# [ Mathematics; Fermat's ] Four substantial Autograph Letters Signed and one APC Signed "J.M. Child" to "Sir Richard [Harington]", on mathematical themes including Fermat's.

Five letters and a postcard, two letters 8vo (total 4pp.), three 4to (total 17 pages), fold marks, good condition. LETTER ONE (6pp., 4to,, 10 Feb.) He starts, "You've done it!!! | I told you that one of your ideas would bear fruit one of these days, and it was a mistaken statement, at least one I think is mistaken, that set me off on a new track which led to success. I've got a [prvot?] for [two algebraic statements given] that is not only foolproof but I'll wager it is the proof used by Fermat." He goes on to give an autobiography, details of education and his ambition to be a mathematician being "knocked out" and accepting teaching elementary maths.He goes on to discuss Fermat;s purchase of "Bachet de Meregrac's edition of Diophantes" and Fermat's work on it ("[…] therefore Fermat could not do it without continued fractions - therefore Fermat could not. In other works Fermat's proof was unsound or he was a liar. | I determined to prove the 'M' was a liarand actually published a little pamphlet in which I think I had rediscovered Fermat's proof without contunued fractions." He had started on his "life's work" "to reconstruct from the beginning the work of Fermat on Theory of Numbers using only the notes by Heath in Diophantes." He has sent a batch of stuff for Harington to work through. The letter ends with two pages of calculations. LETTER TWO (1page, 8 Nov.): Anyway in acknowledgment of your kindness and valuable hints (even if I had to give a twist to them, they provided valuable suggests) I herewith let you be the first person to see [phrase underlined] what I believe is Fermat's original proof [phrase underlined] without the use of any mathematics higher that [sic] Sixth Form (or lower) at school; LETTER THREE (10PP. 4to, 8 Nov.): Mainly mathematics in which he investigates (solves) Fermat's "challenge to English mathematicians - to find the smallest solution of x2 - 6lg2 = 1[..]". The next nine pages comprise mathematical formulae and discussion and he concludes the letter: "I am not patting myself on the back for producing [underlined] a proof of Fermat's great or last theorem: but I am patting myself on the back, front, head and feet for a long and arduous bit of detective work. For, if this solution contains a flaw, I'll bet a £1000 … to a penny it is Fermat's [underlined] Proof. And that's all I was after - to show the know-also that Fermat was neither deluding himself nor was he a liar."; LETTER FOUR (2pp., 8vo, 11 Nov.). He has typed out the last (solution" and feels it is not wrong but "incomplete". He has to consider a "case" (formula given - odd or even). LETTER FIVE( 2pp., 8vo, 15 Nov.): Further discussion of the "uniqueness" of a mathematical statemment, Fermat or one of his correspondents givng a "general solution of the 'sum of three cubes equal to a cube'". Postcard dated Feb 21st (i.e. he says it will be some time before he publishes as I'm going on to the nth powers now I've done the cube, and I'm afraid, if some Great M. saw the method he'd do the rest a couple of hours. At present it's evading me." Note: Works by Child include: The Early Mathematical Manuscripts Of Leibniz (1920); The geometrical lectures of Isaac Barrow, (Chicago, London, Open Court Publishing Company, 1916), also by Isaac Barrow ; The geometrical lectures of Isaac Barrow translated, with notes and proofs, and a discussion on the advance made therein on the work of his predecessors in the infinitesimal calculus, (Chicago, London, Open Court Pub. Co., 1916), also by Isaac Barrow; A theory of natural philosophy / (Chicago : Open Court, 1922); AND works on geometry, calculus and higher algebra: 2. J.M. Child, FORMERLY LECTURER IN MATHEMATICS IN THE UNIVERSITY OF' MANCHESTER LATE HEAD OF MATHEMATICAL DEPARTMENT, TECHNICAL COLLEGE, DERBY FORMERLY SCHOLAR AT JESUS COLLEGE, CAMBRIDGE