It may contain inaccuracies due to the limitations of machine translation. A dialogue on how questioning a 2,000-year-old truth gave birth to a new geometry that reshaped mathematics and our ...

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 ...

Euclidean geometry is a mathematical well-known system attributed to the Greek mathematician Euclid of Alexandria. Euclid's text Elements was the first systematic discussion of geometry. It has been ...

Debates over how geometry is understood and learned date back at least to the days of Plato, with more recent scholars ...

Euclid’s Elements, which presented the state of the art in geometry around 300 B.C., has been extraordinarily influential. This massive, 13-volume compendium set the standard for mathematical ...

Geometry may be one of the oldest branches of mathematics, but it’s much more than a theoretical subject. It’s part of our everyday lives, says Professor Jennifer Taback, and key to understanding many ...

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 ...

This originally appeared in the July/August issue of Discover magazine as "Your Hyperbolic Mind." Support our science journalism by becoming a subscriber. The human brain is both a marvel and 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 ...