Men of Mathematics (57 page)

The net result of the Work was the particularly revolting massacre of May,
1860.
Cauchy did not live to see his labors crowned.

*  *  *

Reputations of great mathematicians are subject to the same vicissitudes as those of other great men. For long after his death—and even today—Cauchy was severely criticized for overproduction and hasty composition. His total output is
789
papers (many of them very extensive works) filling twenty four large quarto volumes. Criticism of this sort always seems rather beside the point if a man has put out a mass of first rate work in addition to some that is not of high quality, and is usually indulged in by men who themselves have done comparatively little, and that little not of the highest order of originality. Cauchy's part in modern mathematics is somewhere not far from the center of the stage. This is now almost universally admitted, if grudgingly in some quarters. Since his death, especially in recent decades, Cauchy's reputation as a mathematician has risen steadily. The methods he introduced, his whole program inaugurating the first period of modern rigor, and his almost unequalled inventiveness have made a mark on mathematics that is, so far as we can now see, destined to be visible for many years to come.

One apparently unimportant detail out of all the mass of new things Cauchy did may be mentioned as an illustration of his prophetic originality. Instead of using the “imaginary”
Cauchy proposed to accomplish all that complex numbers do in mathematics by operating with congruences to the modulus
i
²
+ 1. This was done in 1847. The paper—a short one—attracted but little attention. Yet it is the germ of something—Kronecker's program—that is on its way to revolutionizing some of the fundamental concepts of mathematics. This matter will reappear frequently in later chapters, so we may pass it here with this allusion.

In social contacts Cauchy was extremely polite, not to say oily on occasion as when, for example, he was soliciting subscriptions for one of his jousts. His habits were temperate and in all things except mathematics and religion he was moderate. On the last he lacked ordinary common sense. Everyone who came near him was a prospect for conversion. When William Thomson (Lord Kelvin) as a young man of twenty one called on Cauchy to discuss mathematics, Cauchy spent the time trying to convert his visitor—then a staunch adherent of the Scottish Free Church—to Catholicism.

Cauchy had his share of rows over priority in which his enemies accused him of greed and unfair play. His last year was marred by one such dispute wherein it would seem that Cauchy had no case. But with his usual stubbornness where a matter of principle was involved he braved the outcry and stuck to his point with invincible sweetness and pertinacity.

Another peculiarity added to Cauchy's unpopularity with his scientific colleagues. In scientific academies and societies a man is supposed to base his vote for a candidate only on the candidate's scientific merits; any other procedure is considered bad ethics. Whether rightly or wrongly Cauchy was accused of voting in accordance with his religious and political views. His last years were embittered by what he considered a lack of understanding among his colleagues on this and similar foibles. Neither side could get the point of view of the other.

Cauchy died rather unexpectedly in his sixty eighth year on May 23, 1857. Hoping to benefit a bronchial trouble, he retired to the country to recuperate, only to be smitten with a fever which proved fatal. A few hours before his death he was talking animatedly with the Archbishop of Paris of the charitable works he had in view—charity was one of Cauchy's lifelong interests. His last words were addressed to the Archbishop: “Men pass away but their deeds abide.”

I
. The operations in a pair may be the same, thus
X, X.

II
. For example,
to infinity, obtained by dividing 1 by 1—
x,
is nonsense if
x
is a positive number equal to or greater than 1.

Lobatchewsky's theory was incomprehensible to his contemporaries, appearing as it did to contradict an axiom whose necessity is based only on a prejudice sanctified by thousands of years.
—T
HE
E
DITORS OF
L
OBATCHEWSKY
'
S
W
ORKS

G
RANTING THAT THE COMMONLY ACCEPTED
estimate of the importance of what Copernicus did is correct, we shall have to admit that it is either the highest praise or the severest condemnation humanly possible to call another man the “Copernicus” of anything. When we understand what Lobatchewsky did in the creation of non-Euclidean geometry, and consider its significance for all human thought, of which mathematics is only a small if important part, we shall probably agree that Clifford (1845-1879), himself a great geometer and far more than a “mere mathematician,” was not overpraising his hero when he called Lobatchewsky “The Copernicus of Geometry.”

Nikolas Ivanovitch Lobatchewsky, the second son of a minor government official, was born on November 2, 1793 in the district of Makarief, government of Nijni Novgorod, Russia. The father died when Nikolas was seven, leaving his widow, Praskovia Ivanovna, the care of three young sons. As the father's salary had barely sufficed to keep his family going while he was alive the widow found herself in extreme poverty. She moved to Kazan, where she prepared her boys for school as best she could, and had the satisfaction of seeing them accepted, one after the other, as free scholars at the Gymnasium. Nikolas was admitted in 1802 at the age of eight. His progress was phenomenally rapid in both mathematics and the classics. At the age of fourteen he was ready for the university. In 1807 he entered the University of Kazan (founded in 1805), where he was to spend the next forty years of his life as student, assistant professor, professor, and finally rector.

Hoping to make Kazan ultimately the equal of any university in
Europe, the authorities had imported several distinguished professors from Germany. Among these was the astronomer Littrow, who later became director of the Observatory at Vienna, whom Abel mentioned as one of his excuses for seeing something of “the south.” The German professors quickly recognized Lobatchewsky's genius and gave him every encouragement.

In 1811, at the age of eighteen, Lobatchewsky obtained his master's degree after a short tussle with the authorities, whose ire he had incurred through his youthful exuberance. His German friends on the faculty took his part and he got his degree with distinction. At this time his elder brother Alexis was in charge of the elementary mathematical courses for the training of minor government officials, and when Alexis presently took a sick-leave, Nikolas stepped into his place as substitute. Two years later, at the age of twenty one, Lobatchewsky received a probationary appointment as “Extraordinary Professor” or, as we should say in America, Assistant Professor.

*  *  *

Lobatchewsky's promotion to an ordinary professorship came in
1816
at the unusually early age of twenty three. His duties were heavy. In addition to his mathematical work he was charged with courses in astronomy and physics, the former to substitute for a colleague on leave. The fine balance with which he carried his heavy load made him a conspicuous candidate for yet more work, on the theory that a man who can do much is capable of doing more, and presently Lobatchewsky found himself University Librarian and curator of the chaotically disordered University Museum.

Students are often an unruly lot before life teaches them that generosity of spirit does not pay in the cut-throat business of earning a living. Among Lobatchewsky's innumerable duties from 1819 till the death of the Czar Alexander in 1825 was that of supervisor of all the students in Kazan, from the elementary schools to the men taking post-graduate courses in the University. The supervision was primarily over the political opinions of his charges. The difficulties of such a thankless job can easily be imagined. That Lobatchewsky contrived to send in his reports day after day and year after year to his suspicious superiors without once being called on the carpet for laxity in espionage, and without losing the sincere respect and affection of all the students, says more for his administrative ability than do all the gaudy
orders and medals which a grateful Government showered on him and with which he delighted to adorn himself on state occasions.

The collections in the University Museum to all appearance had been tossed in with a pitchfork. A similar disorder made the extensive library practically unusable. Lobatchewsky was commanded to clean up these messes. In recognition of his signal services the authorities promoted him to the deanship of the Faculty of Mathematics and Physics, but omitted to appropriate any funds for hiring assistance in straightening out the library and the museum. Lobatchewsky did the work with his own hands, cataloguing, dusting and casing, or wielding a mop as the occasion demanded.

With the death of Alexander in 1825 things took a turn for the better. The particular official responsible for the malicious persecution of the University of Kazan was kicked out as being too corrupt for even a government post, and his successor appointed a professional curator to relieve Lobatchewsky of his endless tasks of cataloguing books, dusting mineral specimens, and deverminizing stuffed birds. Needing political and moral support for his work in the University, the new curator did some high politics on his own account and secured the appointment in 1827 of Lobatchewsky as Rector. The mathematician was now head of the University, but the new position was no sinecure. Under his able direction the entire staff was reorganized, better men were brought in, instruction was liberalized in spite of official obstruction, the library was built up to a higher standard of scientific sufficiency, a mechanical workshop was organized for making the scientific instruments required in research and instruction, an observatory was founded and equipped—a pet project of the energetic Rector's—and the vast mineralogical collection, representative of the whole of Russia, was put in order and constantly enriched.

Even the new dignity of his rectorship did not deter Lobatchewsky from manual labor in the library and museum when he felt that his help was necessary. The University was his life and he loved it. On the slightest provocation he would take off his collar and coat and go to work. Once a distinguished foreigner, taking the coatless Rector for a janitor or workman, asked to be shown through the libraries and museum collections. Lobatchewsky showed him the choicest treasures, explaining as he exhibited. The visitor was charmed and greatly impressed by the superior intelligence and courtesy of this obliging Russian worker. On parting from his guide he tendered a handsome
tip. Lobatchewsky, to the foreigner's bewilderment, froze up in a cold rage and indignantly spurned the proffered coin. Thinking it but just one more eccentricity of the high-minded Russian janitor, the visitor bowed and pocketed his money. That evening he and Lobatchewsky met at the Governor's dinner table, where apologies were offered and accepted on both sides.

Lobatchewsky was a strong believer in the philosophy that in order to get a thing done to your own liking you must either do it yourself or understand enough about its execution to be able to criticize the work of another intelligently and constructively. As has been said, the University was his life. When the Government decided to modernize the buildings and add new ones, Lobatchewsky made it his business to see that the work was done properly and the appropriation not squandered. To fit himself for this task he learned architecture. So practical was his mastery of the subject that the buildings were not only handsome and suited for their purposes but, what must be almost unique in the history of governmental building, were constructed for less money than had been appropriated. Some years later (in 1842) a disastrous fire destroyed half Kazan and took with it Lobatchewsky's finest buildings, including the barely completed observatory—the pride of his heart. But due to his energetic cool-headedness the instruments and the library were saved. After the fire he set to work immediately to rebuild. Two years later not a trace of the disaster remained.