Speaker
Description
WIlliam Rowan Hamilton, Royal Astronomer of Ireland from 1827 to 1865, was one of the most prolific and brilliant mathematicians of the XIX century. Mostly known among physicists for his early works in optics and dynamics, starting from 1843 Hamilton devoted himself almost exclusively to the development of quaternions, new mathematical objects he invented in the attempt to extend complex numbers to tridimensional space. Today quaternions are usually remembered as the first example of non-commutative calculus and as an important milestone in the advent of modern abstract algebra. However, in Hamilton’s own view, quaternions were first and foremost geometric objects expressing the intrinsic and coordinate-independent relationship between two directed lines in space. This aspect, which has been often overlooked by later commentators, was clearly perceived by Peter Guthrie Tait, who in 1858 started a long correspondence with Hamilton and became his only true pupil about quaternion methods. In particular, Tait was puzzled by Hamilton’s use of differentials as finite quantities which can be manipulated according to well-defined rules. In this communication I will discuss two unpublished letters from Hamilton to Tait (Letters V and X, MSS TCD/2172) in which the master explained his general view of differential calculus and how, in generalizing its notions to quaternions, he was guided by a re-interpretation of Newton’s geometrical method of the Principia. The result is a new, powerful and coordinate-independent approach to the problem of motions that is extremely interesting, and essential to understand all the physical applications of quaternions.