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 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 ...

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 ...

Quantum Computing Live 'quantum network' being tested in New York — overcoming key hurdles could bring us closer to an 'unhackable' internet Exoplanets Scientists identify 10,000 'impossible' ...