Men of Mathematics (40 page)

“Well, Monsieur Prefect! You too; you have declared war against me?”

“Sire,” Fourier stammered, “my oaths made it a duty.”

“A duty, do you say? Don't you see that nobody in the country is of your opinion? And don't let yourself imagine that your plan of campaign frightens me much. I suffer only at seeing amongst my adversaries
an
Egyptian,
a man who has eaten the bread of the bivouac with me, an old friend! How, moreover, Monsieur Fourier, have you been able to forget that I made you what you are?”

That Fourier, remembering Napoleon's callous abandonment of him in Egypt, could swallow such tripe and like it says a great deal for the goodness of his heart and the toughness of his stomach but precious little for the soundness of his head.

Some days later Napoleon asked the now loyal Fourier:

“What do you think of my plan?”

“Sire, I believe you will fail. You will meet a fanatic on your road, and everything will be over.”

“Bah! Nobody is for the Bourbons—not even a fanatic. As for that, you have read in the papers that they have put me outside the law. I myself will be more indulgent: I shall content myself with putting them outside the Tuileries!”

The leopard's spots and Napoleon's swellhead should be wedded in one proverb instead of pining apart in two.

The second restoration found Fourier in Paris pawning his effects to keep alive. But before he could starve to death old friends took pity on him and got him appointed director of the Bureau of Statistics for the Seine. The Academy tried to elect him to membership in 1816, but the Bourbon government ordered that no friend of their late kicker was to be honored in any way. The Academy stuck to its guns and elected Fourier the following year. This action of the Bourbons against Fourier may seem petty, but beside what they did to poor old Monge it was princely.
Noblesse oblige!

Fourier's last years evaporated in clouds of talk. As Permanent Secretary of the Academy he was always able to find listeners. To say that he bragged of his achievements under Napoleon is putting it altogether too mildly. He became an insufferable, shouting bore. And instead of continuing with his scientific work he entertained his audience with boastful accounts of what he was
going
to do. However, he had done far more than his share for the advancement of science, and if any human work merits immortality, Fourier's does. He did not need to boast or bluff.

Fourier's experiences in Egypt were responsible for a curious habit which may have hastened his death. Desert heat, he believed, was the ideal condition for health. In addition to swathing himself like a mummy he lived in rooms which his uncooked friends said were hotter
than hell and the Sahara desert combined. He died of heart disease (some say an aneurism) on May 16, 1830, in the sixty third year of his life. Fourier belongs to that select company of mathematicians whose work is so fundamental that their names have become adjectives in every civilized language.

*  *  *

Monge's decline was slower and more distressing. After the first restoration Napoleon felt embittered and vindictive toward the snobocracy of his own creation which, naturally, had let him down the moment his power waned. Once more in the saddle Napoleon was inclined to use the butt end of his crop on the skulls of the ungrateful. Monge, good old plebeian that he was, counselled mercy and common sense: Napoleon might some day find himself with his back to the wall (after an earthquake had cut off all means of flight), and be grateful for the support of the ingrates. Cooling off, Napoleon wisely tempered injustice with mercy. For this gracious dispensation Monge alone was responsible.

After Napoleon had run away from Waterloo, leaving his troops to get out of the mess as best they could, he returned to Paris. Fourier's devotion cooled then; Monge's boiled.

The school histories often tell of Napoleon's last dream—the conquest of America. The Mongian version differs and is on a much higher—in fact, incredibly high—plane. Hemmed in by enemies and appalled at the thought of enforced idleness for lack of further European conquest, Napoleon turned his eagle eye West, and in one flashing glance surveyed America from Alaska to Cape Horn. But, like the sick devil he was, Bonaparte longed to become a monk. The sciences alone could satisfy him, he declared; he would become a second and infinitely greater Alexander von Humboldt.

“I wish,” he confessed to Monge, “in this new career to leave works, discoveries, worthy of me.”

What, precisely, are the works which could be worthy of a Napoleon? Continuing, the fallen eagle outlined his dream.

“I need a companion,” he admitted, “to first put me abreast of the present state of the sciences. Then you [Monge] and I will traverse the whole continent, from Canada to Cape Horn; and in this immense journey we shall study all those prodigious phenomena of terrestrial physics on which the scientific world has not pronounced its verdict.” Paranoia?

“Sire,” Monge exclaimed—he was nearly sixty seven—“your collaborator is already found; I will go with you!”

His old self once more, Napoleon curtly dismissed the thought of the willing veteran hampering his lightning marches from Baffin Bay to Patagonia.

“You are too old, Monge. I need a younger man.”

Monge tottered off to find “a younger man.” He approached the fiery Arago as the ideal travelling companion for his energetic master. But Arago, in spite of all his eloquent rhetoric on the gloriousness of glory, had learned his lesson. A general who could desert his troops as Napoleon had done at Waterloo, Arago pointed out, was no leader to follow anywhere, even in easy America.

Further negotiations were rudely halted by the British. By the middle of October Napoleon was exploring St. Helena. The hoard of money which had been put aside for the conquest of America found its way into deeper pockets than those of the scientists, and no “American Institute” rose on the banks of the Mississippi or the Amazon to match its fantastic twin overlooking the Nile.

Having enjoyed the bread of imperialism Monge now tasted the salt. His record as a revolutionist and favorite of the upstart Corsican made his head an extremely desirable object to the Bourbons, and Monge dodged from one slum to another in an endeavor to keep his head on his shoulders. For sheer human pettiness the treatment accorded Monge by the sanctified Bourbons would take a lot of beating. Small enough for anything they stripped the old man of his last honor—one with which the generosity of Napoleon had had nothing whatever to do. In 1816 they commanded that Monge be expelled from the Academy. The academicians, tame as rabbits now, obeyed.

The final touch of Bourbon pettiness graced the day of Monge's funeral. As he had foreseen he died after a prolonged stupor following a stroke. The young men at the Polytechnique, whom he had protected from Napoleon's domineering interference, were the pride of Monge's heart, and he was their idol. When Monge died on July 28, 1818, the Polytechnicians asked permission to attend the funeral. The King denied the request.

Well disciplined, the Polytechnicians observed the ban. But they were more resourceful or more courageous than the timid academicians. The King's order covered only the funeral. The following day they marched in a body to the cemetery and laid a wreath on the grave of their master and friend, Gaspard Monge.

I
. F. J. D. Arago, 1786-1853, astronomer, physicist, and scientific biographer.

Projective geometry has opened up for us with the greatest facility new territories in our science, and has rightly been called a royal road to its own particular field of knowledge.
—F
ELIX
K
LEIN

M
ORE THAN ONCE
during the World War when the French troops were hard pressed and reinforcements nonexistent, the high command saved the day by routing some prima donna out of her boudoir, rushing her to the front, draping her from neck to heels in the tricolor, and ordering her to sing the
Marseillaise
to the exhausted men. Having sung her piece the lady rolled back to Paris in her limousine; the heartened troops advanced, and the following morning a cynically censored press once more unanimously assured a gullible public that “the day of glory has arrived”—with unmentioned casualties.

In 1812 the day of glory was still on its way. Prima donnas did not accompany Napoleon Bonaparte's half-million troops on their triumphal march into Russia. The men did their own singing as the Russians retreated before the invincible Grand Army, and the endless plains rang to the stirring chant which had swept tyrants from their thrones and elevated Napoleon to their place.

All was going as gloriously as the most enthusiastic singer could have wished: six days before Napoleon crossed the Niemen his brilliant diplomatic strategy had indirectly exasperated President Madison into hurling the United States into a distracting war on England; the Russians were running harder than ever on their race back to Moscow, and the Grand Army was doing its valiant best to keep up with the reluctant enemy. At Borodino the Russians turned, fought, and, retired. Napoleon continued without opposition—except from the erratic weather—to Moscow, whence he notified the Czar of his willingness to consider an unconditional surrender of all the
Russian forces. The competent inhabitants of Moscow, led by the Governor, took matters into their own hands, fired their city, burned it to the ground, and smoked Napoleon and all his men out into the void. Chagrined but still master of the situation, Napoleon disregarded this broad hint—the second or third so far vouchsafed to his military obstinacy—that “who killeth with the sword must perish by the sword,” presently ordered his driver to give the horses the lash, and dashed back post-haste over the now frozen plains to prepare for his rendezvous with Blücher at Leipzig, leaving the Grand Army to walk home or freeze as it should see fit.

With the deserted French army was a young officer of engineers, Jean-Victor Poncelet (July 1, 1788-December 23, 1867) who, as a student at the École Polytechnique in Paris, later at the military academy at Metz, had been inspired by the new descriptive geometry of Monge (1746-1818) and the
Géométrie de position
(published in 1803) of the elder Carnot (Lazare-Nicolas-Marguerite Carnot, May 13, 1753-August 2, 1823), whose revolutionary if somewhat reactionary program was devised “to free geometry from the hieroglyphics of analysis.”

In the preface to his classic
Applications d'analyse et de géométrie
(second edition 1862, of the work first published in 1822), Poncelet recounts his experiences in the disastrous retreat from Moscow. On November 18, 1812, the exhausted remnant of the French army under Marshal Ney was overwhelmed at Krasnoï. Among those left for dead on the frozen battlefield was young Poncelet. His uniform as an officer of engineers saved his life. A searching party, discovering that he still breathed, took him before the Russian staff for questioning.

As a prisoner of war the young officer was forced to march for nearly five months across the frozen plains in the tatters of his uniform, subsisting on a meagre ration of black bread. In a cold so intense that the mercury of the thermometer frequently froze, many of Poncelet's companions in misery died in their tracks, but his ruggeder strength pulled him through, and in March, 1813 he entered his prison at Saratoff on the banks of the Volga. At first he was too exhausted to think. But when “the splendid April sun” restored his vitality, he remembered that he had received a good mathematical education, and to soften the rigors of his exile he resolved to reproduce as much as he could of what he had learned. It was thus that he created projective geometry.

Without books and with only the scantiest writing materials at first, he retraced all that he had known of mathematics from arithmetic to higher geometry and the calculus. These first labors were enlivened by Poncelet's efforts to coach his fellow officers for the examinations they must take should they ever see France again. One legend states that at first Poncelet had only scraps of charcoal, salvaged from the meager brazier which kept him from freezing to death, for drawing his diagrams on the wall of his cell. He makes the interesting observation that practically all details and complicated developments of the mathematics he had been taught had evaporated, while the general, fundamental principles remained as clear as ever in his memory. The same was true of physics and mechanics.

In September, 1814, Poncelet returned to France, carrying with him “the material of seven manuscript notebooks written at Saratoff in the prisons of Russia (1813 to 1814), together with divers other writings, old and new,” in which he, as a young man of twenty four, had given projective geometry its strongest impulse since Desargues and Pascal initiated the subject in the seventeenth century. The first edition of his classic, as already mentioned, was published in 1822. It lacked the intimate “apology for his life” which has been used above, but it started a tremendous nineteenth century surge forward in projective geometry, modern synthetic geometry generally, and the geometric interpretation of the “imaginary” numbers that present themselves in algebraic manipulations, giving to such “imaginaries” geometrical interpretations as “ideal” elements of space. It also proposed the powerful and (for a time) controversial “doctrine of continuity,” to be described presently, which greatly simplified the study of geometric configurations by unifying apparently unrelated properties of figures into uniform, self-contained complete wholes. Exceptions and awkward special cases appeared under Poncelet's broader point of view as merely different aspects of things already familiar. The classic treatise also made full use of the creative “principle of duality” and introduced the method of “reciprocation” devised by Poncelet himself. In short, a whole arsenal of new weapons was added to geometry by the young military engineer who had been left for dead on the field of Krasnoï, and who might indeed have died before morning had not his officer's uniform distinguished him as a likely candidate for questioning by the Russian staff.