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 ...

The geometry we learn in school, the so-called Euclidean geometry, is more than 2,000 years old. About two centuries ago, the Russian mathematician Lobachewsky established a new kind of geometry for ...

An icon in the shape of a lightning bolt. Impact Link We’ve all learned “parallel lines never intersect” in high school geometry. But what your teachers failed to explain is that “parallel lines never ...

THIS work will be found really valuable by all students of geometry, especially by those who know little or nothing of the non-Euclidean theories. First of all we have a discussion of the elementary ...

If you enjoyed this article, I’d like to ask for your support. Scientific American has served as an advocate for science and industry for 180 years, and right now may be the most critical moment in ...

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 ...

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 ...