A plea for simpler theorems

Extract

The best mathematicians, from the days of Euclid and before, have defined the terms they use. Now a definition may be a complete fraud, and Euclid was a case in that which hath no part; although to be fair to our greatest text book writer, I am sure he knew a fraud when he perpetrated one. On the other hand, a definition may be a perfect hidden gem. That mighty man Eudoxus was able to define what was meant by the equality of r₁ and r₂, without knowing what r₁ and r₂ were. A lesser man would have thought that impossible, but Eudoxus was not a lesser man, by definition. Euclid and Eudoxus, those great definers, would be proud of much of what we now do in the way of definition. There are still frauds, such as definition by example, so beloved of biologists and new mathematicians. (By the latter we mean those persons who consider their business to be new maths.) And there is that modern phenomenon, the railway definition, where properties are hitched together in series just like the carriages of a train, to create one monster definition, which, on the face of it, and sometimes not only superficially, has no justification and no relevance.