Men of Mathematics (81 page)

Weierstrass was always accessible to his students and sincerely interested in their problems, whether mathematical or human. There was nothing of the “great man” complex about him, and he would as gladly walk home with any of the students—and there were many—who cared to join him as with the most famous of his colleagues, perhaps more gladly when the colleague happened to be Kronecker. He was happiest when, sitting at a table over a glass of wine with a few of his devoted disciples, he became a jolly student again himself and insisted on paying the bill for the crowd.

An anecdote (about Mittag-Leffler) may suggest that the Europe of the present century has partly lost something it had in the 1870's. The Franco-Prussian war (1870-71) had left France pretty sore at Germany. But it had not befogged the minds of mathematicians regarding one another's merits irrespective of their nationalities. The like holds for the Napoleonic wars and the mutual esteem of the French and British mathematicians. In 1873 Mittag-Leffler arrived in Paris from Stockholm all set and full of enthusiasm to study analysis under Hermite. “You have made a mistake, sir,” Hermite told him: “you should follow Weierstrass' course at Berlin. He is the master of all of us.”

Mittag-Leffler took the sound advice of the magnanimous Frenchman and not so long afterward made a capital discovery of his own which is to be found today in all books on the theory of functions. “Hermite was a Frenchman and a patriot,” Mittag-Leffler remarks;
“I learned at the same time in what degree he was also a mathematician.”

*  *  *

The years (1864-97) of Weierstrass' career at Berlin as Professor of Mathematics were full of scientific and human interests for the man who was acknowledged as the leading analyst in the world. One phase of these interests demands more than the passing reference that might suffice in a purely scientific biography of Weierstrass: his friendship with his favorite pupil, Sonja (or Sophie) Kowalewski.

Madame Kowalewski's maiden name was Sonja Corvin-Kroukow-sky; she was born at Moscow, Russia, on January 15, 1850, and died at Stockholm, Sweden, on February 10, 1891, six years before the death of Weierstrass.

At fifteen Sonja began the study of mathematics. By eighteen she had made such rapid progress that she was ready for advanced work and was enamored of the subject. As she came of an aristocratic and prosperous family, she was enabled to gratify her ambition for foreign study and matriculated at the University of Heidelberg.

This highly gifted girl became not only the leading woman mathematician of modern times, but also made a reputation as a leader in the movement for the emancipation of women, particularly as regarded their age-old disabilities in the field of higher education.

In addition to all this she was a brilliant writer. As a young girl she hesitated long between mathematics and literature as a career. After the composition of her most important mathematical work (the prize memoir noted later), she turned to literature as a relaxation and wrote the reminiscences of her childhood in Russia in the form of a novel (published first in Swedish and Danish). Of this work it is reported that “the literary critics of Russia and Scandinavia were unanimous in declaring that Sonja Kowalewski had equalled the best writers of Russian literature in style and thought.” Unfortunately this promising start was blocked by her premature death, and only fragments of other literary works survive. Her one novel was translated into many languages.

Although Weierstrass never married he was no panicky bachelor who took to his heels every time he saw a pretty woman coming. Sonja, according to competent judges who knew her, was extremely good-looking. We must first tell how she and Weierstrass met.

Weierstrass used to enjoy his summer vacations in a thoroughly
human manner. The Franco-Prussian war caused him to forego his usual summer trip in 1870, and he stayed in Berlin, lecturing on elliptic functions. Owing to the war his class had dwindled to only twenty instead of the fifty who heard the lectures two years before. Since the autumn of 1869 Sonja Kowalewski, then a dazzling young woman of nineteen, had been studying elliptic functions under Leo Königsberger (born 1837) at the University of Heidelberg, where she had also followed the lectures on physics by Kirchhoff and Helmholtz and had met Bunsen the famous chemist under rather amusing circumstances—to be related presently. Königsberger, one of Weierstrass' first pupils, was a first-rate publicity agent for his master. Sonja caught her teacher's enthusiasm and resolved to go directly to the master himself for inspiration and enlightenment.

The status of unmarried women students in the 1870's was somewhat anomalous. To forestall gossip, Sonja at the age of eighteen contracted what was to have been a nominal marriage, left her husband in Russia, and set out for Germany. Her one indiscretion in her dealings with Weierstrass was her neglect to inform him at the beginning that she was married.

Having decided to learn from the master himself, Sonja took her courage in her hands and called on Weierstrass in Berlin. She was twenty, very earnest, very eager, and very determined; he was fifty five, vividly grateful for the lift Gudermann had given him toward becoming a mathematician by taking him on as a pupil, and sympathetically understanding of the ambitions of young people. To hide her trepidation Sonja wore a large and floppy hat, “so that Weierstrass saw nothing of those marvelous eyes whose eloquence, when she wished it, none could resist.”

Some two or three years later, on a visit to Heidelberg, Weierstrass learned from Bunsen—a crabbed bachelor—that Sonja was “a dangerous woman.” Weierstrass enjoyed his friend's terror hugely, as Bunsen at the time was unaware that Sonja had been receiving frequent private lessons from Weierstrass for over two years.

Poor Bunsen based his estimate of Sonja on bitter personal experience. He had proclaimed for years that no woman, and especially no Russian woman, would ever be permitted to profane the masculine sanctity of his laboratory. One of Sonja's Russian girl friends, desiring ardently to study chemistry in Bunsen's laboratory, and having been thrown out herself, prevailed upon Sonja to try her powers of
persuasion on the crusty chemist. Leaving her hat at home, Sonja interviewed Bunsen. He was only too charmed to accept Sonja's friend as a student in his laboratory. After she left he woke up to what she had done to him. “And now
that woman
has made me eat my own words,” he lamented to Weierstrass.

Sonja's evident earnestness on her first visit impressed Weierstrass favorably and he wrote to Königsberger inquiring about her mathematical aptitudes. He asked also whether “the lady's personality offers the necessary guarantees.” On receiving an enthusiastic reply, Weierstrass tried to get the university senate to admit Sonja to his mathematical lectures. Being brusquely refused he took care of her himself on his own time. Every Sunday afternoon was devoted to teaching Sonja at his house, and once a week Weierstrass returned her visit. After the first few lessons Sonja lost her hat. The lessons began in the autumn of
1870
and continued with slight interruptions due to vacations or illnesses till the autumn of
1874.
When for any reason the friends were unable to meet they corresponded. After Sonja's death in
1891
Weierstrass burnt all her letters to him, together with much of his other correspondence and probably more than one mathematical paper.

The correspondence between Weierstrass and his charming young friend is warmly human, even when most of a letter is given over to mathematics. Much of the correspondence was undoubtedly of considerable scientific importance, but unfortunately Sonja was a very untidy woman when it came to papers, and most of what she left behind was fragmentary or in hopeless confusion.

Weierstrass himself was no paragon in this respect. Without keeping records he loaned his unpublished manuscripts right and left to students who did not always return what they borrowed. Some even brazenly rehashed parts of their teacher's work, spoiled it, and published the results as their own. Although Weierstrass complains about this outrageous practice in letters to Sonja his chagrin is not over the petty pilfering of his ideas but of their bungling in incompetent hands and the consequent damage to mathematics. Sonja of course never descended to anything of this sort, but in another respect she was not entirely blameless. Weierstrass sent her one of his unpublished works by which he set great store, and that was the last he ever saw of it. Apparently she lost it, for she discreetly avoids the topic—to judge from his letters—whenever he brings it up.

To compensate for this lapse Sonja tried her best to get Weierstrass to exercise a little reasonable caution in regard to the rest of his unpublished work. It was his custom to carry about with him on his frequent travels a large white wooden box in which he kept all his working notes and the various versions of papers which he had not yet perfected. His habit was to rework a theory many times until he found the best, the “natural” way in which it should be developed. Consequently he published slowly and put out a work under his own name only when he had exhausted the topic from some coherent point of view. Several of his rough-hewn projects are said to have been confided to the mysterious box. In 1880, while Weierstrass was on a vacation trip, the box was lost in the baggage. It has never been heard of since.

After taking her degree
in absentia
from Göttingen in 1874, Sonja returned to Russia for a rest as she was worn out by excitement and overwork. Her fame had preceded her and she “rested” by plunging into the hectic futilities of a crowded social season in St. Petersburg while Weierstrass, back in Berlin, pulled wires all over Europe trying to get his favorite pupil a position worthy of her talents. His fruitless efforts disgusted him with the narrowness of the orthodox academic mind.

In October 1875, Weierstrass received from Sonja the news that her father had died. She apparently never replied to his tender condolences, and for nearly three years she dropped completely out of his life. In August, 1878, he writes to ask whether she ever received a letter he had written her so long before that he has forgotten its date. “Didn't you get my letter? Or what can be preventing you from confiding freely in me, your best friend as you so often called me, as you used to do? This is a riddle whose solution only you can give me. . . .”

In the same letter Weierstrass rather pathetically begs her to contradict the rumor that she has abandoned mathematics: Tchebycheff, a Russian mathematician, had called on Weierstrass when he was out, but had told Borchardt that Sonja had “gone social,” as indeed she had. “Send your letter to Berlin at the old address,” he concludes; “it will certainly be forwarded to me.”

Man's ingratitude to man is a familiar enough theme; Sonja now demonstrated what a woman can do in that line when she puts her
mind to it. She did not answer her old friend's letter for two years although she knew he had been unhappy and in poor health.

The answer when it did come was rather a letdown. Sonja's sex had got the better of her ambitions and she had been living happily with her husband. Her misfortune at the time was to be the focus for the flattery and unintelligent, sideshow wonder of a superficially brilliant mob of artists, journalists, and dilettant litterateurs who gabbled incessantly about her unsurpassable genius. The shallow praise warmed and excited her. Had she frequented the society of her intellectual peers she might still have lived a normal life and have kept her enthusiasm. And she would not have been tempted to treat the man who had formed her mind as shabbily as she did.

In October,
1878,
Sonja's daughter “Foufie” was born.

The forced quiet after Foufie's arrival roused the mother's dormant mathematical interests once more, and she wrote to Weierstrass for technical advice. He replied that he must look up the relevant literature before venturing an opinion. Although she had neglected him, he was still ready with his ungrudging encouragement. His only regret (in a letter of October,
1880)
is that her long silence has deprived him of the opportunity of helping her. “But I don't like to dwell so much on the past—so let us keep the future before our eyes.”

Material tribulations aroused Sonja to the truth. She was a born mathematician and could no more keep away from mathematics than a duck can from water. So in October,
1880
(she was then thirty), she wrote begging Weierstrass to advise her again. Not waiting for his reply she packed up and left Moscow for Berlin. His reply, had she received it, might have caused her to stay where she was. Nevertheless when the distracted Sonja arrived unexpectedly he devoted a whole day to going over her difficulties with her. He must have given her some pretty straight talk, for when she returned to Moscow three months later she went after her mathematics with such fury that her gay friends and silly parasites no longer recognized her. At Weierstrass' suggestion she attacked the problem of the propagation of light in a crystalline medium.

In
1882
the correspondence takes two new turns, one of which is of mathematical interest. The other is Weierstrass' outspoken opinion that Sonja and her husband are unsuited to one another, especially as the latter has no true appreciation of her intellectual merits. The mathematical point refers to Poincaré, then at the beginning of his
career. With his sure instinct for recognizing young talent, Weierstrass hails Poincaré as a coming man and hopes that he will outgrow his propensity to publish too rapidly and let his researches ripen without scattering them over too wide a field. “To publish an article of real merit every week—that is impossible,” he remarks, referring to Poincaré's deluge of papers.

Sonja's domestic difficulties presently resolved themselves through the sudden death of her husband in March
1883.
She was in Paris at the time, he in Moscow. The shock prostrated her. For four days she shut herself up alone, refused food, lost consciousness the fifth day, and on the sixth recovered, asked for paper and pencil, and covered the paper with mathematical formulas. By autumn she was herself again, attending a scientific congress at Odessa.