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 1924–25...

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Infinity

During a visit to the Institute in the 1970s, the mathematician John Horton Conway, then of Cambridge, spent the ten most interesting minutes of his life. Invited to deliver a talk to the undergraduate math club at Princeton, Conway made his way...

Richard Schwartz, Member (2003–04) in the School of Mathematics and the Chancellor’s Professor of Mathematics at Brown University, discusses really large numbers, as well as the different sizes of infinity and the different forms of infinite space.

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 ones on...

I sometimes like to think about what it might be like inside a black hole. What does that even mean? Is it really “like” anything inside a black hole? Nature keeps us from ever knowing. (Well, what we know for sure is that nature keeps us from...

It is noteworthy that as between two proofs of a theorem mathematicians will prefer the one which, as they say, is more “elegant,” a term which has primarily an aesthetic rather than a logical significance. It is a striking fact that creative...

This 2007 lecture by Enrico Bombieri, Professor Emeritus in the School of Mathematics, explores how mathematics has arrived at its present pragmatic view of infinity and some of the counterintuitive paradoxes, as well as some of the positive results...