What is a group? Algebraists teach that this is supposedly a set with two operations that satisfy a load of easily-forgettable axioms. This definition provokes a natural protest: why would any sensible person need such pairs of operations? [...]
What is a smooth manifold? In a recent American book I read that Poincaré was not acquainted with this (introduced by himself) notion and that the “modern” definition was only given by Veblen in the late 1920s: a manifold is a topological space which satisfies a long series of axioms.
For what sins must students try and find their way through all these twists and turns? Actually, in Poincaré’s Analysis Situs there is an absolutely clear definition of a smooth manifold which is much more useful than the “abstract” one.
(Interesting talk, do read.)
Sir William Jones is incorrectly viewed as the discoverer of the Indo-European language family and founder of modern historical linguistics [...]
The second and more important point is that Jones cannot be considered the founder of modern historical linguistics because he did not use the comparative method, the crucial innovation that distinguishes modern historical linguistics from its predecessors.
Sigh. Let’s not forget people who actually caused us to perceive the world differently, and leave it to pedantic types to define who invented what.
Update: Some background. In 1786, William Jones gave the third annual discourse at the Asiatic Society which he had founded in Calcutta, and observed similarities between Sanskrit and Greek/Latin, and postulated that they had a common origin in a possibly extinct language (now known as Proto-Indo-European). Specifically, he said the following (which is quoted in at least 620 books according to Google):
The Sanscrit language, whatever be its antiquity, is of a wonderful structure; more perfect than the Greek, more copious than the Latin, and more exquisitely refined than either, yet bearing to both of them a stronger affinity, both in the roots of verbs and the forms of grammar, than could possibly have been produced by accident; so strong indeed, that no philologer could examine them all three, without believing them to have sprung from some common source, which, perhaps, no longer exists; there is a similar reason, though not quite so forcible, for supposing that both the Gothic and the Celtic, though blended with a very different idiom, had the same origin with the Sanscrit; and the old Persian might be added to the same family.
This caused a great furore, made everyone sit up and take notice, captured their imagination, and set them to work discovering similarities and doing historical linguistics or comparative linguistics or whatever it’s called. It may be true (it is) that others had hypothesised common origins before Jones did, and that Jones’s methods were flawed, but the fact is that (whether with superior rhetoric, or by being in the right circumstances, or out of just random chance) Jones was the one who made headlines and caused later work.
So it is fine to say that he was not the “founder of modern historical linguistics”, but to say that his role has “often been over-estimated”…