Todhunter was sent to a school in Hastings but did not show any promise even being described as 'unusually backward'. However, after being sent to a new school set by J B Austin from London, Isaac made excellent progress.
After leaving school he became an assistant school master at a school in Peckham but attended evening classes at London University where he was taught by De Morgan. He passed the entrance examinations and won a scholarship to study mathematics at London University, where, in addition to De Morgan, he was taught by Sylvester. While taking his degree course Todhunter also worked as a mathematics teacher at a large school in Wimbledon. He obtained a BA from University College London in 1842 and then an MA in 1844 with a prize for the top mark in the examination.
He went to St John's College Cambridge, entering the College in 1844 and becoming senior wrangler and Smith's prizeman in 1848. He was elected a fellow of the college in 1849 and taught there for 15 years. He also undertook work as a private tutor and P G Tait and E J Routh were among his pupils. One of his pupils was Leslie Stephen, the father of the author Virginia Woolf, who studied mathematics at Cambridge with Todhunter as his tutor. Stephen gave a delightful description of Todhunter as follows:-
He lived in a perfect atmosphere of mathematics: his books, all ranged in the neatest order, and covered with uniform brown paper, were mathematical. His talk, to us at any rate, was one round mathematics. Even his chairs and tables strictly limited to the requirements of pupils, and the pattern on his carpet, seemed to breath mathematics. By what mysterious process it was that he accumulated stores of miscellaneous information and knew all about the events of the time (for such I afterwards discovered to be the fact) I have never been able to guess. Probably he imbibed it through the pores of his skin. Still less can I imagine how it came to pass that he published a whole series of excellent mathematical works. He probably wrote them in momentary interstices of time between one pupil's entering his sanctum and another leaving it.In  there is a description of Todhunter's interests which suggests that he had more interests outside mathematics than his students realised:-
Todhunter's life was mainly that of a studious recluse. His sustained industry and methodical distribution of his time enabled him to acquire a wide acquaintance with general and foreign literature; and besides being a sound Latin and Greek scholar, he was familiar with French, German, Spanish, Italian, and also Russian, Hebrew, and Sanscrit. He was well versed in the history of philosophy, and on three occasions acted as examiner for the moral sciences tripos. His habits and tastes were singularly simple; and to a gentle kindly disposition he united a high sense of honour, a warm sympathy with all that was calculated to advance the cause of genuinely scientific study in the university, and considerable humour.
Todhunter married Louisa Anna Maria Davies. They had four children Edward (born 1867), Arthur (born 1869), Agnes (born 1870),and Herbert (born 1875).
Todhunter progressed from fellow to principal mathematical lecturer at St John's College where he resisted all attempts to reduce the central role of Euclid in mathematics courses. Sylvester had said in his British Association address of 1869:-
I should rejoice to see ... Euclid honourably shelved or buried deeper than ever did plummet sound, out of the schoolboy's reach....Todhunter replied:-
Whatever may have produced the dislike to Euclid in the illustrious mathematician..., there is no ground for supposing that he would have been better pleased with the substitutes which are now offered and recommended in its place.Todhunter was always ready to respond to arguments and when Tait said:-
From the majority of the papers in our few mathematical journals, one would almost be led to fancy that British mathematicians have too much pride to use a simple method, while an unnecessarily complex one be had.Todhunter replied:-
I take down some of these volumes, and turning over the pages I find article after article by Profs Cayley, Salmon and Sylvester, not to mention many other highly distinguished names. The idea of amending the elaborate essays of these eminent mathematicians seems to me something like the audacity recorded in poetry with which a superhuman hero climbs to the summit of the Indian Olympus and overturns the thrones of Vishnu, Brahma and Siva.In 1864 Todhunter resigned his fellowship at St John's College, which he was forced to do as he wished to marry. His marriage to Louisa Anna Maria Davies took place on 13 August 1864. Todhunter had been elected a fellow of the Royal Society in 1862. He became a founding member of the London Mathematical Society in 1865 along with De Morgan.
In 1874 Todhunter was elected as an honorary fellow of St John's College but he was taken ill in 1880 and, from that time on, his health deteriorated. He became progressively more paralysed with an illness which led to his death.
Todhunter is best known for his textbooks and his writing on the history of mathematics. Among his textbooks are Analytic Statics (1853), Plane Coordinate Geometry (1855), Examples of Analytic geometry in Three Dimensions (1858). He also wrote some more elementary texts, for example Algebra (1858), Trigonometry (1859), Theory of Equations (1861), Euclid (1862), Mechanics (1867) and Mensuration (1869).
Among his books on the history of mathematics are A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace (1865, reprinted 1965) and History of the Mathematical Theories of Attraction (1873).
The wide circulation of his books is described in :-
No mathematical treatises on elementary subjects probably ever attained so wide a circulation; and, being adopted by the Indian government, they were translated into Urdu and other Oriental languages.Todhunter received many awards for his contributions to mathematics. In addition to the fellowship of the Royal Society he served on its Council in 1874, the same year in which he was awarded the Adams Prize for his work Researches on the calculus of variations.
Article by: J J O'Connor and E F Robertson