BIOGRAPHY.

PROF. E. B. SEITZ, M. L. M. S.

Professor Seitz, a distinguished mathematician of his day, was born in Fairfield Co., O., Aug. 24, 1846, and died at Kirksville, Mo., Oct. 8, 1883. His father, Daniel Seitz, was born in Rockingham Co., Va., Dec. 17, 1791, and was twice married. His first wife's name was Elizabeth Hite, of Fairfield Co., O., by whom he had eleven children. His second wife's name was Catharine Beery, born in the same county, Apr. 11, 1808, whom he marr.ed Apr. 15, 1832. This woman was blessed by four sons and three daughters. Mr. Seitz followed the occupation of a farmer and was an industrious and substantial citizen. He died near Lancaster, O., Oct. 14, 1864, in his seventy-third year; having been a resident of Fairfield Co. for sixty-three years.

Professor Seitz, the third son by his father's second marriage, passed his boyhood on a farm, and like most men who have become noted, had only the advantages of a common school education. Possessing a great thirst for learning, he applied himself diligently to his books in private and became a very fine scholar in the English branches, especially excelling in arithmetic. It was told the author, by his nephew, Mr. Huddle, that when Professor Seitz was in the field with a team, he would solve problems while the horses rested. Often he would go to the house and get in the garret where he had a few algebras upon which he would satiate his intellectual appetite. This was very annoying to his father who did not see the future greatness of his son, and many and severe were the floggings he received for going to his favorite retreat to gain a victory over some difficult problem upon which he had been studying while following the plow. Though the way seemed obstructed, he completed algebra at the age of fifteen, without an instructor. He chose teaching as his profession which he followed with gratifying success until his death. He took a mathematical course in the Ohio Wesleyan University in 1870. In 1872, he was elected one of the teachers in the Greenville High School, which position he held till_1879. On the 24th of June, 1875, he married Miss Anna E. Kerlin, one of Darke county's most refined ladies. In 1879, he was elected to the chair of mathematics in the Missouri State Normal School, Kirksville, Mo., which position he held till death called him from the confines of earth, ere his star of fame had reached the zenith of its glory. He was stricken by that "demon of death," typhoid fever, and passed the mysterious shades, to be numbered with the silent majority, on the 8th of October, 1883. On the 11th_of March, 1880, he was elected a member of the London Mathematical Society, being the fifth American so honored.

He began his mathematical career in 1872, by contributing solutions to the problems proposed in the "Stairway" department of the Schoolday Magazine, conducted by Artemas Martin. His masterly and original solutions of difficult Average and Probability problems, soon attracted universal attention among mathematicians. Dr. Martin being desirous to know what works he had treating on that difficult subject, was greatly surprised to learn that he had no works upon the subject, but had learned what he knew about that difficult department of mathematical science by studying the problems and solutions in the Schoolday Magazine. Afterwards, he contributed to the Analyst, the Mathematical Visitor, the Mathematical Magazine, the School Visitor, and the Educational Times, of London, Eng.

In all of these journals, Professor Seitz was second to none, as his logical and classical solutions of Average and Probability problems, rising as so many monuments to his untiring patience and indomitable energy and perseverance will attest. His name first appeared as a contributor to the Educational Times in Vol. XVIII., of Reprint, 1873. From that time until his death the Reprint is adorned with some of the finest product of his mighty intellect.

On page 21, Vol. II., he has given the above solution. This problem had been proposed in 1864 by the great English mathematician, Prof. Woolhouse, who solved it with great labor. It was said by an eminent mathematician of that day that the task of writing out a copy of that solution was worth more than the book in which it was published.

No other mathematician seemed to have the courage to investigate the problem after Prof. Woolhouse gave his solution to the world, till Professor Seitz took it up and demontsrated it so elegantly in half a page of ordinary type, that he fairly astonished the mathematicians of both Europe and America. Prof. Woolhouse was the best English authority on Probabilities even before Professor Seitz was born.

It was the solution of this problem that won for Professor Seitz the acknowledgment of his superior ability to solve difficult Probability problems over any other living man in the world.

In studying his solutions, one is struck with the simplicity to which he has reduced the solutions of some of the most intricate problems. When he had grasped a problem in its entirety, he had mastered all problems of that class. He would so vary the condition in thinking of one special problem and in effecting a solution that he had generalized all similar cases, so exhaustive was his analyses. Behind the words he saw all the ideas represented. These he translated into symbols, and then he handled the symbols with a facility that has rarely been surpassed.

What he might have accomplished in his maturer years, had he turned his splendid powers to investigations in higher and more fruitful fields of mathematics, no man may say. The solving of problems alone is not a high form of mathematical research. While problem solving is very beneficial and essential at first, yet, if one confines himself to that sort of work exclusively, it becomes a waste of time.

He was a man of the most singularly blameless life; his disposition was amiable; his manner gentle and unobtrusive; and his decision, when circumstances demanded it, was prompt and firm as the rocks. He did nothing from impulse; he carefully considered his course and came to conclusions which his conscience approved; and when his decision was made, it was unalterable.

Professor Seitz was not only a good mathematician, but he was also proficient in other branches of knowledge. His mind was cast in a large mold. "Being devout in heart as well as great in intellect, 'signs and quantities were to him but symbols of God's eternal truth' and 'he looked through nature up to nature's God.' Professor Seitz, in the very appropriate words of Dr. Peabody regarding Benjamin Pierce, Professor of Mathematics and Astronomy in Harvard University, 'saw things precisely as they are seen by the infinite mind. He held the scales and compasses with which eternal wisdom built the earth, and meted out the heavens. As a mathematician, he was adored by his friends with awe. As a man, he was a Christian in the whole aim and tenor of life.'

Professor Seitz did not gain his knowledge from books, for his library consisted of only a few books and periodicals. He gained such a profound insight in the subtle relations of numbers by close application with which he was particularly gifted. He was not a mathematical genius, that is, as ususally understood, one who is born with mathematical powers fully developed. But he was a genius in that he was especially gifted with the power to concentrate his mind upon any subject he wished to investigate. This happy faculty of concentrating all his powers of mind upon one topic to the exclusion of all others, and viewing it from all sides, enabled him to proceed with certainty where others would become confused and disheartened. Thread by thread and step by step, he took up and followed out long lines of thought and arrived at correct conclusions. The darker and more subtle the question appeared to the average mind, the more eagerly he investigated it. No conditions were so complicated as to discourage him. His logic was overwhelming.

BIOGRAPHY.

RENE DESCARTES.

René Descartes, the first of the modern school of mathematicians, was born at La Haye, a small town on the right bank of the Creuse and about midway between Tours and Poitiers, on March 31st, 1596, and died at Stockholm, on February 11th, 1650. "The house is still shown where he was born, and a metairie about three miles off still retains the name of Les Cartes. His family on both sides was of Poitevin descent and had its headquarters in the neighboring town of Châtterault, where his grandfather had been a physician. His father, Joachim Descartes, purchased a commission as counsellor in the Parlement Rennes and thus introduced the family into that demi-noblesse of the robe of which, in stately isolation between the bourgeoisie and the high nobility, maintained a lofty rank in the hierarchy of France. For one-half of each year required for residence the elder Descartes removed, with his wife, Jeanne Brochard, to Rennes. Three children, all of whom first saw the light at La Haye, sprang from the union, a son, who afterwards succeeded to his father in the Parlement, a daughter who married a M. du Crevis, and a second son, René. His mother, who had been ailing beforehand, never recovered from her third confinement; and the motherless infant was intrusted to a nurse, whose care Descartes in after years remembered by a small pension."*

Descartes, who early showed an inquisitive mind, was called by his father, “my philosopher." At the age of eight, Descartes was sent to the school of La Flèche, which Henry IV had lately founded and endowed for the Jesuits, and here he continued from 1604 to 1612. Of the education here given, of the equality maintained among the pupils, and of their free intercourse, he spoke at a later period in terms of high praise. Descartes himself enjoyed exceptional privileges. His feeble health excused him from the morning duties, and thus early he acquired the habit of matutinal reflection in bed, which clung to him throughout life. When he visited Pascal in 1647, he told him that the only way to do good work in mathematics and to preserve his health was never to allow any one to make him get up in the morning before he felt inclined to do so. Even at this period he had begun to distrust the authority of tradition and his teachers.

Two years before leaving school (1610) he was selected as one of twenty-four gentlemen who went forth to receive the heart of the murdered king as it was borne to its resting place at La Flèche. During the winter of 1612, he completed his preparations for the world by lessons in horsemanship and fencing; and then in the spring of 1613 he started for Paris to be introduced to the world of fashion. Fortunately the spirit of dissipation did not carry him very far, the worst being a passion for gaming. Here through the medium of the Jesuits he made the acquaintance of Mydorge, one of the foremost mathematicians of France, and renewed his schoolboy friendship with Father Mersenne, and together with them he devoted the two years of 1615 and 1616 to the study of mathematics.

"The withdrawal of Mersenne in 1614 to a post in the provinces was the signal for Descartes to abandon social life and shut himself up for nearly two years in a secluded house of the Faubourg St. Germain. Accident, however, betrayed the secret of his retirement; he was compelled to leave his mathematical investigations and to take a part in entertainments, where the only thing that chimed in with his theorizing *Britannica Encyclopedia, Ninth Edition.

reveries was the music. The scenes of horror and intrigue which marked the struggle for supremacy between the various leaders who aimed at guiding the politics of France made France no fit place for a student and held out little honorable prospect for a soldier. Accordingly, in May, 1617, Descartes, now twenty-one years of age, set out for the Netherlands, and took service in the army of Prince Maurice of Orange, one of the greatest generals of the age, who had been engaged for some time in a war with the Spanish forces in Belgium. At Breda, he enlisted as a volunteer, and the first and only pay which he accepted he kept as a curiosity through life. There was a lull in the war; and the Netherlands were distracted by the quarrels of Gomarists and Arminians. During the leisure thus arising, Descartes one day, as he roved through Breda, had his attention drawn to a placard in the Dutch tongue; and as the language of which he never became perfectly master, was then strange to him, he asked a bystander to interpret it in either French or Latin. The stranger, who happened to be Isaac Beeckman, principal of the College of Dort, offered with some surprise to do so into Latin, if the inquirer would bring him a solution of the problem for the advertisement was one of those challenges which the mathematicians of the age, in the spirit of the tournament of chivalry, were accustomed to throw down to all comers, daring them to discover a geometrical mystery known as they fancied to themselves alone. Descartes promised and fulfilled; and a friendship grew up between him and Beeckman only by the literary dishonesty of the latter, who in later years took credit for the novelty contained in a small essay on music (Compendium Musicae) which Descartes wrote at this period and intrusted to Beeckman."*

broken

The unexpected test of his mathematical attainments afforded by the solution of the problem referred to, its solution costing him only a few hours study, made the uncongenial army life distasteful to him, but under family influence and tradition, he remained a soldier, and was pursuaded at the commencement of the thirty years' war to volunteer under Count de Bucquoy in the army of Bavaria. The winter of 1619, spent in quarters at Neuburg on the Danube, was the critical period in his life. Here, in his warm room (dans un poele), he indulged those meditations which afterwards led to the Discours de la Methode (Discourse of Method). It was here that, on the eve of St. Martin's day, November 10, 1619, he "was filled with enthusiasm, and discovered the foundations of a marvelous science."

He retired to rest with anxious thoughts of his future career, which haunted him through the night in three dreams, that left deep impressions on his mind. "Next day," he says, "I began to understand the first principles of my marvelous discovery." Thus the date of his philosophical conversion is fixed to a day. This day marks the birth of modern mathematics. His discovery, viz., the coöperation of ancient geometry and algebra, is epoch-making in the history of mathematics.

It is frequently stated that Descartes was the first to apply algebra to geometry. This statement is not true, for Vieta and others had done this before him, and even the Arabs sometimes used algebra in connection with geometry. "The new step that Descartes did take was the introduction into geometry of an analytical method based on the notion of variables and constants, which enabled him to represent curves by algebraic equations. In the Greek geometry, the idea of motion was wanting, but with Descartes it became a very fruitful conception. By him a point was determined in position by its distances from two fixed lines or axes. These distances varied with every change of position in the point. This geometric idea of co-ordinate representation together with the algebraic idea of two variables in one equation having an indefinite number of simultaneous values, furnished a method for the study of loci, *Encyclopedia Britannica, Ninth Edition.

which is admirable for the generality of its solutions. Thus the entire conic sections of Appollonius is wrapped up and contained in a single equation of the second degree."+

"Descartes found in mathematics, as did Kant and Comte, the type of all faultless thought; and he proved his appreciation of his insight by the invention of a new symbolic mechanism and artifice for the applications of algebra to geometry (Analytic Geometry, as it is now called, which, in a growing sense, let it be said, existed before him), and by his discoveries in the theory of equations, which were fundamental in their importance.'

After a short sojourn in Paris, Descartes moved to Holland, then at the height of its power. There for twenty years he lived, giving up all his time to philosophy and mathematics. Science, he says, may be compared to a tree, metaphysics is the root, physics is the trunk, and the three chief branches are mechanics, medicine, and morals, these forming the three applications of our knowledge, namely, to the external world, to the human body, and to the conduct of life; and with these subjects alone his writings are concerned.

He spent the time from 1629 to 1633 writing Le Monde, a work embodying an attempt to give a physical theory of the universe; but finding its publication likely to bring on him the hostility of the Church, and having no desire to pose as a martyr, he abandoned it. The incomplete manuscript was published in 1664.

He then devoted himself to composing a treatise on universal science; this was published at Leyden in 1637 under the title Discourse de la méthode pour bien conduire sa raison et chercher la verité dans les sciences, and was accompanied with three appendices entitled La Dioptrique, Les Méléores, and La Géométrie. It is from the last of these that the invention of analytical geometry dates. In 1641, he published a work called Meditations, in which he explained at some length his views of philosophy as sketched out in the Discourse. In 1644, he issued the Principia Philosophiae, the greater part of which was devoted to physical science especially the laws of motion and the theory of vortices. In his theory of vortices, he commences with a discussion of motion; and then lays down ten laws of nature, of which the first two are almost identical with the first two as laid down by Newton. The remaining eight are inaccurate. He next proceeds to a discussion of the nature of matter which he regards uniform in kind though there are three forms of it. He assumes that the matter of the universe is in motion, that this motion is constant in amount, and that the motion results in a number of vortices. He states that the sun is the center of an immense whirlpool of this matter, in which the planets float and are swept round like straws in a whirlpool of water.

Each planet is supposed to be the center of a secondary whirlpool by which its satellites are carried, and so on. All of these assumptions are arbitrary and unsupported by any investigation. It is a little strange that a man who began his philosophical reasonings by doubting all things and finally coming to cogito, ergo sum should have made assumptions so groundless.

While Descartes was a philosopher of a very high type, yet his fame will ever rest on his researches in mathematics. The first important problem solved by Descartes in his geometry is the problem of Pappus, viz.: "Given several straight lines in a plane, to find the locus of a point such that perpendiculars, or, more generally, straight lines at given angles, drawn from the point to the given lines, shall satisfy that the product of certain of them shall be in given ratio to the product of the rest." "The most important case of this problem is to find the locus of a point such that the product of the perpendiculars on m given lines be in a constant tCajori's History of Mathematics.

The Open Court, August, 1898.