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Arthur Cayley
Times obituary
By the death of Professor Arthur Cayley, which we regret to announce as having occurred at Cambridge on Saturday night, England has lost its greatest mathematician. From this statement no one will dissent, and few, we believe, would demur to placing Professor Cayley in the first rank of mathematicians of any time and any country. In these columns it would be out of place to analyze in detail the work he has done, and on which his fame will rest, even if this were possible. As he was never a public man, never had any "career" in the ordinary sense of the term, was always the student, and almost a recluse, we can do little more than briefly recall a few of the facts of his life and work.
Arthur Cayley was born at Richmond, Surrey, on August 16, 1821, being the second son of a partner in a firm of Russian merchants, whose home was in St. Petersburg When Arthur was only years of age the family returned permanently to England and fixed their residence at Blackheath. At a very early age he showed great aptitude and liking for arithmetical calculations; though it used to be said of him in later years that he was unable to count the change for a shilling. It was probably fortunate that his father was persuaded not to bring up his son in business, as he originally intended. After some years at a school at Blackheath and at King's College, London (the Principal of which soon discerned his pupil's mathematical genius), Cayley was sent to Cambridge at the age of 17. In mathematics he carried all before him, and in 1842 he naturally came out as Senior Wrangler and First Smith's Prizeman. It is of interest to note that Sic Gabriel Stokes was the Senior Wrangler of the previous year and Professor Adams of the following year.
Cayley was made a Fellow of his college (Trinity) in 1842, but, as he did not take holy orders, this source of income was good then only for seven years. Ultimately, when he returned to Cambridge, he was made an elected foundation Fellow, an honour of extreme rarity. Meantime, however, he had to find some other means of making a living, and, soon after taking his degree, he became a pupil of the eminent conveyancer, Mr. Christie. Needless to say, he was a most distinguished pupil, and after he was called to the Bar (at Lancoln's Inn, in 1849), Mr. Christie was only too glad to put abundance of work in his way. But his first love, mathematics, never lost its hold over him; indeed, during the whole of his active career as a barrister he was constantly busy with mathematical work, contributing to many periodicals and societies at home and abroad. It was in 1863 that he married and returned to Cambridge to fill the newly instituted Sadlerian Professorship of Mathematics. Previous to that date we find the titles of some 300 papers by him in the Royal Society list, which gives some indication of his unceasing activity. It would seem that it was only in 1852 that he made his first contribution to the Royal Society, and in the same year he was elected a Fellow. Of course, by accepting the modern Cambridge professorship, he sacrificed brilliant prospects at the Bar and, no doubt, considerably reduced his income; but that was a matter that did not trouble him and, in time, considerably increased his University emoluments.
It was not with Cayley as is too often the case with men of high original faculty in science; he was as admirable a teacher as he was an investigator. While he was cosmopolitan in his mathematics, he was a master in every branch. One of the best judges, Mr. J. W. L. Glaisher, has described him as the greatest living master of algebra." It is well known that Cayley's papers, problems and investigations are often far beyond the comprehension of the ordinary mathematician. This is so well accounted for by Professor Salmon in the excellent paper on Cayley in the series of "Science Worthies," published in Nature, Vol. 28 (to which we express our indebtedness), that we cannot do better than quote the passage: -
As Cayley is not afraid of hard work himself, so it is necessary for the readers of his papers not to be easily discouraged by formidable calculations. But, in my opinion, it is not this so much that makes Cayley's papers difficult to read as the fact that he usually proceeds by the synthetic, not the analytic, method. It usually happens that a mathematical inquirer begins by proposing to himself some comparatively simple question. By the time he has found the answer to it the subject opens on him; the first question suggests others, the theorem first discovered is found to admit of wide generalizations, and perhaps it may be found that these could have been arrived at in quite another way. When the time comes for the inquirer to publish his results to the world, the most attractive course is to take his readers by exactly the same road he has travelled himself, beginning with the simple problem which firmly attracted attention, and lending on step by step to the highest results arrived at. Cayley, on the contrary, usually begins by trying to establish at once the highest generalizations he has solved, writing down equations, and proceeding to make calculations as to the good of which he has not taken his readers into confidence. The consequence is that few master his papers but those who have found a clue to them by some pravious work in the same direction.
With such a professor, of course, it was only students of the highest mathematics, thoroughly in sympathy with their master, that could derive any good from this teaching. But among them he was regarded with a reverence almost akin to worship. We shall not attempt to refer in detail to any of Professor Cayley's work. Mathematicians say that he is likely to be best remembered as the creator of an entirely new tranch of mathematics by his discovery of the Theory of Invariants. Professor Salmon says:-
This has given quite a new aspect to several departments of mathematics. It has introduced such a host of new ideas, and consequently of new words, that a Senior Wrangler of 40 years ago, who had not kept pace with modern investigations, would and, on taking up a book of the present day on geometry or algebra, that he could not read it without a glossary must go to school again to learn what the writer was sposking of. The knowledge which mathematicians now possess of the structure of algebraic formulas is as different from what it was before Cayley's time as the knowledge of the human body possessed by one who has dissected it and knows its internal structure is different from that of one who has only seen it from the outside.
The Royal Society contains the titles of 724 papers and memoirs by Cayley down to 1883, and since then he must have brought the number up to well over 800. These are being collected into a series of ten volumes quarto by the University of Cambridge, and it is to be hoped that the publication will be continued, even although the author and editor has died.
Absorbed as he was in mathematics, Professor Cayley invariably showed his sympathy with human life and interests, and especially with education; he even occasionally manifested an interest in politics. He was an early member of the Alpine Society. He was familiar with many European languages. In 1882 he was invited by the Johns Hopkins University in Baltimore to give a series of lectures, which he did in the winter session of that year. He was president of the Southport meeting of the British Association in 1883, and, as may be imagined, his presidential address was not calculated to arouse much interest among a typical Association audience. From the Royal Society he received both the Royal and the Copley medal. He was in 1890 made an officer of the Legion of Honour by the President of the French Republic, and was an honorary member of many learned societies at home and abroad. As might have been expected, Professor Cayley was a man of the most simple habits and of absolute modesty. He will be missed by not a few warm and devoted friends.
By the death of Professor Arthur Cayley, which we regret to announce as having occurred at Cambridge on Saturday night, England has lost its greatest mathematician. From this statement no one will dissent, and few, we believe, would demur to placing Professor Cayley in the first rank of mathematicians of any time and any country. In these columns it would be out of place to analyze in detail the work he has done, and on which his fame will rest, even if this were possible. As he was never a public man, never had any "career" in the ordinary sense of the term, was always the student, and almost a recluse, we can do little more than briefly recall a few of the facts of his life and work.
Arthur Cayley was born at Richmond, Surrey, on August 16, 1821, being the second son of a partner in a firm of Russian merchants, whose home was in St. Petersburg When Arthur was only years of age the family returned permanently to England and fixed their residence at Blackheath. At a very early age he showed great aptitude and liking for arithmetical calculations; though it used to be said of him in later years that he was unable to count the change for a shilling. It was probably fortunate that his father was persuaded not to bring up his son in business, as he originally intended. After some years at a school at Blackheath and at King's College, London (the Principal of which soon discerned his pupil's mathematical genius), Cayley was sent to Cambridge at the age of 17. In mathematics he carried all before him, and in 1842 he naturally came out as Senior Wrangler and First Smith's Prizeman. It is of interest to note that Sic Gabriel Stokes was the Senior Wrangler of the previous year and Professor Adams of the following year.
Cayley was made a Fellow of his college (Trinity) in 1842, but, as he did not take holy orders, this source of income was good then only for seven years. Ultimately, when he returned to Cambridge, he was made an elected foundation Fellow, an honour of extreme rarity. Meantime, however, he had to find some other means of making a living, and, soon after taking his degree, he became a pupil of the eminent conveyancer, Mr. Christie. Needless to say, he was a most distinguished pupil, and after he was called to the Bar (at Lancoln's Inn, in 1849), Mr. Christie was only too glad to put abundance of work in his way. But his first love, mathematics, never lost its hold over him; indeed, during the whole of his active career as a barrister he was constantly busy with mathematical work, contributing to many periodicals and societies at home and abroad. It was in 1863 that he married and returned to Cambridge to fill the newly instituted Sadlerian Professorship of Mathematics. Previous to that date we find the titles of some 300 papers by him in the Royal Society list, which gives some indication of his unceasing activity. It would seem that it was only in 1852 that he made his first contribution to the Royal Society, and in the same year he was elected a Fellow. Of course, by accepting the modern Cambridge professorship, he sacrificed brilliant prospects at the Bar and, no doubt, considerably reduced his income; but that was a matter that did not trouble him and, in time, considerably increased his University emoluments.
It was not with Cayley as is too often the case with men of high original faculty in science; he was as admirable a teacher as he was an investigator. While he was cosmopolitan in his mathematics, he was a master in every branch. One of the best judges, Mr. J. W. L. Glaisher, has described him as the greatest living master of algebra." It is well known that Cayley's papers, problems and investigations are often far beyond the comprehension of the ordinary mathematician. This is so well accounted for by Professor Salmon in the excellent paper on Cayley in the series of "Science Worthies," published in Nature, Vol. 28 (to which we express our indebtedness), that we cannot do better than quote the passage: -
As Cayley is not afraid of hard work himself, so it is necessary for the readers of his papers not to be easily discouraged by formidable calculations. But, in my opinion, it is not this so much that makes Cayley's papers difficult to read as the fact that he usually proceeds by the synthetic, not the analytic, method. It usually happens that a mathematical inquirer begins by proposing to himself some comparatively simple question. By the time he has found the answer to it the subject opens on him; the first question suggests others, the theorem first discovered is found to admit of wide generalizations, and perhaps it may be found that these could have been arrived at in quite another way. When the time comes for the inquirer to publish his results to the world, the most attractive course is to take his readers by exactly the same road he has travelled himself, beginning with the simple problem which firmly attracted attention, and lending on step by step to the highest results arrived at. Cayley, on the contrary, usually begins by trying to establish at once the highest generalizations he has solved, writing down equations, and proceeding to make calculations as to the good of which he has not taken his readers into confidence. The consequence is that few master his papers but those who have found a clue to them by some pravious work in the same direction.
With such a professor, of course, it was only students of the highest mathematics, thoroughly in sympathy with their master, that could derive any good from this teaching. But among them he was regarded with a reverence almost akin to worship. We shall not attempt to refer in detail to any of Professor Cayley's work. Mathematicians say that he is likely to be best remembered as the creator of an entirely new tranch of mathematics by his discovery of the Theory of Invariants. Professor Salmon says:-
This has given quite a new aspect to several departments of mathematics. It has introduced such a host of new ideas, and consequently of new words, that a Senior Wrangler of 40 years ago, who had not kept pace with modern investigations, would and, on taking up a book of the present day on geometry or algebra, that he could not read it without a glossary must go to school again to learn what the writer was sposking of. The knowledge which mathematicians now possess of the structure of algebraic formulas is as different from what it was before Cayley's time as the knowledge of the human body possessed by one who has dissected it and knows its internal structure is different from that of one who has only seen it from the outside.
The Royal Society contains the titles of 724 papers and memoirs by Cayley down to 1883, and since then he must have brought the number up to well over 800. These are being collected into a series of ten volumes quarto by the University of Cambridge, and it is to be hoped that the publication will be continued, even although the author and editor has died.
Absorbed as he was in mathematics, Professor Cayley invariably showed his sympathy with human life and interests, and especially with education; he even occasionally manifested an interest in politics. He was an early member of the Alpine Society. He was familiar with many European languages. In 1882 he was invited by the Johns Hopkins University in Baltimore to give a series of lectures, which he did in the winter session of that year. He was president of the Southport meeting of the British Association in 1883, and, as may be imagined, his presidential address was not calculated to arouse much interest among a typical Association audience. From the Royal Society he received both the Royal and the Copley medal. He was in 1890 made an officer of the Legion of Honour by the President of the French Republic, and was an honorary member of many learned societies at home and abroad. As might have been expected, Professor Cayley was a man of the most simple habits and of absolute modesty. He will be missed by not a few warm and devoted friends.
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