IN a recent number of NATURE (June 30) there appeared a review of a book by G. Mannoury on the philosophy of mathematics, and the reviewer emphasised a statement of the author to the effect that the ...

Non-Euclidean geometries occupy much of the book’s latter half, and their discovery is a fascinating episode of intellectual history. Euclid’s parallel postulate amounts to saying that, given a line ...

In 1847, an eccentric British mathematician named Oliver Byrne released a new edition of Euclid’s famous mathematical treatise, The Elements of Geometry. Byrne added a rather longwinded but ultimately ...

Bernhard Riemann was a man with a hypothesis. He was confident that it was true, probably. But he didn’t prove it. And attempts over the last century and a half by others to prove it have failed. A ...

IT is interesting to compare the attitudes of the two most recent writers in English who deal with Euclidean geometry. Sir Thomas Heath, in the second edition of his three-volume translation of the ...