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Henry John Stephen Smith was born on November 12, 1826, and was the fourth child of his parents. His father, John Smith, was a barrister-at-law, and graduated from Trinity College, Dublin, and afterwards from Brasenose College, Oxford, in order to shorten the residency at the Inns of Court that was required before he could be called to the bar. At the Temple, he was the law pupil of Henry John Stephen, serjeant-at-law, the editor of "Blackstone's Commentaries," and the pupil gave his master's name to the younger of his two sons.
When Henry Smith was just two years old, his father died. There were four children, two sons and two daughters, the eldest of whom, a girl, was but nine years of age; and to their education the widow thenceforth devoted herself. Chiefly in order to give her children the better opportunity of education which England afforded, Mrs. Smith left Ireland, and after spending some time on the Isle of Man, at Harborne near Birmingham, and at Leamington, she moved in 1831 to Ryde, on the Isle of Wight, where she remained for nearly ten years. Mrs. Smith was a most accomplished lady, and an intense delight in learning was one of the ruling impulses of her life. She taught her children herself, and until Henry was over eleven, he remained under her exclusive care and teaching. He was able to read when he was three years old, and while still between four and five he began to display the desire for learning and the capacity for acquiring knowledge that distinguished him ever afterward. When he was between eleven and twelve, his mother, who had been reading Greek plays, Herodotus, and Thucydides with the boys, began to feel unable to cope with the further difficulties of Latin and Greek composition, and Mr. R. Wheler Bush became their tutor for some months. In a letter to the Times of February 12, 1883, Mr. Bush gave an account of his pupil's work, from which the following is an extract:
"In the years 1838-39, Henry Smith, then a boy of eleven years of age, read with me for about nine months at Ryde, on the Isle of Wight. He had previously been taught by his widowed mother, a remarkably clever and highly educated woman. After reading with Henry Smith, I had extensive experience with boys during a headmastership of more than thirty-three years, but I have often remarked that Henry Smith's brilliant talents prevented me from ever being truly astonished at the abilities of any subsequent pupil. His power of memory, quickness of perception, indefatigable diligence, and intuitive grasp of whatever he studied were very remarkable at that early age. What he got through during those few months, and the way in which he got through it, have never ceased to surprise me. From a record which I have before me, I see that during that short time he read all of Thucydides, Sophocles, and Sallust, twelve books of Tacitus, the greater part of Horace, Juvenal, Persins, and several plays by Aeschylus and Euripides. I also see that he got up six books of Enelid, and algebra to simple equations; that he read a considerable quantity of Hebrew; and that, among other things, he learned all the Odes of Horace by heart. I could scarcely understand at the time how he contrived at his early age to translate so well and so accurately the most difficult speeches of Thucydides, without notes or commentary to guide him. He was a deeply interesting boy, singularly modest, lovable, and affectionate."
Mr. Bush was succeeded by two other tutors of less ability, and Mrs. Smith found that adequate teaching for Henry could not be obtained from resident tutors. She accordingly removed him to Oxford in the autumn of 1840, when he became the daily pupil of the Rev. H. Highton. In the summer of 1841, Mr. Highton was appointed to a mastership at Rugby. He was accompanied by his pupil, who, being only fifteen, was disqualified by age from entering the sixth form, although possessing sufficient knowledge. He was placed in the upper fifth and in "the twenty" until the Midsummer holidays of 1842, when, having been allowed the privilege of bidding farewell to Dr. Arnold, as a boy who would commence the next term in the sixth form, he returned home, where the news of Dr. Arnold's sudden death followed him the next day. He went back to Rugby and soon became the head boy under Dr. Tait.
On the death of his elder brother from consumption in September 1843, he was removed from Rugby and remained with his family at Nice through the winter, almost without classical books and without even a Greek lexicon. He spent the summer of 1844 in Switzerland, and at the beginning of October, it was thought that he should return to Rugby for a few weeks' preparation before going to Oxford to try for the Balliol Scholarship in November. He was successful in obtaining the scholarship and joined his family at Rome before Christmas. Though winter was one of great enjoyment to him, he made rapid progress in knowledge and cultivation while diligently studying the antiquities of the city.
He accompanied his family in June 1845 to Frascati, where in August he was struck by malaria, the effects of which invalidated him for nearly two years. The winter was spent at Naples, the malady slowly wearing itself out In May 1846 he was taken to Wiesbaden, where the waters rapidly restored his health. It was not, however, considered expedient that he should resume his interrupted course at Oxford until Easter 1847. The intervening winter was spent in Paris, and like the preceding one, it was a time when he made rapid intellectual progress. He remembered with particular pleasure the lectures of Arago and Milne Edwards. After the Faster term of 1847, he was never absent from Oxford for a single term until his death. In the summer of 1847 he visited Wiesbaden once more, returning with his family to England in October. Until his mother's death in 1857, his vacations were all spent with his family, the Christmas and Easter holidays primarily in London, and the summers in Germany, Switzerland, or Austria.
He won the Ireland Scholarship in the Lent term of 1848, and obtained a first class in both the classical and mathematical schools in the Lent term of 1849. He gained the Senior Mathematical Scholarship in 1851. He was elected a Fellow of Balliol in 1850, and resided in college until 1857, when, after his mother's death, his only surviving sister, Miss Eleanor E. Smith, came to Oxford, and from that time onwards they lived together. He was elected Savilian Professor of Geometry in 1861 in succession to Professor Baden-Powell, and in 1874 he was appointed Kesper of the University Museum. He then moved to the residence attached to the Museum, and lived there with his sister until his death
After taking his degree he wavered between classics and mathematics, but not for long; the latter soon attracted him, and with a power that steadily increased from year to year. His first two papers, which were geometrical, were published in 1852 in the Proceedings of the Ashmolean Society and the Cambridge and Dublin Mathematical Journal. His next paper was titled "De Compositione numerorum primorum forme ex duobus quadratis," was published in Crelle's Journal for 1855. This was his first contribution to the subject to which he was to devote his life, and with which his name will forever be associated. For the ten years from 1854 to 1864, he devoted himself to the Theory of Numbers, the most extensive and the most difficult of all the branches of pure mathematics, and mastered everything that had been published on it. The results of this enormous amount of research are contained in his Report on the Theory of Numbers, which appeared in the British Association volumes from 1859 to 1865. Although incomplete, this magnificent Report occupies nearly 250 pages and forms an enduring monument to the power and genius of its author. It is quite unique of its kind and presents a comprehensive view of the current state of the most intricate department of mathematics, and only those who have had the opportunity to use it can truly appreciate the remarkable grasp the author demonstrated of all the processes and methods and literature of the subject. It is a model of brief, clear, and precise exposition, and is remarkable for the same perfection of form, condensed mode of statement of processes, and what may be termed "mathematical good taste" that distinguished all his work.
Not only does the Report contain a complete account of the wonderful series of discoveries of Gauss and his successors, hut there is also much original matter, though with characteristic modesty it is but rarely that it is distinguished in any way from theorems that are merely quoted But the amount of original work he accomplished was far greater than he could find room for in the Report, and the chief results of his own discoveries were communicated to the Royal Society in two elaborate memoirs: one on systems of linear indeterminate equations and congruences, and the other on the orders and genera of ternary quadratic forms, which were printed in the Philosophical Transactions for 1861 and 1867. The two major divisions into which the Theory of Numbers may be divided are the Theory of Congruences and the Theory of Forms, and these papers contain contributions of the highest generality and importance to both branches of the subject. The solution of the problem of representing numbers by binary quadratic forms is one of Gauss's great achievements, and the fundamental principles upon which the treatment of such questions must rest were given by him in Disquisitiones Arithmeticae. Ganss added some results relating to ternary quadratic forms, but the extension from two to three indeterminates was the work of Eisenstein, who, in his memoir "Neue Theoreme der hohen Arithmetik" (New Theorems of Higher Arithmetic), defined the ordinal and generic characters of ternary quadratic forms of an uneven determinant; and, in the case of definito forms, assigned the weight of any order or genus. But he did not consider forms of an even determinant, nor give any demonstrations of his work, and these omissions are what Professor Smith provided in his extensive memoir on the subject, which affords a complete classification of ternary quadratic forms. Professor Smith, however, did not confine himself to the case of three indeterminates, but succeeded in establishing the principles on which the extension to the general case of n indeterminates depends, and obtained the general formula; thus effecting the greatest advance made in the subject since the publication of Gauss's memorable work that so entirely changed the aspect of the whole Theory of Numbers. A brief account of Professor Smith's methods and results appeared in the Proceedings of the Royal Society (vol. xiii, 1864, pp. 199–203, and vol. xvi, 1868, pp. 197–208) in two notices, "On the Order and Genera of Quadratic Forms Containing More Than Three Indeterminates." In the second of these notices, after giving the general formulale, Prof. Smith remarks that, though the demonstrations are simple in principle, they require attention to a great number of details with respect to which it is very easy to fall into error, and he adds "so soon as they can be put into a convenient form they shall be submitted to the Royal Society;" but unfortunately he was closely occupied with other researches during all that remained of his life, and when death removed him so suddenly last year they still lay unpublished in his notebooks.
In this second notice, he also remarks at the conclusion that the theorems which have been given by Jacobi, Eisenstein, and in such great profusion by Liouville, relating to the representation of numbers by four squares and other simple quadratic forms, are deducible by a uniform method from the principles indicated in the paper, and he proceeds, "So also are the theorems relating to the representation of numbers by six and eight squares, which are implicitly contained in the developments given by Jacobi in the Fundamenta Nova. As the series of theorems relating to the representation of numbers by sums of squares ceases, for the reason assigned by Eisenstein, when the number of squares surpasses eight, it is of some importance to complete it. The only cases which have not been fully considered are those of five and seven squares. The principal theorems relating to the case of five squares have indeed been given by Eisenstein (Crelle's Journal, vol. xxxv, p. 368); but he has considered only those numbers which are not divisible by any square. We shall here complete his enunciation of those theorems, and shall add the corresponding theorems for the case of seven squares." The class of theorems in question (i.e., the number of representations of a number as a sum of squares) was shown by Eisenstein to be limited to eight squares. The solutions in the cases of two, four, and six squares may be obtained by means of elliptic functions, i.e., by purely algebraic methods, but the cases in which the number of squares is uneven involve the special processes peculiar to the Theory of Numbers. Eisenstein gave the solution in the case of three squares, and he also left a statement of the solution he had obtained in the case of five squares. His results, however, were published without demonstration, and applicable only to numbers having a particular form. Fourteen years later, in ignorance of Professor Smith's work, the demonstration and completion of Eisenstein's theorems for five squares were chosen by the French Academy as the subject of their "Grand Prix des Sciences Mathématiques." When Professor Smith saw the announcement of the prize subject in February 1882, his time was engrossed with work relating to elliptic functions, and besides having a great dislike for becoming a competitor, especially under the circumstances, he was very reluctant to leave, even for a short time, his work. At the request, however, of a member of the commission who had proposed the prize, he undertook to write out the demonstration of his general theorems as far as was required to prove the results in the special case of five squares. The dissertation was submitted on the day of his appointment (June 1, 1882), and only a month after his death, in March 1883, the prize of 3,000 francs was awarded to him, with another prize also being awarded to M. Minkowski. No episode could more strikingly illustrate the extent of Professor Smith's research, or the distance he had advanced beyond his contemporaries, than that a question whose solution he had provided in 1867, as a corollary from the general formula governing the entire class of investigations to which it belonged, should have been regarded by the French Academy as one whose solution was of such difficulty and importance as to be worthy of their great prize. It also affords a singular illustration of the little attention that works destined to become classical attract during the lifetime of their creators. In the Royal Society's Proceedings, Professor Smith's statement of his results relating to five squares and seven squares occupies only a single page, but his dissertation (which has been printed by the French Academy), although it relates only to the case of five squares, occupies 72 pages. Many of the proposals contained therein are general, but the demonstrations are not supplied for the case of seven squares. Professor Smith was also the author of important papers in which he succeeded in extending to complex quadratic forms many of Gauss's investigations relating to real quadratic forms.
He was led by his researches on the Theory of Numbers to the Theory of Elliptic Functions; and on this subject he has published results since 1864 scarcely inferior in importance to his achievements in the former theory. His third subject was Modern Geometry, in which he was without a rival in this country, and of which he showed the same perfect mastery. Pure mathematics is divisible into two great branches, the Theory of Numbers, or "Arithmetic," which is the theory of discrete magnitude, and Algebra, the theory of continuous magnitude, the aims and methods of the two subjects being quite distinct. A characteristic of Professor Smith's work, no less than of Gauss's, is the "arithmetical" mode of treatment that runs through the whole of it, no matter what the subject; and his great command over the processes of this science is everywhere conspicuous. Special reference should be made to one of his papers in the Atti of the Accademia dei Lincei for 1877, in which he established a very remarkable analytical relation connecting the modular equation of orders and the theory of binary quadratic forms belonging to the positive determinant n. In this paper, the modular curve is represented analytically by a curve in such a manner as to present an actual geometrical image of the complete systems of the reduced quadratic forms belonging to the determinant, and a geometrical interpretation is given to the ideas of class, equivalence, and reduced form. His papers on Elliptic Functions and the higher singularities of curves were published chiefly in the Proceedings of the Mathematical Society. At the time of his death, he was engaged in a memoir on the "Theta and Omega Functions," which he left nearly complete, with 150 quarto pages of it being in type; the latter portion, however, had not been revised in proof by him. This was the menair which he was forced to put aside for a time, in order to write out from his notes of 1866-67 the dissertation on the problem of five squares for the French Academy. In 1868 he was awarded the Steiner Prize of the Berlin Academy for a geometrical memoir "Sur quelques Problèmes cubiques et biquadratiques." He was asked to contribute to the memorial volume to Chelini, published at Milan in 1881 by Cremona and Beltrami, and he wrote a paper in Latin on continuous fractions. He also wrote the introduction to the collected edition of Clifford's mathematical papers (1882).
Professor Smith's collected mathematical works will be issued by Oxford University Press in two volumes quarto. His lectures on Geometry and Theory of Numbers will also be published as textbooks, the former being reproduced from the notes of pupils who attended them. In the early years of his work he had published his research but sparingly, and it was only as the mass of results accumulated that the necessity for publication pressed upon him.
The excellence and completeness that distinguished all that Gauss ever published was a characteristic of Professor Smith's work, and, as in Gauss's case, it was the result of extreme thought, care, and elaboration. He was a great admirer of Gauss, and the following words of his relating to Gauss are quoted here in their entirety, as they perfectly describe, and in his own language, the objects which Professor Smith himself so successfully kept in view in all that he wrote:
"If we except the great name of Newton (and the exception is one which Gauss himself would have been delighted to make), it is probable that no mathematician of any age or country has ever surpassed Gauss in the combination of an abundant fertility of invention with an absolute rigorousness in demonstration, which the ancient Greeks themselves might have envied. It may be admitted, without any disparagement to the eminence of such great mathematicians like Euler and Cauchy were so overwhelmed by the exuberant wealth of their own creations, and so fascinated by the interest attached to the results they achieved, that they did not greatly care to expend their time arranging their ideas in a strictly logical order, or even establishing them by irrefutable proof propositions which they instinctively felt, and could almost see, to be true. With Gauss the case was otherwise.
It may seem paradoxical, but it is probably nevertheless true, that it is precisely the effort after a logical perfection of form which has rendered the writings of Gauss open to the charge of obscurity and unnecessary difficulty. The fact is that there is neither obscurity nor difficulty in his writings as long as we read them in the submissive spirit in which an intelligent schoolboy is made to read his Euclid. Every assertion that is made is fully proved, and the assertions succeed one another in a perfectly just, analogical order; there is nothing so far of which we can complain about. But when we have finished the porusal we soon begin to feel that our work is but begun, that we are still standing on the threshold of the temple, and that there is a secret which lies behind the veil, and is as yet concealed from No vestige appears of the process by which the result itself was obtained, perhaps not even a trace of the considera- tions which suggested the successive steps of the demonstration. Gauss says, more than once, that for brevity he only gives the synthesis, and suppresses the analysis of his propositions. Pouca sed matura were the words with which he delighted to describe the character which he endeavoured to impress upon his mathematical writings. If, on the other hand, we turn to a memoir of Euler's, there is a sort of free and luxuriant grace- fulness about the whole performance which tells of the quiet pleasure which Euler must have taken in each step of his work; but we are conscious, nevertheless, that we are at an immense distance from the severe grandeur of design which is character of all Gauss's greater efforts. The preceding criticism, if just, ought not to appear wholly trivial, for though it is quite true that in any mathematical work the substance is immensely surpassingly more important than the form, yet it cannot be doubted that many mathematical memoirs of our own time suffer greatly (if we may dare to say so) from a certain slovenliness in the mode of presentation, and that (whatever may be the value of their contents) they are stamped with a character of slight- ness and perishability which contrasts strongly with the adventurous solidity and elear, robust modeling which (we may be sure) will keep the writings of Gauss from being forgotten long after the chief results and methods contained in them have been incorporated into treatises more easily read, and have come to form a part of the common patrimony of all working mathe- maticians. And we must never forget (what in an age so fertile of new mathematical conceptions as our own we are only too apt to forget) that it is the business of mathematical science not only to discover new truths and new methods, but also to establish them, at whatever cost of time and labour, upon a basis of irrefragable reasoning.
"The μαθηματικός πιθανολογῶν has no more right to be listened to now than he had in the days of Aristotle; but it must be acknowledged that since the invention of the 'royal roads' of analysis, defective modes of reasoning and of proof have had a chance of gaining traction which they never had before. It is not the greatest, but it is perhaps not the least, of Gauss's claim to the admiration of mathematicians, that while fully penetrating with a sense of the vastness of the science, he exacted the utmost rigorousness in every part of it, never passed over a difficulty as if it did not exist, and never accepted a theorem as true beyond the limits within which it could actually be demonstrated."
These words describe not only Professor Smith's views but the quality of his own work. His one care was that it should be imperishable; and the words "adamantine solidity" express better than any others could do the character of what he has left. He spared no time or effort to ensure that his work was as complete in its details as in its main results, and that it was as perfect in form as in substance. He wished that what he did should be done for all time, and that it should also receive from his own hand the form which it was to retain.
He was President of Section A of the British Association at Bradford in 1873 and of the Mathematical Society from 1874 to 1876. The presidential addresses he delivered at Bradford and upon vacating the latter office are masterpieces of graceful writing that bear record to his wonderfully extensive knowledge and rare combination of gifts. As an expounder of mathematics before an audience, he was unsurpassed for clarity, and his singular charm of manner gave him a remarkable power of capturing the attention of those present. Perhaps his faultless method of exposition and peculiar grace of manner were never more apparent than at the Mathematical Society on December 12, 1882—the last occasion on which he was ever to lay before a society the results of his remarkable power of penetrating into the innermost structure, as it were, of mathematical truth.
His contributions to general literature were not numerous; a memoir of his friend Professor Conington and an essay on the Plurality of Worlds were the most important. The articles on Arithmetical Instruments and on Geometrical Instruments and Models, which he wrote for the handbook published in connection with the Special Loan Exhibition of Scientific Apparatus at South Kensington in 1876, should also be noted.
He was appointed a member of the Royal Commission on Scientific Instruction and the Advancement of Science in 1870 on the death of Professor W. A. Miller; and he was also a member of the Oxford University Commission, appointed in 1877. In both Commissions, he performed a great deal of very heavy work; and knowing how short the time for which he was to be spared was, it is impossible not to regret the great amount of time and anxiety that were thus exacted from him. A considerable portion of the report of the former Commission, including the part which related to the Universities of Oxford and Cambridge, was drafted by him..
In 1877, on the reconstitution of the managing body of the Meteorological Office, as recommended by the Treasury Commission in 1876, Professor Smith was requested to accept the chairmanship of the new council. This office, which involved weekly visits to London, in addition to council meetings, which usually took place once a fortnight, he still held at his death. During the five and a half years of his presidency, he never missed a meeting, and he always devoted at least two hours to considering the business on the agenda. The minutes were always revised by him in manuscript before they were printed. In 1879, he was requested by the Council to attend the International Meteorological Congress in Rome, where his wide and varied knowledge and great personal influence were felt throughout the entire meeting and contributed greatly to its success.
He was elected a Fellow of the Royal Society in 1861. On April 12 of the same year, he was elected a Fellow of this Society. He was an LL.D. of Cambridge and Dublin.
It is difficult to give an idea of the position Professor Smith held in Oxford and in society generally, so brilliant were his attainments, and so great and so varied his personal and social gifts. In an article on him in the Times of February 10, 1883, it was truly said: "It is probable that of the thousands of Englishmen who knew Henry Smith, scarcely one in a hundred ever thought of him as a mathematician at all. He was a classical scholar of wide knowledge and exquisite taste, and there were few who talked to him on English, French, German, or Italian literature who were not struck by his extensive knowledge, his capacious memory, and his sound critical judgment." The writer might have added that, even of the few who did think of him as a mathematician, there were still fewer who had any suspicion of the place he held in mathematical science, or of his intense devotion to the subject. The following extracts from the Spectator of February 17 will help to convey some impression of his personal character:
"Many even of those who are aware that a man in the fulness of his powers is just dead, whose brilliant intellectual attainments have probably not been surpassed by any other of their English contemporaries may, nevertheless, be surprised at the regret so widely felt and so loudly expressed over the loss of one who wrote no great books, patented no great invention, amassed no fortune, made no famous speeches, and led no conspicuous movement, political or social. Measured by the popular measure of publicity and fame, Professor Henry Smith would hardly seems to most of us to have been one of the great men of the time. Yet it would be difficult, among the world's celebrities, to find one who was his superior in gifts and nature... His mental attainments were of the highest order. A finished classical scholar, a mathematician of some European distinction, a considerable metaphysician, a trained master of most branches of knowledge—literary, economic, and scientific—an adequate linguist, and a man of sound judgment, perfect temper, and wise aptitude for affairs, he combined with his other special excellences a deliriant gaiety of mind and a brilliant conversational power, which made him one of the most accomplished and attractive figures in any educated company in which he moved.
... Vanity or self-seeking, every form of mental intemperance and extravagance, seemed to have no place in anything that he ever said or did... Among the many friends, acquaintances, and admirers whose thoughts have in the last few days been saddened or sobered by the unexpected death of a brilliant man of genius, there are none who will not readily accord Professor Henry Smith the tribute of unaffected respect for what, without extravagance, may be termed his extraordinary powers of mind, his gentle and Lælian wisdom, and the sweetness of character which never made an enemy, lost a friend, or sought a personal advantage for itself." Referring to his influence at Oxford, the article proceeds: "For nearly thirty years no more attractive, brilliant, or genial figure was to be found in the perturbed society of the University. Some happy combination of judgment and temper made him acceptable even to those with whose opinions he had nothing in common. He had the great art of never pressing a victory home, and of bearing defeat with pleasant equanimity." His business acumen, his modesty, his wisdom, and his complete freedom from egotism and dogmatic presumption—a delicate gaiety that never flagged, wit that sparkled without wounding, and which incessantly rose to real brilliance—made him not merely an effective personage in the Oxford world, but universally acceptable in any society, whatever the shade of its opinions. As by degrees his attainments were recognized, both in England and abroad, his influence at Oxford naturally deepened, but neither within nor without the University did he grasp opportunities of notoriety. Such power and authority as he possessed he held without an effort, without solicitation, apparently without any personal satisfaction in them. In offices of friendship he was constant; In any public or civic duty that came in his way, he was unobtrusive; no good or benevolent work ever needed a helping hand, but his was at its service, without ostentation and without any expectation of personal advantage. The notice of him in the Athenaeum closed with the words: "No one, probably, has ever had a larger circle of private friends to lament his loss. He had all the gifts which win and preserve attachment; not only sincerity, constancy, depth of feeling and liveliness of sympathy, but a sweetness and nobility of nature to which no words can render adequate testimony."
In commenting on his nomination as one of the Oxford University Commissioners, Mr. Grant Duff said in the House of Commons: "The Savilian Professor of Geometry is not merely in the first rank of European mathematicians, but he would be a man of very extraordinary achievements even if you could abstract from him the whole of his mathematical accomplishments. He was the most distinguished scholar of his day at Oxford. But Professor Smith's extraordinary achievements are the least of his recommendations for the office of Commissioner. His chief recommendations for that office are the solidity of his judgment, his great experience of Oxford business, his services on the Science Commission, and his conciliatory character, which made him perhaps the only man in Oxford who is without an enemy, as sharp as are the contentions of that very divided seat of learning." Those who knew Professor Smith will feel that even these quotations fail to convey any adequate idea of the extent and brilliance of his achievements and powers.
The amount of time and thought that he devoted to the Royal Commissions, Boards of Delegates at Oxford, the Meteorological Office, and Committees and Councils of Societies was very great, and it seems almost incredible that one who lived such an active and busy life, lived in the midst of men and affairs, should have been the author of intellectual achievements in the most abstract and complicated of the sciences, which will rank as scarcely second to any in the century. His influence and position he owed to his personal qualities alone, and many of those who thought they knew him best had the least idea how incessantly he was occupied with mathematical research. The cold severity of his mathematical writings forms a curious contrast to the brilliant gaiety of his manner, and future generations, who will know him only from his writings, will find it hard to believe what they will find recorded of their anthor. In the character of his work he closely resembles Gauss, but no two lives could be more different
An accident to his leg confined him to his sofa during part of 1882, but he seemed to have nearly recovered from its effects when he was seized with the illness which so soon carried him off. He was a regular attendant at the Council Meetings of this Society, and, at the time of his death, was a Vice-President. At the meeting of Council on February 2, 1883, the writer of this notice received from him at Burlington House a letter—almost the last which he ever wrote—in which he said: "I cannot be at the R.A.S. tomorrow. It is no fault of mine. I shall see you on the ninth, I hope." The ninth was the date of the Anniversary Meeting, but at seven o'clock on that morning he died, and the first words spoken by the President, upon taking the chair, were to announce to the Fellows the loss they had just suffered. He was buried at Oxford on February 13 . Conspicuous among those who stood by his grave was Mr. Spottiswoode, himself so soon to be removed.
J. W. L. G
When Henry Smith was just two years old, his father died. There were four children, two sons and two daughters, the eldest of whom, a girl, was but nine years of age; and to their education the widow thenceforth devoted herself. Chiefly in order to give her children the better opportunity of education which England afforded, Mrs. Smith left Ireland, and after spending some time on the Isle of Man, at Harborne near Birmingham, and at Leamington, she moved in 1831 to Ryde, on the Isle of Wight, where she remained for nearly ten years. Mrs. Smith was a most accomplished lady, and an intense delight in learning was one of the ruling impulses of her life. She taught her children herself, and until Henry was over eleven, he remained under her exclusive care and teaching. He was able to read when he was three years old, and while still between four and five he began to display the desire for learning and the capacity for acquiring knowledge that distinguished him ever afterward. When he was between eleven and twelve, his mother, who had been reading Greek plays, Herodotus, and Thucydides with the boys, began to feel unable to cope with the further difficulties of Latin and Greek composition, and Mr. R. Wheler Bush became their tutor for some months. In a letter to the Times of February 12, 1883, Mr. Bush gave an account of his pupil's work, from which the following is an extract:
"In the years 1838-39, Henry Smith, then a boy of eleven years of age, read with me for about nine months at Ryde, on the Isle of Wight. He had previously been taught by his widowed mother, a remarkably clever and highly educated woman. After reading with Henry Smith, I had extensive experience with boys during a headmastership of more than thirty-three years, but I have often remarked that Henry Smith's brilliant talents prevented me from ever being truly astonished at the abilities of any subsequent pupil. His power of memory, quickness of perception, indefatigable diligence, and intuitive grasp of whatever he studied were very remarkable at that early age. What he got through during those few months, and the way in which he got through it, have never ceased to surprise me. From a record which I have before me, I see that during that short time he read all of Thucydides, Sophocles, and Sallust, twelve books of Tacitus, the greater part of Horace, Juvenal, Persins, and several plays by Aeschylus and Euripides. I also see that he got up six books of Enelid, and algebra to simple equations; that he read a considerable quantity of Hebrew; and that, among other things, he learned all the Odes of Horace by heart. I could scarcely understand at the time how he contrived at his early age to translate so well and so accurately the most difficult speeches of Thucydides, without notes or commentary to guide him. He was a deeply interesting boy, singularly modest, lovable, and affectionate."
Mr. Bush was succeeded by two other tutors of less ability, and Mrs. Smith found that adequate teaching for Henry could not be obtained from resident tutors. She accordingly removed him to Oxford in the autumn of 1840, when he became the daily pupil of the Rev. H. Highton. In the summer of 1841, Mr. Highton was appointed to a mastership at Rugby. He was accompanied by his pupil, who, being only fifteen, was disqualified by age from entering the sixth form, although possessing sufficient knowledge. He was placed in the upper fifth and in "the twenty" until the Midsummer holidays of 1842, when, having been allowed the privilege of bidding farewell to Dr. Arnold, as a boy who would commence the next term in the sixth form, he returned home, where the news of Dr. Arnold's sudden death followed him the next day. He went back to Rugby and soon became the head boy under Dr. Tait.
On the death of his elder brother from consumption in September 1843, he was removed from Rugby and remained with his family at Nice through the winter, almost without classical books and without even a Greek lexicon. He spent the summer of 1844 in Switzerland, and at the beginning of October, it was thought that he should return to Rugby for a few weeks' preparation before going to Oxford to try for the Balliol Scholarship in November. He was successful in obtaining the scholarship and joined his family at Rome before Christmas. Though winter was one of great enjoyment to him, he made rapid progress in knowledge and cultivation while diligently studying the antiquities of the city.
He accompanied his family in June 1845 to Frascati, where in August he was struck by malaria, the effects of which invalidated him for nearly two years. The winter was spent at Naples, the malady slowly wearing itself out In May 1846 he was taken to Wiesbaden, where the waters rapidly restored his health. It was not, however, considered expedient that he should resume his interrupted course at Oxford until Easter 1847. The intervening winter was spent in Paris, and like the preceding one, it was a time when he made rapid intellectual progress. He remembered with particular pleasure the lectures of Arago and Milne Edwards. After the Faster term of 1847, he was never absent from Oxford for a single term until his death. In the summer of 1847 he visited Wiesbaden once more, returning with his family to England in October. Until his mother's death in 1857, his vacations were all spent with his family, the Christmas and Easter holidays primarily in London, and the summers in Germany, Switzerland, or Austria.
He won the Ireland Scholarship in the Lent term of 1848, and obtained a first class in both the classical and mathematical schools in the Lent term of 1849. He gained the Senior Mathematical Scholarship in 1851. He was elected a Fellow of Balliol in 1850, and resided in college until 1857, when, after his mother's death, his only surviving sister, Miss Eleanor E. Smith, came to Oxford, and from that time onwards they lived together. He was elected Savilian Professor of Geometry in 1861 in succession to Professor Baden-Powell, and in 1874 he was appointed Kesper of the University Museum. He then moved to the residence attached to the Museum, and lived there with his sister until his death
After taking his degree he wavered between classics and mathematics, but not for long; the latter soon attracted him, and with a power that steadily increased from year to year. His first two papers, which were geometrical, were published in 1852 in the Proceedings of the Ashmolean Society and the Cambridge and Dublin Mathematical Journal. His next paper was titled "De Compositione numerorum primorum forme ex duobus quadratis," was published in Crelle's Journal for 1855. This was his first contribution to the subject to which he was to devote his life, and with which his name will forever be associated. For the ten years from 1854 to 1864, he devoted himself to the Theory of Numbers, the most extensive and the most difficult of all the branches of pure mathematics, and mastered everything that had been published on it. The results of this enormous amount of research are contained in his Report on the Theory of Numbers, which appeared in the British Association volumes from 1859 to 1865. Although incomplete, this magnificent Report occupies nearly 250 pages and forms an enduring monument to the power and genius of its author. It is quite unique of its kind and presents a comprehensive view of the current state of the most intricate department of mathematics, and only those who have had the opportunity to use it can truly appreciate the remarkable grasp the author demonstrated of all the processes and methods and literature of the subject. It is a model of brief, clear, and precise exposition, and is remarkable for the same perfection of form, condensed mode of statement of processes, and what may be termed "mathematical good taste" that distinguished all his work.
Not only does the Report contain a complete account of the wonderful series of discoveries of Gauss and his successors, hut there is also much original matter, though with characteristic modesty it is but rarely that it is distinguished in any way from theorems that are merely quoted But the amount of original work he accomplished was far greater than he could find room for in the Report, and the chief results of his own discoveries were communicated to the Royal Society in two elaborate memoirs: one on systems of linear indeterminate equations and congruences, and the other on the orders and genera of ternary quadratic forms, which were printed in the Philosophical Transactions for 1861 and 1867. The two major divisions into which the Theory of Numbers may be divided are the Theory of Congruences and the Theory of Forms, and these papers contain contributions of the highest generality and importance to both branches of the subject. The solution of the problem of representing numbers by binary quadratic forms is one of Gauss's great achievements, and the fundamental principles upon which the treatment of such questions must rest were given by him in Disquisitiones Arithmeticae. Ganss added some results relating to ternary quadratic forms, but the extension from two to three indeterminates was the work of Eisenstein, who, in his memoir "Neue Theoreme der hohen Arithmetik" (New Theorems of Higher Arithmetic), defined the ordinal and generic characters of ternary quadratic forms of an uneven determinant; and, in the case of definito forms, assigned the weight of any order or genus. But he did not consider forms of an even determinant, nor give any demonstrations of his work, and these omissions are what Professor Smith provided in his extensive memoir on the subject, which affords a complete classification of ternary quadratic forms. Professor Smith, however, did not confine himself to the case of three indeterminates, but succeeded in establishing the principles on which the extension to the general case of n indeterminates depends, and obtained the general formula; thus effecting the greatest advance made in the subject since the publication of Gauss's memorable work that so entirely changed the aspect of the whole Theory of Numbers. A brief account of Professor Smith's methods and results appeared in the Proceedings of the Royal Society (vol. xiii, 1864, pp. 199–203, and vol. xvi, 1868, pp. 197–208) in two notices, "On the Order and Genera of Quadratic Forms Containing More Than Three Indeterminates." In the second of these notices, after giving the general formulale, Prof. Smith remarks that, though the demonstrations are simple in principle, they require attention to a great number of details with respect to which it is very easy to fall into error, and he adds "so soon as they can be put into a convenient form they shall be submitted to the Royal Society;" but unfortunately he was closely occupied with other researches during all that remained of his life, and when death removed him so suddenly last year they still lay unpublished in his notebooks.
In this second notice, he also remarks at the conclusion that the theorems which have been given by Jacobi, Eisenstein, and in such great profusion by Liouville, relating to the representation of numbers by four squares and other simple quadratic forms, are deducible by a uniform method from the principles indicated in the paper, and he proceeds, "So also are the theorems relating to the representation of numbers by six and eight squares, which are implicitly contained in the developments given by Jacobi in the Fundamenta Nova. As the series of theorems relating to the representation of numbers by sums of squares ceases, for the reason assigned by Eisenstein, when the number of squares surpasses eight, it is of some importance to complete it. The only cases which have not been fully considered are those of five and seven squares. The principal theorems relating to the case of five squares have indeed been given by Eisenstein (Crelle's Journal, vol. xxxv, p. 368); but he has considered only those numbers which are not divisible by any square. We shall here complete his enunciation of those theorems, and shall add the corresponding theorems for the case of seven squares." The class of theorems in question (i.e., the number of representations of a number as a sum of squares) was shown by Eisenstein to be limited to eight squares. The solutions in the cases of two, four, and six squares may be obtained by means of elliptic functions, i.e., by purely algebraic methods, but the cases in which the number of squares is uneven involve the special processes peculiar to the Theory of Numbers. Eisenstein gave the solution in the case of three squares, and he also left a statement of the solution he had obtained in the case of five squares. His results, however, were published without demonstration, and applicable only to numbers having a particular form. Fourteen years later, in ignorance of Professor Smith's work, the demonstration and completion of Eisenstein's theorems for five squares were chosen by the French Academy as the subject of their "Grand Prix des Sciences Mathématiques." When Professor Smith saw the announcement of the prize subject in February 1882, his time was engrossed with work relating to elliptic functions, and besides having a great dislike for becoming a competitor, especially under the circumstances, he was very reluctant to leave, even for a short time, his work. At the request, however, of a member of the commission who had proposed the prize, he undertook to write out the demonstration of his general theorems as far as was required to prove the results in the special case of five squares. The dissertation was submitted on the day of his appointment (June 1, 1882), and only a month after his death, in March 1883, the prize of 3,000 francs was awarded to him, with another prize also being awarded to M. Minkowski. No episode could more strikingly illustrate the extent of Professor Smith's research, or the distance he had advanced beyond his contemporaries, than that a question whose solution he had provided in 1867, as a corollary from the general formula governing the entire class of investigations to which it belonged, should have been regarded by the French Academy as one whose solution was of such difficulty and importance as to be worthy of their great prize. It also affords a singular illustration of the little attention that works destined to become classical attract during the lifetime of their creators. In the Royal Society's Proceedings, Professor Smith's statement of his results relating to five squares and seven squares occupies only a single page, but his dissertation (which has been printed by the French Academy), although it relates only to the case of five squares, occupies 72 pages. Many of the proposals contained therein are general, but the demonstrations are not supplied for the case of seven squares. Professor Smith was also the author of important papers in which he succeeded in extending to complex quadratic forms many of Gauss's investigations relating to real quadratic forms.
He was led by his researches on the Theory of Numbers to the Theory of Elliptic Functions; and on this subject he has published results since 1864 scarcely inferior in importance to his achievements in the former theory. His third subject was Modern Geometry, in which he was without a rival in this country, and of which he showed the same perfect mastery. Pure mathematics is divisible into two great branches, the Theory of Numbers, or "Arithmetic," which is the theory of discrete magnitude, and Algebra, the theory of continuous magnitude, the aims and methods of the two subjects being quite distinct. A characteristic of Professor Smith's work, no less than of Gauss's, is the "arithmetical" mode of treatment that runs through the whole of it, no matter what the subject; and his great command over the processes of this science is everywhere conspicuous. Special reference should be made to one of his papers in the Atti of the Accademia dei Lincei for 1877, in which he established a very remarkable analytical relation connecting the modular equation of orders and the theory of binary quadratic forms belonging to the positive determinant n. In this paper, the modular curve is represented analytically by a curve in such a manner as to present an actual geometrical image of the complete systems of the reduced quadratic forms belonging to the determinant, and a geometrical interpretation is given to the ideas of class, equivalence, and reduced form. His papers on Elliptic Functions and the higher singularities of curves were published chiefly in the Proceedings of the Mathematical Society. At the time of his death, he was engaged in a memoir on the "Theta and Omega Functions," which he left nearly complete, with 150 quarto pages of it being in type; the latter portion, however, had not been revised in proof by him. This was the menair which he was forced to put aside for a time, in order to write out from his notes of 1866-67 the dissertation on the problem of five squares for the French Academy. In 1868 he was awarded the Steiner Prize of the Berlin Academy for a geometrical memoir "Sur quelques Problèmes cubiques et biquadratiques." He was asked to contribute to the memorial volume to Chelini, published at Milan in 1881 by Cremona and Beltrami, and he wrote a paper in Latin on continuous fractions. He also wrote the introduction to the collected edition of Clifford's mathematical papers (1882).
Professor Smith's collected mathematical works will be issued by Oxford University Press in two volumes quarto. His lectures on Geometry and Theory of Numbers will also be published as textbooks, the former being reproduced from the notes of pupils who attended them. In the early years of his work he had published his research but sparingly, and it was only as the mass of results accumulated that the necessity for publication pressed upon him.
The excellence and completeness that distinguished all that Gauss ever published was a characteristic of Professor Smith's work, and, as in Gauss's case, it was the result of extreme thought, care, and elaboration. He was a great admirer of Gauss, and the following words of his relating to Gauss are quoted here in their entirety, as they perfectly describe, and in his own language, the objects which Professor Smith himself so successfully kept in view in all that he wrote:
"If we except the great name of Newton (and the exception is one which Gauss himself would have been delighted to make), it is probable that no mathematician of any age or country has ever surpassed Gauss in the combination of an abundant fertility of invention with an absolute rigorousness in demonstration, which the ancient Greeks themselves might have envied. It may be admitted, without any disparagement to the eminence of such great mathematicians like Euler and Cauchy were so overwhelmed by the exuberant wealth of their own creations, and so fascinated by the interest attached to the results they achieved, that they did not greatly care to expend their time arranging their ideas in a strictly logical order, or even establishing them by irrefutable proof propositions which they instinctively felt, and could almost see, to be true. With Gauss the case was otherwise.
It may seem paradoxical, but it is probably nevertheless true, that it is precisely the effort after a logical perfection of form which has rendered the writings of Gauss open to the charge of obscurity and unnecessary difficulty. The fact is that there is neither obscurity nor difficulty in his writings as long as we read them in the submissive spirit in which an intelligent schoolboy is made to read his Euclid. Every assertion that is made is fully proved, and the assertions succeed one another in a perfectly just, analogical order; there is nothing so far of which we can complain about. But when we have finished the porusal we soon begin to feel that our work is but begun, that we are still standing on the threshold of the temple, and that there is a secret which lies behind the veil, and is as yet concealed from No vestige appears of the process by which the result itself was obtained, perhaps not even a trace of the considera- tions which suggested the successive steps of the demonstration. Gauss says, more than once, that for brevity he only gives the synthesis, and suppresses the analysis of his propositions. Pouca sed matura were the words with which he delighted to describe the character which he endeavoured to impress upon his mathematical writings. If, on the other hand, we turn to a memoir of Euler's, there is a sort of free and luxuriant grace- fulness about the whole performance which tells of the quiet pleasure which Euler must have taken in each step of his work; but we are conscious, nevertheless, that we are at an immense distance from the severe grandeur of design which is character of all Gauss's greater efforts. The preceding criticism, if just, ought not to appear wholly trivial, for though it is quite true that in any mathematical work the substance is immensely surpassingly more important than the form, yet it cannot be doubted that many mathematical memoirs of our own time suffer greatly (if we may dare to say so) from a certain slovenliness in the mode of presentation, and that (whatever may be the value of their contents) they are stamped with a character of slight- ness and perishability which contrasts strongly with the adventurous solidity and elear, robust modeling which (we may be sure) will keep the writings of Gauss from being forgotten long after the chief results and methods contained in them have been incorporated into treatises more easily read, and have come to form a part of the common patrimony of all working mathe- maticians. And we must never forget (what in an age so fertile of new mathematical conceptions as our own we are only too apt to forget) that it is the business of mathematical science not only to discover new truths and new methods, but also to establish them, at whatever cost of time and labour, upon a basis of irrefragable reasoning.
"The μαθηματικός πιθανολογῶν has no more right to be listened to now than he had in the days of Aristotle; but it must be acknowledged that since the invention of the 'royal roads' of analysis, defective modes of reasoning and of proof have had a chance of gaining traction which they never had before. It is not the greatest, but it is perhaps not the least, of Gauss's claim to the admiration of mathematicians, that while fully penetrating with a sense of the vastness of the science, he exacted the utmost rigorousness in every part of it, never passed over a difficulty as if it did not exist, and never accepted a theorem as true beyond the limits within which it could actually be demonstrated."
These words describe not only Professor Smith's views but the quality of his own work. His one care was that it should be imperishable; and the words "adamantine solidity" express better than any others could do the character of what he has left. He spared no time or effort to ensure that his work was as complete in its details as in its main results, and that it was as perfect in form as in substance. He wished that what he did should be done for all time, and that it should also receive from his own hand the form which it was to retain.
He was President of Section A of the British Association at Bradford in 1873 and of the Mathematical Society from 1874 to 1876. The presidential addresses he delivered at Bradford and upon vacating the latter office are masterpieces of graceful writing that bear record to his wonderfully extensive knowledge and rare combination of gifts. As an expounder of mathematics before an audience, he was unsurpassed for clarity, and his singular charm of manner gave him a remarkable power of capturing the attention of those present. Perhaps his faultless method of exposition and peculiar grace of manner were never more apparent than at the Mathematical Society on December 12, 1882—the last occasion on which he was ever to lay before a society the results of his remarkable power of penetrating into the innermost structure, as it were, of mathematical truth.
His contributions to general literature were not numerous; a memoir of his friend Professor Conington and an essay on the Plurality of Worlds were the most important. The articles on Arithmetical Instruments and on Geometrical Instruments and Models, which he wrote for the handbook published in connection with the Special Loan Exhibition of Scientific Apparatus at South Kensington in 1876, should also be noted.
He was appointed a member of the Royal Commission on Scientific Instruction and the Advancement of Science in 1870 on the death of Professor W. A. Miller; and he was also a member of the Oxford University Commission, appointed in 1877. In both Commissions, he performed a great deal of very heavy work; and knowing how short the time for which he was to be spared was, it is impossible not to regret the great amount of time and anxiety that were thus exacted from him. A considerable portion of the report of the former Commission, including the part which related to the Universities of Oxford and Cambridge, was drafted by him..
In 1877, on the reconstitution of the managing body of the Meteorological Office, as recommended by the Treasury Commission in 1876, Professor Smith was requested to accept the chairmanship of the new council. This office, which involved weekly visits to London, in addition to council meetings, which usually took place once a fortnight, he still held at his death. During the five and a half years of his presidency, he never missed a meeting, and he always devoted at least two hours to considering the business on the agenda. The minutes were always revised by him in manuscript before they were printed. In 1879, he was requested by the Council to attend the International Meteorological Congress in Rome, where his wide and varied knowledge and great personal influence were felt throughout the entire meeting and contributed greatly to its success.
He was elected a Fellow of the Royal Society in 1861. On April 12 of the same year, he was elected a Fellow of this Society. He was an LL.D. of Cambridge and Dublin.
It is difficult to give an idea of the position Professor Smith held in Oxford and in society generally, so brilliant were his attainments, and so great and so varied his personal and social gifts. In an article on him in the Times of February 10, 1883, it was truly said: "It is probable that of the thousands of Englishmen who knew Henry Smith, scarcely one in a hundred ever thought of him as a mathematician at all. He was a classical scholar of wide knowledge and exquisite taste, and there were few who talked to him on English, French, German, or Italian literature who were not struck by his extensive knowledge, his capacious memory, and his sound critical judgment." The writer might have added that, even of the few who did think of him as a mathematician, there were still fewer who had any suspicion of the place he held in mathematical science, or of his intense devotion to the subject. The following extracts from the Spectator of February 17 will help to convey some impression of his personal character:
"Many even of those who are aware that a man in the fulness of his powers is just dead, whose brilliant intellectual attainments have probably not been surpassed by any other of their English contemporaries may, nevertheless, be surprised at the regret so widely felt and so loudly expressed over the loss of one who wrote no great books, patented no great invention, amassed no fortune, made no famous speeches, and led no conspicuous movement, political or social. Measured by the popular measure of publicity and fame, Professor Henry Smith would hardly seems to most of us to have been one of the great men of the time. Yet it would be difficult, among the world's celebrities, to find one who was his superior in gifts and nature... His mental attainments were of the highest order. A finished classical scholar, a mathematician of some European distinction, a considerable metaphysician, a trained master of most branches of knowledge—literary, economic, and scientific—an adequate linguist, and a man of sound judgment, perfect temper, and wise aptitude for affairs, he combined with his other special excellences a deliriant gaiety of mind and a brilliant conversational power, which made him one of the most accomplished and attractive figures in any educated company in which he moved.
... Vanity or self-seeking, every form of mental intemperance and extravagance, seemed to have no place in anything that he ever said or did... Among the many friends, acquaintances, and admirers whose thoughts have in the last few days been saddened or sobered by the unexpected death of a brilliant man of genius, there are none who will not readily accord Professor Henry Smith the tribute of unaffected respect for what, without extravagance, may be termed his extraordinary powers of mind, his gentle and Lælian wisdom, and the sweetness of character which never made an enemy, lost a friend, or sought a personal advantage for itself." Referring to his influence at Oxford, the article proceeds: "For nearly thirty years no more attractive, brilliant, or genial figure was to be found in the perturbed society of the University. Some happy combination of judgment and temper made him acceptable even to those with whose opinions he had nothing in common. He had the great art of never pressing a victory home, and of bearing defeat with pleasant equanimity." His business acumen, his modesty, his wisdom, and his complete freedom from egotism and dogmatic presumption—a delicate gaiety that never flagged, wit that sparkled without wounding, and which incessantly rose to real brilliance—made him not merely an effective personage in the Oxford world, but universally acceptable in any society, whatever the shade of its opinions. As by degrees his attainments were recognized, both in England and abroad, his influence at Oxford naturally deepened, but neither within nor without the University did he grasp opportunities of notoriety. Such power and authority as he possessed he held without an effort, without solicitation, apparently without any personal satisfaction in them. In offices of friendship he was constant; In any public or civic duty that came in his way, he was unobtrusive; no good or benevolent work ever needed a helping hand, but his was at its service, without ostentation and without any expectation of personal advantage. The notice of him in the Athenaeum closed with the words: "No one, probably, has ever had a larger circle of private friends to lament his loss. He had all the gifts which win and preserve attachment; not only sincerity, constancy, depth of feeling and liveliness of sympathy, but a sweetness and nobility of nature to which no words can render adequate testimony."
In commenting on his nomination as one of the Oxford University Commissioners, Mr. Grant Duff said in the House of Commons: "The Savilian Professor of Geometry is not merely in the first rank of European mathematicians, but he would be a man of very extraordinary achievements even if you could abstract from him the whole of his mathematical accomplishments. He was the most distinguished scholar of his day at Oxford. But Professor Smith's extraordinary achievements are the least of his recommendations for the office of Commissioner. His chief recommendations for that office are the solidity of his judgment, his great experience of Oxford business, his services on the Science Commission, and his conciliatory character, which made him perhaps the only man in Oxford who is without an enemy, as sharp as are the contentions of that very divided seat of learning." Those who knew Professor Smith will feel that even these quotations fail to convey any adequate idea of the extent and brilliance of his achievements and powers.
The amount of time and thought that he devoted to the Royal Commissions, Boards of Delegates at Oxford, the Meteorological Office, and Committees and Councils of Societies was very great, and it seems almost incredible that one who lived such an active and busy life, lived in the midst of men and affairs, should have been the author of intellectual achievements in the most abstract and complicated of the sciences, which will rank as scarcely second to any in the century. His influence and position he owed to his personal qualities alone, and many of those who thought they knew him best had the least idea how incessantly he was occupied with mathematical research. The cold severity of his mathematical writings forms a curious contrast to the brilliant gaiety of his manner, and future generations, who will know him only from his writings, will find it hard to believe what they will find recorded of their anthor. In the character of his work he closely resembles Gauss, but no two lives could be more different
An accident to his leg confined him to his sofa during part of 1882, but he seemed to have nearly recovered from its effects when he was seized with the illness which so soon carried him off. He was a regular attendant at the Council Meetings of this Society, and, at the time of his death, was a Vice-President. At the meeting of Council on February 2, 1883, the writer of this notice received from him at Burlington House a letter—almost the last which he ever wrote—in which he said: "I cannot be at the R.A.S. tomorrow. It is no fault of mine. I shall see you on the ninth, I hope." The ninth was the date of the Anniversary Meeting, but at seven o'clock on that morning he died, and the first words spoken by the President, upon taking the chair, were to announce to the Fellows the loss they had just suffered. He was buried at Oxford on February 13 . Conspicuous among those who stood by his grave was Mr. Spottiswoode, himself so soon to be removed.
J. W. L. G
Henry Smith's obituary appeared in Journal of the Royal Astronomical Society 44 (1884), 138-149.