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
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
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
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...