Trinity College, Cambridge
May 23. 1836
My dear Talbot
I have got your paper in my possession & I have read it with great interest & pleasure. I do not feel myself quite authorized to report upon it, untill I have finished a more careful study of Legendre’s <1> comment on Abel’s theorem <2> than I have ever read before. What a pity it is, that you suppressed your discovery so long. The report will be made this week. I am glad that you have been attending to Jerrards <3> papers of the general solution of equations of high orders. I know his brother & they have been referred to me with greater importunity than I like. I must study them carefully before the Bristol meeting <4> which is no slight task. Hamilton <5> has I believe found out the fallacy or at least he says that he has done so & he is not likely to be mistaken for next to Jacobi, <6> he is the greatest analyst of this age. It is a very difficult thing to form a negative, in speculations of this kind. I hope you will approfondir this subject & if you clearly see the fallacy, that you will state it. Lubbock <7> was disposed to think, that in a certain sense he had solved the problem
My dear Talbot
Most Truly yours
Wm H. F. Talbot Esq
1. Adrien Marie Legendre, Traité des fonctions elliptiques et des intégrals eulériennes avec des tables pour en faciliter le calcul numérique (Paris: Huzard-Courcier) 1825. Supplements printed 1828.
2. Niels Henrik Abel (1802–1829), mathematician wrote his theorem in 1824. It was lost in Paris, re-discovered in 1828, and proved the impossibility of solving equations of the fifth degree (quintic equations) through the use of radicals.
3. George Jerrard (1804–1863), mathematician, generalized Erland Bring’s 1786 reduction of a quintic equation to show that a transformation could be applied to an equation of a degree of n to remove several of the terms. It is believed that he knew nothing of Bring’s reduction, and the removal of terms was not considered to be an adequate solution of the problem of equations above the quadratic.
4. The Sixth Meeting of the British Association for the Advancement of Science took place in August 1836.
5. Sir William Rowan Hamilton (1805–1865), Irish mathematician.
6. Carl Gustav Jacob Jacobi (1804–1851).
7. Sir John William Lubbock, 3rd Baronet (1803–1865), mathematician & astronomer.