The modest family library soon proved utterly insufficient to occupy the mind of this young, enthusiastic student; and his father, sympathetic to his ardent curiosity, took him to Lyons from time to time, where he might have the opportunity to consult volumes of various kinds that might catch his fancy. At this time, his old mathematical tendency reasserted itself. He wished to learn something about the higher mathematics. He found in a library in Lyons the works of Bernoulli and of Euler. When the delicate-looking boy, whom the librarian considered little more than a child, put in his request to the town library for these serious mathematical works, the old gentleman said to him: "The works of Bernoulli and Euler! What are you thinking of, my little friend? These works figure among the most difficult writings that ever came from the mind of man." "I hope to be able to understand them," replied the boy. "I suppose you know," said the librarian, "that they are written in Latin." This was a disagreeable surprise for young Ampère. As yet he had not studied Latin. He went home, resolved, however, to remove this hindrance to his study of the higher mathematics. At the end of the month, owing to his assiduity, the obstacle had entirely disappeared; and though he could read only mathematical Latin and had later to study the language from another standpoint, in order to understand the classics, he was now able to pursue the study of mathematics in Latin to his heart's content.
The even tenor of the boy's life, deeply engaged as he was in studies of every description, was destined to be very seriously disturbed. When he was but fourteen, in 1789, the Revolution came, with its glorious promise and then its awful consummation. Ampère's father was seriously alarmed at the revolutionary course things were taking in France, and had the fatal inspiration to leave his country home and betake himself to the city of Lyons. For a time, he occupied a position as magistrate. After the siege of Lyons, the revolutionary tribunal established there took up the project of making the Lyonnese patriotic, as they called it, by properly punishing the citizens for their failure to sympathize at first with the revolutionary government, and soon a series of horrible massacres began. New victims were claimed every day, and Ampère's father was one of those who had to suffer. The real reason for his condemnation was that he had accepted a position under the old government, though the pretext stated on the warrant for his arrest was that he was an aristocrat. This is the only evidence we have that the Ampère family was in any way connected with the nobility. The day on which he was sentenced to die, Jean Jacques Ampère wrote to his wife a letter of sublime simplicity, in which his Christian resignation of spirit, his lofty courage, yet thoroughly practical commonsense, are manifest. He warned his wife to say nothing about his fate to their daughter Josephine, though he hoped that his son would be better able to stand the blow, and perhaps prove a consolation to his mother.
The news proved almost too much for the young Ampère, and for a time his reason was despaired of. All his faculties seemed to be shocked for the moment into insensibility. Biographers tell us that he wandered around, building little piles of sand, gazing idly at the stars or vacantly into space, wearing scarcely any of the expression of a rational being. His friends could harbor only the worst possible expectations for him, and even his physical health suffered so much that it seemed he would not long survive. One day, by chance, Rousseau's "Letters on Botany" fell into his hands. They caught his attention, and he became interested in their charming narrative style, and as a result, his reason awoke once more. He began to study botany in the field, and soon acquired a taste for the reading of Linnæus. At the same time, classic poetry, especially such as contained descriptions of nature, once more appealed to him, and so he took up his classical studies. He varied the reading of the poets with dissections of flowers, and yet succeeded in following both sets of studies so attentively that, forty years afterward, he was still perfectly capable of taking up the technical description of the plants that he had then studied, and while acting as a university inspector, he composed 150 Latin verses during his horseback rides from one inspection district to another, without ever having to consult a gradus or a dictionary for the quantities, yet without making a single mistake. His memory for subjects once learned, was almost literally infallible.
Something of his love for nature can be appreciated from an incident of his early manhood, which is not without its amusing side. Ampère was very near-sighted, and had been able to read books all his life only by holding them very close to his eyes. This makes it all the more difficult to understand how he succeeded in reading so much. His near-sightedness was so marked that he had no idea of beauties of scenery beyond him, and was often rather put out at the enthusiastic description of scenes through which he passed en diligence, when his fellow-travelers spoke of the beauties of the scenes around them. Ampère, like most people who do not share, or at least appreciate, the enthusiasm of others for beautiful things around them, was in this mood, mainly because he was not able to see them in the way that others did, and, therefore, could not have the same pleasure in them. This lack in himself was unconscious, of course, as in all other cases, and, far from lessening, rather emphasized the tendency to be impatient with others, and rather made him more ready to think how foolish they were to go into ecstasies over something that to him was so insignificant.
One day, while Ampère was making the journey along the Saone into Lyons, it happened that there sat beside him on the stage-coach a young man who suffered from near-sightedness very nearly in the same degree as Ampère himself, but whose myopia had been corrected by means of properly fitting glasses. These glasses were just exactly what Ampère needed in order to correct his vision completely. The young fellows became interested in each other, and, during the course of their conversation, his companion suggested to Ampère, seeing how near-sighted he was, that he should try his glasses. He put them on, and at once nature presented herself to him under an entirely different aspect. The vision was so unexpected, that the description which he had so often heard from his fellow-travelers, but could not appreciate, now recurred to him, and he could not help exclaiming in raptures, "Oh! what a smiling country! What picturesque, graceful hills! How the rich, warm tones are harmoniously blended in the wonderful union of sky and mountain vista!" All of these now spoke emphatically to his delicate sensibility, and a new world was literally revealed to him. Ampère was so overcome by this unexpected sight, which gave him so much pleasure, that he burst into tears from depth of emotion, and could not satisfy himself with looking at all the beauties of nature that had been hidden from him for so long. Ever after, natural scenery was one of the greatest pleasures that he had in life, and the beauties of nature, near or distant, meant more to him than any other gratification of the senses.
In spite of the fact that Ampère had devoted considerable attention to acoustics as a young man, and had studied the ways in which the waves of air by which sounds are formed and propagated, he had absolutely no ear for music, and was as tone-deaf as he had been blind before his discovery with regard to the glasses. Musical notes constituted a mathematical problem for Ampère, but nothing more. This continued to be the case until about thirty years of age. Then, one day, he attended a musical soirée, at which the principal portions of the program were taken from Glück. It is easy to understand that this master of harmony possessed no charms for a tone-deaf young man. He became uneasy during the course of the musical program, and his uneasiness became manifest to others. After the selections of the German composer were finished, however, some simple but charming melodies were unexpectedly introduced, and Ampère suddenly found himself transported into a new world. If we are to believe his biographers, once more his emotion was expressed by an abundance of tears, which Ampère seems to have had at command and to have been quite as ready to give way to in public as any of Homer's heroes of the olden time. Blind until he was nearly twenty, he used to say of himself, he had been deaf until he was thirty. In spite of his failure to respond in youth, once it had been awakened to appreciation, his soul vibrated profoundly to all the beauties of color and sound, and, later in life, they gave rise in him to depths of emotion which calmer individuals of less delicate sensibilities could scarcely understand, much less sympathize with.
Between his two supreme experiences in vision and sound, there had come to Ampère another and even profounder emotion. He tells the story himself, in words that probably express his feelings better than any possible description of his biographer could do, and that show us how wonderfully sensitive his soul was to emotion of all kinds. He had just completed his twenty-first year when he fell head over heels in love. Though he wrote very little, as a rule, he has left us a rather detailed description in diaries, evidently kept for the purpose, of the state of his feelings at this time. These bear the title, "Amorum," the story of his love. On the first page these words occur: "One day as I was taking an evening walk, just after the setting of the sun, making my way along a little brook," then there is a hiatus, and he was evidently quite unable to express all that he felt. It seems that he was gathering botanical specimens, wearing an excellent set of spectacles ever since his adventure on the stage-coach had shown him the need of them, when he suddenly perceived at some distance two young and charming girls who were gathering flowers in the field. He looked at one of them, and he knew that his fate was sealed. Up to that time, as he says, the idea of marriage had never occurred to him. One might think that the idea would occur very gently at first, then grow little by little; but that was not Ampère's way. He wanted to marry her that very day. He did not know her name; he did not know her family; he had never even heard her voice, but he knew that she was the destined one.
Fortunately for the young lady and himself, she had very sensible parents. They demanded how he would be able to support a wife. Ampère was quite willing to do anything that they should suggest. His father had left enough to support the family, but not enough to enable him to support a wife in an independent home; and until he had some occupation, the parents of his bride-to-be refused to listen to his representations. For a time, he consented to be a salesman in a silk store in Lyons, in order to have some occupation which might eventually give him enough money to enable him to marry. Fortunately, however, he was diverted from a commercial vocation which might thus have absorbed a great scientist, and arrangements were made which permitted him to continue his intellectual life, yet have the woman of his choice. She was destined to make life happier far for him than is the usual lot of man, and he was ever ready to acknowledge how much she meant for his happiness.
With literature, poetry, love and settling down in life to occupy him, it is hard to think of Ampère as a young man doing great work in science, but he did; and his work deservedly attracted attention even from his very early years. It was in pure mathematics, perhaps, above all other branches, that Ampère attracted the attention of his generation. Ordinary questions he did not care for. Problems which the fruitless efforts of twenty centuries had pronounced insoluble attracted him at once. Even the squaring of the circle claimed his attention for a while, though he got well beyond it even before his boyhood passed away. There is a manuscript note from the Secretary of the Academy of Lyons, which shows that on July 8th, 1788, Ampère, then not quite thirteen years of age, addressed to that learned body a paper on the "Squaring of the Circle." Later, during the same year, he submitted an analogous memoir, entitled, "The Rectification of an Arc of a Circle, less than a Semi-circumference."
Arago says that he was tempted to suppress this story of Ampère's coquetting with so dangerous a problem, for Ampère rather flattered himself that he had almost solved it. It was only after Arago recalled how many geniuses in mathematics had occupied themselves with this same problem, that he saw his way clearly not to share the scruples of those who might think this incident a reflection on Ampère's mathematical genius. After all, Anaxagoras, Hippocrates, Archimedes and Apollonius, among the ancients, and among the moderns, Willebrod Snell, Huyghens, Gregory, Wallis, and finally Newton, the mathematician of the heavens, occupied themselves seriously with this very problem. Arago even notes that some men, by their speculations on the squaring of the circle, were led to distinguished discoveries, and mentions the name of Father Grégoire de Saint-Vincent, the distinguished Flemish mathematician of the Society of Jesus, to whom, as a direct result of his studies in attempted circle-squaring, we owe the discovery of the properties of hyperbolic space, limited by the curve and its asymptotes, as well as the expansion of log (1 + x) in ascending powers of x. Montucla, the historian of mathematics, writing of Père Saint-Vincent, said that, "No one ever squared the circle with so much ability or with so much success." There was, however, a fallacy in his magnificent work which was pointed out by the celebrated Huyghens.