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 ...

Grid cells, space-mapping neurons of the entorhinal cortex of rodents, could also work for hyperbolic surfaces. A new study tests a model (a computer simulation) based on mathematical principles, that ...

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 ...