Mathematics is distinguished from the sciences by the freedom it enjoys in choosing basic assumptions from which consequences can be deduced by applying the laws of logic. We call the basic ...

Automated theorem proving in geometry systems unites symbolic logic, computer algebra and machine learning to verify and discover geometric propositions without human intervention. Historically rooted ...

Mathematical knowledge has puzzled philosophers for millennia. The LSE’s own Imre Lakatos coined the term “Euclidean Programme” for the historically dominant way of thinking about this phenomenon. In ...

There is no satisfactory theory of three-dimensional non-Euclidean geometry, from an intuitional point of view, unless it gives us a clear three-dimensional image in our ordinary space, assuming, of ...

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 ...