**Thomas Scott Fiske**'s parents were Thomas Scott Fiske Sr. and Clara Pittman. The book [1], published in 1867, clearly cannot mention the subject of this biography. However, it mentions his father, Thomas Scott Fiske Sr., who was the first son of David Fiske (born 1792) and his first wife Abigail Nourse. David and Abigail Fiske married in January 1823. David Fiske was a farmer and deacon in the Congregational Church of Amherst. Thomas Scott Fiske Sr. (born 22 November 1823) was David and Abigail Fiske's first child. He [1]:-

Both Thomas Scott Fiske Sr. and Clara Pittman were descended from English families. Thomas Scott Fiske Jr, the subject of this biography, had a younger brother James Porter Fiske who was born in New York City on 22 November 1866. James Porter Fiske became a surgeon and we shall say a little more about him later in this biography. Thomas Scott Fiske Jr attended the Old Trinity Church School in New York City, then the Pingry School in Elizabeth, New Jersey. Fiske entered Columbia College in 1882, thirty years before it became Columbia University, receiving his A.B. in 1885 and his A.M. in 1886. From 1886 to 1888 he was both an assistant at Columbia College and undertaking research for his doctorate.... emigrated to St Louis about1848.[He]removed thence, at an early day, to New Orleans, and subsequently to California, where he engaged in the banking business, amassed some property, and returned East ...

In 1887, in Fiske's second year of graduate studies, Howard Van Amringe suggested that he should spend at least six months in England at the University of Cambridge. He arrived with letters of introduction written by G L Rives, a trustee of Columbia College who had been a fifth wrangler in the mathematical tripos at Cambridge in 1872. With letters addressed to Arthur Cayley, James Glaisher, Andrew Forsyth and George Darwin, Fiske was well placed to take advantage of his time at Cambridge. He writes in [8]:-

Back in the United States, Fiske completed his research being awarded his doctorate in 1888 after submitting his thesis... on my arrival at Cambridge I was treated as a guest and was invited to attend any mathematical lectures whatsoever in which I might be interested. Scientifically I benefited most from the instruction and advice of Forsyth and from my reading with Dr H W Richmond, who consented to give me private lessons. However, from Dr J W L Glaisher, who made me an intimate friend, who spent many an evening with me in heart to heart talks, who took me to meetings of the London Mathematical Society and the Royal Astronomical Society, and entertained me with gossip about scores of contemporary and earlier mathematicians, I gained more in a general way than from anyone else. As for Cayley, I had attended only a few of his lectures on the 'Calculus of the Extraordinaires' when one day he slipped on the icy pavement and suffered a fracture of the leg which brought the lectures to an end. Before the end of my stay, however, I had the pleasure of dining with Mr and Mrs Cayley in their home.

*The Theory of Concomitants of Algebraic Form*. He was appointed as a tutor in mathematics at Columbia University in 1888 and was successively promoted to instructor in 1891, adjunct professor in 1894, and full professor in 1897. He held the post of professor at Columbia from then until he retired in 1936. We will give more details below of the roles he played both nationally and at Columbia University. However, let us record here that from 1889 to 1895 he was in charge of instruction in mathematics at Barnard College and acted as Dean of Barnard College in 1899.

Fiske is of little importance as a research mathematician. He published a few papers on elliptic integrals and surface integrals during his career, as well as a number of papers on mathematical education. Later in his career he wrote some encyclopaedia articles on elliptic functions, functions of real and complex variables and a couple of others. He was the author of 'Theory of Functions of a Complex Variable' which was contained in Merriam and Woodward's *Course of Higher Mathematics*. Fiske's monograph *Theory of Functions of a Complex Variable* was published by John Wiley & Sons in 1906.

His real importance, however, is that he was the founder of the American Mathematical Society in 1888. He writes in [8]:-

He announced the first meeting of the new society with the following message:-On my return to New York I was filled with the thought that there should be a stronger feeling of comradeship among Americans who were interested in mathematics, and I proposed to two fellow students, Jacoby and Stabler, that we should try to organise a local mathematical society.

He described the reaction in [8]:-It is proposed by some recent students of the graduate school of Columbia College to establish a mathematical society for the purpose of preserving, supplementing, and utilizing the results of their mathematical studies.

In early 1891 they began to prepare to publish aOn November24,1888, we three, together with Professors Van Amringe and Rees and a graduate student, Maclay, met for the purpose of organising a New York Mathematical Society. We agreed upon the desirability of joining to our group all mathematicians resident in New York and the neighbourhood. However, at the end of the first year our society had only eleven members. In December,1889, five new members were admitted including McClintock and Pupin. Five members were admitted during1890; one in January,1891; and one in February,1891.

*Bulletin*. Fiske designed the size and colour of the cover to be the same as James Glaisher's

*Messenger of Mathematics*where he had published papers written using the material from his thesis. The style of the

*Bulletin*was, however, more modelled on the French

*Bulletin des Sciences Mathématiques*and the German

*Zeitschrift für Mathematik und Physik*. Soon, the members of the New York Mathematical Society realised that, for a number of reasons, it was being considered as a national society and they changed its name to the American Mathematical Society in 1894. Fiske served the new Society in a variety of ways, for example as secretary from 1888 to 1895, as treasurer from 1890 to 1891, as editor-in-chief of the

*Bulletin*of the American Mathematical Society from 1891 to 1899, as vice-president of the Society from 1898 to 1901, as editor of the

*Transactions*of the American Mathematical Society from 1899 to 1905 and as president of the Society from 1903 to 1904. On 29 December 1904 Fiske delivered his Presidential Address to the Eleventh Annual Meeting of the American Mathematical Society. He chose as his topic

*Mathematical Progress in America*. Fiske said [10]:-

In tracing the development of pure mathematics in America it seems convenient to recognize three periods. The first period extends from colonial days up to the establishment of the Johns Hopkins University in1876; the second period extends from the establishment of the Johns Hopkins University up to1891, when the New York Mathematical Society took on a national character and began the publication of its 'Bulletin'; the third period extends from1891up to the present time.

R C Archibald [3] talks of:-

On 1 February 1913, Fiske married Natalie Page of New York City. We promised above to give more details of Fiske's roles both within Columbia University and also broader roles. He was appointed as secretary of the College Entrance Examination Board in 1902 and he was appointed chairman of the Committee on Instruction, Columbia University Faculty of Pure Science in 1910. He was a fellow of the American Association for the Advancement of Science, and a member of the Association of Teachers of Mathematics of Middle States and Maryland, being president of that Association in 1905-1906. He was the first chairman of Council of American Federation of Teachers of Mathematics and the Natural Sciences in 1906-1907, chairman of the Committee on Mathematical Examinations in America, International Commission on Teaching of Mathematics, 1911, and examiner in Mathematics, New York State Education Department, 1909-1911.... the enormous debt which the Society owes to its able Founder, whose enthusiastic activities on her behalf during the first fifteen years of her existence, were so unremitting and so wise.

Fiske was on the staff at Columbia University for 48 years and, of course, he taught many courses and had many different colleagues through these years [11]:-

We choose to take an example of one year, namely 1920-21, and look at the Mathematics Department at Columbia and see which courses were being taught in that year. Fiske was teaching two courses: 'Fundamental concepts in mathematics'; and 'Theory of functions'. W(illiam) Benjamin Fite (1869-1932) was teaching 'Advanced calculus', and 'Differential equations'; Frank Nelson Cole was teaching 'Algebra'; George Adams Pfeiffer (1889-1943) was teaching 'Analysis situs'; Joseph Fels Ritt was teaching 'Topics in theory of functions'; Edward Kasner was running the 'Seminar in differential geometry'; David Eugene Smith was teaching 'History of mathematics', and 'Practicum in the history of mathematics'; while Cassius Jackson Keyser (1862-1947) was teaching 'Philosophy of mathematics'. Keyser had enrolled as a graduate student at Columbia University, earning the MA in 1896 and the Ph.D. in 1901. He spent the rest of his career at Columbia, becoming the Adrain Professor of Mathematics (1904-27) and Head of the department (1910-16). He retired in 1927.He was an enthusiastic lecturer, equally interested in undergraduate and graduate work, inspiring many students. His main courses were in the theory of functions and differential equations.

At about the time we have chosen to look at the mathematics courses at Columbia University, a young student Carolyn Eisele was beginning her undergraduate studies there. Eisele went on to become a world leading expert on C S Peirce and was appointed as a professor of mathematics at Hunter College. She is the author of [6] and she ends that paper by explaining that what she has written:-

We promised near the beginning of this biography to say a little about Fiske's brother, James Porter Fiske. James also studied at Columbia University but he became a medic, qualifying with an M.D. from the College of Physicians and Surgeons in 1891. He practised in New York City, specialising in surgery and correction of deformities in children. In 1941, when James Fiske was 74 years old, he was killed in a three car collision while returning from Los Angeles to New York. The article [5] states:-... is in part not only a tribute to the mathematical and logical ingenuity of one C S Peirce but to that most enthusiastic promoter of the cause of mathematics, Thomas S Fiske. Since the last quarter century has been devoted to adding mathematical and scientific brushstrokes to the Peirce portrait, the writer now recalls with great satisfaction the impact of the Fiske lectures in a graduate course at Columbia University in the mid-twenties. In those days Columbia University was not granting doctorates in mathematics to women. In the course of sympathizing with my friend Helen and myself and advising us on a future course of action, Professor Fiske walked us merrily down Broadway to42^{nd}Street one evening after class, all the while plying us with fruit from the stands along the line in those different times. How much one might have learned from him about the C S Peirce who was to absorb so much of the writer's attention so many years later!

Due to the illness of Professor Fiske, he has not been told of his brother's death.

**Article by:** *J J O'Connor* and *E F Robertson*