"Theoretical mathematics"
Очень интересная дискуссия о математической строгости и многом-многом другом

"Theoretical mathematics'': Toward a cultural synthesis of mathematics and theoretical physics
Arthur Jaffe, Frank Quinn

On proof and progress in mathematics
William P. Thurston
(вот это просто не могу не процитировать:

An interesting phenomenon in spatial thinking is that scale makes a big difference. We can think about little objects in our hands, or we can think of bigger human-sized structures that we scan, or we can think of spatial structures that encompass us and that we move around in. We tend to think more effectively with spatial imagery on a larger scale: it’s as if our brains take larger things more seriously and can devote more resources to them.

Про подобные штуки много интересного объясняется в замечательной книге Александра Боровика Mathematics Under The Microscope.)

Responses to "Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics'', by A. Jaffe and F. Quinn 
Michael Atiyah, Armand Borel, G. J. Chaitin, Daniel Friedan, James Glimm, Jeremy J. Gray, Morris W. Hirsch, Saunder MacLane, Benoit B. Mandelbrot, David Ruelle, Albert Schwarz, Karen Uhlenbeck, René Thom, Edward Witten, Christopher Zeeman

Response to comments on "Theoretical mathematics''
Arthur Jaffe, Frank Quinn