mathematical Society), vol. 13 (1904): 40–53.
- 27.
This is a strictly lunar calendar without any connection to the solar year. Herein partly lay the difficulty of the problem, which despite numerous attempts had not been previously solved.
- 28.
A popular presentation of the results appeared as “Eine Formel zur Verwandlung jüdischer Daten in mohammedanische” (A Formula for Converting Jewish Dates into Muhammadan Dates) in the journal published by Markus Brann, Monatsschrift für Geschichte und Wissenschaft des Judentums 53 (1909): 736–743.
- 29.
The Land of Israel was under Ottoman rule at the time.**
- 30.
A. Fraenkel, “Die Berechnung des Osterfestes,” Journal für die reine und angewandte Mathematik (commonly referred to as Crelle’s Journal), no. 138 (1910): 133–146.
- 31.
Transcendental numbers and squaring the circle:
As the Pythagorean school already discovered in the sixth century bce and initially treated as an esoteric secret, there are “irrational” numbers, which cannot be expressed as the ratio of integers \( \frac{\mathrm{m}}{\mathrm{n}} \). The simplest such number is \( \sqrt{2} \), the length of the diagonal of a square with a side length of 1.
Since \( \sqrt{2} \) is a root of the equation x2–2 = 0, it seemed reasonable to assume that all irrational numbers could be expressed as roots of “algebraic equations” of the form:
$$ {\mathrm{a}}_0{\mathrm{x}}^{\mathrm{n}} + {\mathrm{a}}_1{\mathrm{x}}^{\mathrm{n}\hbox{-} 1} + \dots + {\mathrm{a}}_{\mathrm{n}\hbox{-} 2}{\mathrm{x}}^2 + {\mathrm{a}}_{\mathrm{n}\hbox{-} 1}\mathrm{x} + {\mathrm{a}}_{\mathrm{n}} = 0 $$with a0,… an integers. All such roots are called “algebraic numbers.”
In 1851, this assumption was shown to be false: thus, there are also non-algebraic numbers, which are called “transcendental.” The best-known transcendental number is π, and Lindemann proved its transcendence in 1882.
Only quantities that solve linear and quadratic equations (n = 1 or n = 2) can be constructed by using a straightedge and a compass. These are special and the simplest kind of algebraic numbers. Because a circle with a radius r has a circumference of 2πr and an area of πr2, it is impossible, for example, even with far more complex instruments than a straightedge and a compass, to square the circle, that is, to construct a square with the same area as a circle of a given radius.
- 32.
Fermat’s theorem was finally proven in 1995, after more than 350 years, by Andrew Wiles of Princeton and Oxford.**
- 33.
In series 3, vol. 4 of the Archiv der Mathematik und Physik, around 1902, Wolfskehl set a calendar exercise, namely, to determine the proof of one of the formulas he gave for calculating the date of the Gregorian Easter. For many years, the problem remained unsolved until I became aware of it as a young student in 1910, and solved it immediately. The proof I proposed was published in the same journal in 1911, in series 3, vol. 17. The solution was long in coming not because the problem was particularly difficult, but apparently because no mathematician who was also knowledgeable about calendars had shown an interest in it.
- 34.
See explanation of lecture fees on pages 67–68.**
- 35.
See, for example, the brochure with a preface by Thomas Mann, Kampf um München als Kulturzentrum (The Struggle for Munich as a Cultural Center), Munich: R. Pflaum, 1926. It includes six speeches (by Thomas Mann, Heinrich Mann, Leo Weismantel, Willi Geiger, Walter Courvoisier, and Paul Renner) given in an overcrowded lecture hall in Munich. From Thomas Mann’s speech: “Unfortunately it has well-nigh reached the point that anyone in Germany who displays any trace of saneness is thought to be a Jew and thus is done for.” This publication spurred a correspondence between Mann and myself.
- 36.
See footnote 10 in Chap. 1, page 4.**
- 37.
It became the Leibniz Institute for Astrophysics in 2011.**
- 38.
For more details, see the obituaries by Arnold Sommerfeld, Die Naturwissenschaften 4 (1916): 453–457, and Otto Blumenthal, Jahresbericht der Deutschen Mathematiker-Vereinigung 26 (1918): 56–75.
- 39.
See A. A. Fraenkel, “Jewish Mathematics and Astronomy,” Scripta Mathematica 25 (1960): 33–47.
- 40.
At the 80th Assembly of German Natural Scientists and Physicians.**
- 41.
Hermann Minkowski, “Space and Time,” in Hendrik A. Lorentz, Albert Einstein, Hermann Minkowski, and Hermann Weyl, The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity (New York: Dover, 1952), 75–91, here: 75.**
- 42.
Graetz had no connections to the Jewish community at that time. However, after the First World War he came closer to Judaism. For example, in the late 1920s, when the Nazis were already powerful in Munich, he presided over a meeting in which I told academics about Hebrew University.
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Fraenkel, A.A. (2016). Childhood and Adolescence in Munich (1891–1910). In: Cohen-Mansfield, J. (eds) Recollections of a Jewish Mathematician in Germany. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-30847-0_2
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