Abstract
In the spring of 1906 Stanisław Jolles, professor of descriptive geometry at the Charlottenburg Polytechnic in Berlin, came to Lwów with his wife on family business having to do with certain factories near Lwów owned by Mrs. Jolles. This lady happened to know my cousin’s mother, so she and her husband paid us a visit at 10 Gołąb Street. The professor was soon informed that the subtenant—that is, I—wanted to be a mathematician, whereupon he immediately exclaimed: “Junger Mann, packen Sie Ihren Koffer und fahren Sie nach G¨ottingen!” My Father’s reaction to Jolles’ “categorical imperative”, when I came back to Jasło at the end of the 1905–1906 academic year, was lukewarm, but Mother favored the idea keenly—all the more so because she knew how eager I was. Thus it was that I transferred to G¨ottingen in the autumn of 1906. I travelled via Wrocław, Berlin, and Halle, and, finally, Eichenberg. The Eichenberg–G¨ottingen train was a local one and almost empty; its only passengers were a few locals and some students wearing bright little caps. From the Bovenden station onwards I had a good view of the landscape of the place where I was to spend the next several years: low hills covered with deciduous forest, and in the foreground the steeple of the Johannis Church and some reddish roofs. The only colors were rust, brown, tan, and yellow: such were the land, the autumn leaves, and the roof tiles.
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Notes
- 1.
“Young man, pack your trunk and go to G¨ottingen!”
- 2.
Breslau in German.
- 3.
The terms “cold-blooded” and “hot-blooded” as applied to horses, relate to temperament. “Cold bloods”, such as draft horses and some ponies, are more suitable for slow, heavy work, while “hot bloods” have been bred for speed and endurance. Of course, all horses are warm-blooded in the biological sense.
- 4.
David Hilbert (1862–1943), German mathematician. One of the most influential and universal mathematicians of the nineteenth and early twentieth centuries. In 1900 he proposed a list of 23 problems which strongly influenced the course of much of the mathematical research of the twentieth century. Arrived in G¨ottingen in 1895 to lead the mathematics department.
- 5.
Constantin Carath´eodory (1873–1950), Greek mathematician. First studied engineering in Belgium. Completed his graduate studies in G¨ottingen over the period 1902–1904 under the supervision of Minkowski.
- 6.
Hermann Minkowski (1864–1909), German mathematician of Lithuanian-Jewish descent. Invented the number-theoretic technique known as the “geometry of numbers”, and formulated the special theory of relativity in geometrical terms, among other things. Joined Hilbert in G¨ottingen in 1902.
- 7.
Gustav Herglotz (1881–1953), German mathematician. Studied in Vienna and Munich. Completed his graduate studies in G¨ottingen under Felix Klein.
- 8.
Antoni Łomnicki (1881–1941), Polish mathematician, educated at Lwów University and the University of G¨ottingen. Appointed professor at the Lwów Polytechnic in 1920, where Banach worked as his Assistent. Murdered by the Gestapo in Lwów in 1941.
- 9.
Władysław Dziewulski (1878–1962), Polish astronomer and mathematician. Professor at the Stefan Batory University in Wilno, and then the Nicolaus Copernicus University in Toruń.
- 10.
Wacław Dziewulski (1882–1938), Polish physicist, editor, and sometime professor at the Stefan Batory University in Wilno.
- 11.
Leon Chwistek (1884–1944), Polish avant-garde painter, theoretician of modern art, literary critic, logician, philosopher, and mathematician. Professor of Logic at the University of Lwów from 1929 to 1940, when, being sympathetic to Marxism-Leninism, he took political refuge in the Soviet Union, where he continued his scientific research and political activism. Believed that reality could be described only from multiple points of view: the physical, the popular, the phenomenal, and the visionary/intuitive. He became Steinhaus’ brother-in-law. Born in Kraków, he died in Barvikha, near Moscow, in 1944.
- 12.
Tadeusz Banachiewicz (1882–1954), Polish astronomer, mathematician, and geodesist. Moved to G¨ottingen in 1905 following the closure of the Polish Warsaw University by the Russian government. At the Jagiellonian University of Kraków between the wars, he became a member of the Polish Academy of Sciences in 1922. A lunar crater and a planetoid are named after him.
- 13.
Włodzimierz Stożek (1883–1941), Polish mathematician of the Lwów school. Murdered by Germans in Lwów in July 1941 during the “Massacre of Lwów Professors.”
- 14.
Antoni Przeborski (1871–1941), Polish mathematician. After beginning his academic career in Kharkov, Ukraine, he and his family managed, during the turmoil of the Russian civil war, to escape to Warsaw, where he held the position of Professor of Theoretical Mechanics till 1939.
- 15.
Kazimierz Horowicz (1884–1920), Polish statistician. After studying at the Russian University in Warsaw, obtained a doctorate in G¨ottingen. Took up actuarial mathematics on returning to Warsaw.
- 16.
Jan Króo (1885–?), Polish theoretical physicist and mathematician. Defended his doctoral thesis in G¨ottingen.
- 17.
Eustachy Żyliński (1889–1954), Polish mathematical logician. Member of the interwar Lwów school of mathematics. Joint supervisor with Steinhaus of Orlicz’s Ph.D. thesis. During World War II worked in the underground Lwów University (1941–1944). Appointed Consul General to Ukraine in 1946. Head of the mathematics department at the Silesian Institute of Technology 1946–1951.
- 18.
The period 1905–1907 was one of upheaval in Congress Poland, stimulated in part by the 1905 revolution in Russia itself.
- 19.
That part of Poland ruled by Russia since 1815, also called Congress Poland.
- 20.
Studentenverbindungen, similar to fraternities, but of older provenance, and including alumni (Altherren and Hohe Damen) once active in the corporation, who partly finance the corporation and help the active students in other ways. Some corporations’ members wear distinguishing colored caps and ribbons, mainly on ceremonial occasions. Most student corporations date back to the mid-nineteenth century or earlier.
- 21.
That is, Altherren—members who had finished their studies.
- 22.
“Innkeeper’s daughter”, or, in a specialized sense, daughter of the house where a student had board and lodgings.
- 23.
Historic city in west-central Poland. From 1815 capital of the semi-autonomous Grand Duchy of Posen under Prussian hegemony, but, following the uprisings of 1848, reduced in status to the capital city of the Prussian province of Posen.
- 24.
The region with Poznań as its chief city, the core of the early Polish state.
- 25.
Sigismund II Augustus (1520–1572), Grand Duke of Lithuania from 1529, King of Poland from 1530, and King of the Polish-Lithuanian Commonwealth when Lithuania and Poland were united into one state in 1569.
- 26.
The University of G¨ottingen was founded in 1734 by the Elector of Hanover, who was at the same time King George II of Great Britain.
- 27.
The House of Hanover was a younger branch of the older House of Welf.
- 28.
Louis Spohr (1784–1859), German composer, violinist, and conductor.
- 29.
Joseph Joachim (1831–1907), Hungarian violinist, conductor, and composer.
- 30.
Carl Friedrich Gauss (1777–1855), considered one of the three or four greatest mathematicians of all time.
- 31.
Wilhelm Eduard Weber (1804–1859), famous German physicist.
- 32.
Gottfried August B¨urger (1747–1794), German poet. Studied law at the University of G¨ottingen from 1768. His poem Lenore, by virtue of its dramatic force and vivid realization of the supernatural, made his name a household word in G¨ottingen.
- 33.
Johann Peter Gustav Lejeune Dirichlet (1805–1859), a preeminent German mathematician.
- 34.
C. F. Gauss, Werke, Volumes 1–6, Dieterich, G¨ottingen 1863–1874; Volumes 7–12, Teubner, Leipzig 1900–1917, Springer, Berlin 1922–1933.
- 35.
He was actually married to Felix Mendelssohn’s youngest sister.
- 36.
Georg Friedrich Bernhard Riemann (1826–1866), German mathematician of genius. Made fundamental contributions to several areas of mathematics and physics.
- 37.
Jean-Baptiste Joseph de Fourier (1768–1830), outstanding French mathematician. Highly placed administrator under Napoleon. Proposed a mathematical theory of heat conduction, in connection with which he introduced the trigonometric series bearing his name.
- 38.
Felix Klein (1849–1925), German mathematician. Worked on function theory and the associated discrete groups, non-Euclidean geometry, and the connections between geometries and their groups of transformations.
- 39.
Marius Sophus Lie (1842–1899), Norwegian mathematician. Inventor of the theory of “continuous symmetry”, that is, of “Lie groups”, as they are now called, together with their “Lie algebras”.
- 40.
Jakob Steiner (1796–1863), Swiss mathematician. Professor of geometry in Berlin from 1834.
- 41.
Friedrich Althoff (1839–1908), then departmental director in the Royal Prussian Ministry for Ecclesiastical, Educational, and Medical Affairs.
- 42.
Carl David Tolm´e Runge (1856–1927), German mathematician, physicist, and spectroscopist. Co-developer of the “Runge–Kutta method” of modern numerical analysis. Took up the chair in applied mathematics in G¨ottingen in 1904.
- 43.
Johann Benedict Listing (1808–1882), German mathematician. First to introduce the term “topology” in an article of 1847. (Deceased long before the author’s arrival in G¨ottingen!)
- 44.
Ludwig Prandtl (1875–1953), German scientist. First to describe the boundary layer and its importance for drag and streamlining.
- 45.
Hermann Theodor Simon (1870–1918), who founded a division of applied electricity at G¨ottingen in 1907.
- 46.
Emil Johann Wiechert (1861–1928), German geophysicist. Appointed director of the Geophysical Laboratory at G¨ottingen in 1898.
- 47.
Arnold Johannes Wilhelm Sommerfeld (1868–1951), outstanding German theoretical physicist. Pioneered developments in atomic and quantum physics.
- 48.
Persons who have achieved the Habilitation, a degree somewhat higher than the Ph.D. qualifying them to give lectures, and opening the way to a regular university position.
- 49.
Paul Koebe (1882–1945), German mathematician. Completed his graduate studies at the University of Berlin in 1905. First to prove, with Poincar´e, the “Uniformization Theorem” of complex analysis.
- 50.
A German physicist. Lived from 1850 to 1919. The term “tensor” with its modern meaning was introduced by him in 1899.
- 51.
German physicist. Studied under Planck, and worked as his assistant. Lived from 1875 till 1922.
- 52.
Obtained his Ph.D. in G¨ottingen in 1904 under the supervision of Max Abraham. Gradually shifted the focus of his interests from theoretical physics to the philosophy of science. Lived from 1881 till 1940.
- 53.
Karl Schwarzschild (1873–1916), German physicist. Found in 1915 the exact solution—the “Schwarzschild solution”—of the Einstein equations of general relativity in the case of an isolated non-rotating spherical body, latterly become important in connection with the physics of black holes. He died the following year from a painful autoimmune disease contracted while at the Russian front in World War I.
- 54.
Martin Brendel (1862–1939), German astronomer.
- 55.
This work gives a complete list of axioms for Euclidean geometry.
- 56.
Kazan′ was the city in Russia where Nikola˘ı Lobachevski˘ı (1792–1856), one of the inventors of non-Euclidean geometry, had been a professor.
- 57.
Hilbert’s family was actually Reformed Protestant, a common religious denomination in Prussia at the time.
- 58.
Ernst Friedrich Ferdinand Zermelo (1871–1953), German mathematician. Worked on the foundations of mathematics. In particular, proved that the Axiom of Choice implies that every set can be well-ordered. The Zermelo–Fr¨ankel axioms of set theory have become standard. (Steinhaus later formulated a weaker version of the Axiom of Choice, his so-called “Determination Axiom”.)
- 59.
Georg Ferdinand Ludwig Philipp Cantor (1845–1918), the inventor of general set theory, since become, in the form of the Zermelo–Fr¨ankel axioms in conjunction with predicate logic, the standard foundation of mathematics. Defined both the transfinite cardinal and ordinal numbers, together with their arithmetics.
- 60.
The mathematical reading room.
- 61.
The mark was worth $0.25 in 1905 US currency, so three marks would be worth about $18 today.
- 62.
By 1906, seven volumes of Gauss’ collected works had been published; the final volume appeared only in 1933.
- 63.
Pierre de Fermat (1601–1665), French lawyer and amateur mathematician of genius. Credited with founding modern number theory. Made notable contributions to analytic geometry and the differential calculus. Best known for “Fermat’s Last Theorem”.
- 64.
Augustin-Louis Cauchy (1789–1857), outstanding French mathematician and physicist. Worked in many areas of mathematics. Laid the foundations of modern analysis in terms of limits and continuity.
- 65.
Charles Hermite (1822–1901), influential French analyst, algebraist, and number theorist.
- 66.
Edmund Georg Hermann Landau (1877–1938), German-Jewish number theorist and complex analyst.
- 67.
Julius (Gyula) K˝onig (1849–1913), Jewish-Hungarian mathematician. After completing his mathematical studies in Berlin, he was appointed docent at Budapest University in 1871, and, in 1873, professor at the Technical University of Budapest, where he remained for the rest of his life. His paper on quadratic reciprocity appeared in Acta Mathematica in 1898. His son D´enes also became a distinguished mathematician.
- 68.
Wacław Franciszek Sierpiński (1882–1969), Polish mathematician. Made outstanding contributions to set theory, number theory, and topology. Three well-known fractals are named after him: the Sierpiński triangle, carpet, and curve.
- 69.
That is, as Cantor had discovered earlier, there is a bijection between the real line and the plane. The space-filling curves of Peano, Hilbert, and Sierpiński determine analogous continuous surjections, which cannot, however, also be injective.
- 70.
F´elix ´ Edouard Justin ´ Emile Borel (1871–1956), French mathematician. One of the pioneers of measure theory and its application to probability theory.
- 71.
Over the last decades of the twentieth century an alternative movement developed, called “visual culture”, whose proponents attempt to discard preconceived ideas of what is or is not “art”, and examine every visual object by its own lights, or how it impinges on the viewer directly, unfiltered by mere stuffy tradition—as opposed to a healthy critical tradition.
- 72.
Georges Raymond Constantine Rodenbach (1855–1898), Belgian symbolist poet and novelist.
- 73.
Building used by B´eguines, members of lay sisterhoods of the Roman Catholic Church, consisting of religious women who sought to serve God without retiring from the world.
- 74.
Frederick William Victor Albert of Prussia (1859–1941), the last German Emperor (Kaiser) and King of Prussia, ruling from 1888 to 1918. Dismissed Bismarck in 1890 and launched Germany on a bellicose new course in foreign affairs culminating in his support for Austria-Hungary in the crisis of July 1914 that led to World War I.
- 75.
This doubtless applied only to the Walloons, the inhabitants of the southern French-speaking region of Belgium, and not to the Dutch-speaking Flemish.
- 76.
A language very close to Dutch.
- 77.
Viennese writer and poet, a key figure in the rise of early modernism in Vienna.
- 78.
Maximilian Harden (born Felix Ernst Witkowski) (1861–1927), influential German journalist and editor.
- 79.
Hitler’s Austrian Anschluss in 1938.
- 80.
This may be ¨Uber den physiologischen Schwachsinn des Weibes (“On the Physiological Feeblemindedness of Women”), published in 1900 by the German neurologist P. J. M¨obius (1853–1907), who believed that excessive thinking makes women ill.
- 81.
Performed and published in 1921.
- 82.
One of the main points of Kraus’ writings was to show the great evils inherent in seemingly small errors, including linguistic errors or carelessness.
- 83.
The traditional western Christian name for the site of Jesus’ crucifixion. Also called Calvary.
- 84.
A hundred years later, it all seems more like a storm in a teacup.
- 85.
In German Bl¨umchenkaffee, referring to brewed coffee so thin one could see through it the flower placed at the bottom of the cup.
- 86.
Hermann Muthesius (1861–1927), German architect, publicist, and diplomat. Promoted ideas of the English arts and crafts movement in Germany, and influenced the later movement of German modernism in architecture.
- 87.
´Emile Gall´e (1846–1904), French artist in glasswork, revolutionized the art of glass sculpture by combining his own ideas with such ancient techniques as enamelling, cameo, and inlaying.
- 88.
An art magazine of the time that helped popularize in Germany the new “art nouveau” style of art, architecture and applied art that peaked in popularity around the turn of the twentieth century. Die Jugend means “The youth”.
- 89.
The capital of the electorate of Hesse-Cassel from 1567 until it was annexed by Prussia in 1866, when it was merged into a new Prussian province called Hesse-Nassau. In the early nineteenth century, the brothers Grimm lived in Kassel and collected and wrote most of their fairy tales there.
- 90.
The highest mountain in the Harz range.
- 91.
The Bald Mountain, second highest peak of the Świętokrzyskie (Holy Cross) Mountains in south-central Poland.
- 92.
“The early comer gets a good spot.”
- 93.
Sierpiński came to G¨ottingen in 1907 for a few months’ study.
- 94.
The Hanseatic League was an economic alliance of trading cities and their guilds maintaining a trade monopoly along the coast of northern Europe, lasting from the thirteenth to seventeenth centuries.
- 95.
Residents of Hamburg.
- 96.
Respectively assistant judge, district administrator, principal of a Gymnasium.
- 97.
A Junker was a member of the landed nobility of Prussia.
- 98.
The year Germany was unified into a politically and administratively integrated nation state, with Wilhelm of Prussia as Emperor Wilhelm I of the German Empire.
- 99.
Jacques Bainville (1879–1936), French historian and journalist. Well known as a Germanophobe. A staunch monarchist, active against Dreyfus.
- 100.
The House of Hohenzollern is that of the dynasty of electors, kings, and emperors of Prussia, Germany, and Romania, originating in Swabia in the eleventh century.
- 101.
Former small states in Germany.
- 102.
“Flying Leaves”, a humorous, illustrated German weekly, published in Munich between 1845 and 1944.
- 103.
A French op´era-bouffe by Jacques Offenbach, ridiculing court favoritism and military paraphernalia.
- 104.
Immer feste druff means “Always strongly at them”, or, essentially, “Always give it to them!”. Also the title of a satirical poem by Karl Kraus.
- 105.
Alsace-Lorraine had been annexed by Germany at the time of the Franco-Prussian war in 1871, and was a source of continuing resentment for the French.
- 106.
In January, 1904 the Herero people of German South-West Africa—present-day Namibia—rebelled against German colonial rule. The rebellion was put down, and the Herero were driven into the desert where many died of thirst.
- 107.
To administer as a Mandated Territory on behalf of the League of Nations.
- 108.
Marie Ennemonde Camille Jordan (1838–1922), remembered for the Jordan curve theorem and the Jordan normal form of a group, among other things. Charles ´ Emile Picard (1856–1941), known in particular for the “Picard group” of a linear differential equation. ´Edouard Jean-Baptiste Goursat (1858–1936), famous for his Cours d’analyse math´ematique. Joseph Alfred Serret (1819–1885), remembered in particular for the Frenet–Serret formulae of the differential geometry of a space curve.
- 109.
Edward John Routh (1831–1907), English mathematician. Contributed to the systematization of the mathematical theory of mechanics. Horace Lamb (1849–1934), English mathematician. Headed the Mathematics Department of the University of Adelaide from 1875 to 1885, when he took up a chair in Victoria University (now the University of Manchester). Two of his influential textbooks are Infinitesimal Calculus and Higher Mechanics.
- 110.
Maurycy Pius Rudzki (1862–1916), Polish geophysicist. Established a chair of geophysics at Jagiellonian University in Kraków in 1895. Author of “Geophysics”.
- 111.
Otto Toeplitz (1881–1940), German-Jewish mathematician working mainly in functional analysis. Appointed extraordinary professor at the University of Kiel in 1913, moving to Bonn in 1928. Emigrated to Palestine in 1939.
- 112.
Max Born (1882–1970), outstanding German physicist and mathematician. Nobel laureate for physics in 1954.
- 113.
Richard Courant (1888–1972), German-American mathematician. Studied at the universities of Breslau (Wrocław), Z¨urich, and G¨ottingen, where he eventually became Hilbert’s assistant. Emigrated from Germany to the US via Cambridge in 1933. Obtained a professorship at New York University in 1936, where he founded a highly successful institute of applied mathematics (since 1964 named the Courant Institute of Mathematical Sciences). Coauthored with Hilbert Methods of Mathematical Physics and with Herbert Robbins the popularization What is mathematics?
- 114.
Paul Ehrenfest (1880–1933), Austrian-Dutch physicist and mathematician. Contributed to statistical mechanics and quantum mechanics. Studied under Ludwig Boltzmann. A severe depressive, he committed suicide in 1933. His wife Tatyana Alekseevna Afanaseva (1876–1964) was also a mathematician and collaborated with her husband in his work.
- 115.
Danish mathematician and star soccer player. Invented the field of almost periodic functions. Brother of Niels Bohr. Lived from 1887 to 1951.
- 116.
Albert Abraham Michelson (1852–1931), American physicist known for his work on the speed of light, and especially for the Michelson–Morley experiment. First American to receive the Nobel Prize in any science (in 1907).
- 117.
Paul Friedrich Wolfskehl (1856–1906), German industrialist with an interest in mathematics.
- 118.
In 1770, Edward Waring asked if for each positive integer k there exists an associated positive integer s such that every sufficiently large natural number is the sum of at most s kth powers of natural numbers.
- 119.
This is the function defined by
$$\displaystyle{\zeta (s) = \frac{1} {1^{s}} + \frac{1} {2^{s}} + \frac{1} {3^{s}} + \cdots }$$for real s > 1, continued analytically to the complex plane. First considered by Euler in 1740, later by Chebyshev for all real s > 1, and, finally, by Riemann, who showed that the above function ζ(s) is defined for all complex s with real part greater than 1, and can be analytically continued to a function defined for all s ≠ 1. In 1859 Riemann published a paper establishing a close relationship between the zeros of the “Riemann zeta function” and the distribution of primes.
- 120.
Alexander Moszkowski (1851–1934), Berlin humorist and journalist.
- 121.
German liberal newspaper published from 1872 to 1939.
- 122.
Paul Ehrlich (1854–1915), medical scientist. With Sahachiro Hata he developed Salvarsan, the first effective treatment for syphilis, in 1910. Nobel laureate for medicine in 1908.
- 123.
Alfred Pringsheim (1850–1941), German mathematician and patron of the arts. Worked mainly in complex analysis. Great admirer and patron of Wagner.
- 124.
At that time belonging to the part of Poland ruled by Prussia.
- 125.
Student corporations of a special type, inspired by both liberal and nationalistic ideas.
- 126.
Lads, members of the Burschenschaften.
- 127.
A lake in Bavaria, near the border with Austria.
- 128.
A resort town in Bavaria.
- 129.
Third highest mountain in Germany. Not far from Berchtesgaden.
- 130.
Vilnius in Lithuanian.
- 131.
Restaurant serving a midday meal.
- 132.
“Psychoanalysis is that mental illness for which it fancies itself the cure.”
- 133.
Henrik Antoon Lorentz (1853–1928), Dutch physicist. Proposed that moving bodies contract in the direction of their motion, in order to explain the result of the Michelson–Morley experiment, whence “Lorentz transformations”. The same explanation had been advanced earlier by the Irish physicist George Fitzgerald, so the supposed contraction is also called the “Fitzgerald–Lorentz contraction.” Joint Nobel laureate for physics, with Peter Zeeman, in 1902.
- 134.
Ernst Haeckel (1834–1919), eminent German biologist, naturalist, and philosopher.
- 135.
Stanisław Wyspiański (1869–1907), famous Polish playwright, painter, and poet.
- 136.
The Song of Warsaw, written in 1831 on the occasion of the November Uprising against Russian rule in 1830–1831.
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Steinhaus, H. (2015). Göttingen. In: Burns, R., Szymaniec, I., Weron, A. (eds) Mathematician for All Seasons. Vita Mathematica, vol 18. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-21984-4_4
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