“This therefore, is mathematics: she reminds you of the invisible forms of the soul; she gives light to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes oblivion and...

In the beginning of the twentieth century, the University of Göttingen was one of the top research centers for mathematics in the world. The mathematician David Hilbert was a well-established professor there, and during the winter semester of...

In 2012–13, the Institute’s School of Mathematics hosted a special year devoted to the topic “Univalent Foundations of Mathematics,” organized by Steve Awodey, Professor at Carnegie Mellon University, Thierry Coquand, Professor at the University...

From the data, you have this remnant of a real object that you want to resurrect. Before you can start to do that, the first thing you need to know is, is it really coming from such and such an object? Are there some good tests or signatures for that?

In 1900, David Hilbert published a list of twenty-three open questions in mathematics, ten of which he presented at the International Congress of Mathematics in Paris that year. Hilbert had a good nose for asking mathematical questions as the...