... it is impossible to explain honestly the beauties of the laws of nature in a way that people can feel, without their having some deep understanding of mathematics. I am sorry, but this seems to be the case.
         Richard Feynman

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• January 2013. Site was rewritten in html5/css3. Some pages won't display correctly until you update your (ancient) browser.

What's New in Articles

• Nov 11, 2009. New version of Points on Shimura varieties over finite fields: the conjecture of Langlands and Rapoport 2008b

What's New in Course Notes

• May 5, 2013. New version of Lie Algebras, Algebraic Groups, ...LAG
• April 15, 2012. GT, FT, and ANT now available for ereaders

What's New in Expository Notes

• May 2, 2013. New version of Commutative Algebra. CA
• March 18, 2012. The Work of John Tate For Abel prize volume.
• May 13, 2011. TeXed version of Tannakian Categories (with Deligne)

What's New in Documents

• January 23, 2010. Complete notes from the famous 1964 Woods Hole conference.

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But then I felt possessed by an aura of inspiration that allowed me to improvise credible answers and miraculous lucky guesses. Except in mathematics, which not even God could make me understand.
         Gabriel García Márquez, Living to Tell the Tale, p204.

Early on I noticed that mathematicians live in a world inaccessible to common mortals ... They are a special breed possessed by an intense cerebral life; simultaneously living on two distinct levels of consciousness, they are at once present and able to carry on normally and yet are immersed in the abstractions that form the core of their lives.
         Françoise Ulam (Stanislaw Ulam's wife).

I came into the room, which was half dark, and presently spotted Lord Kelvin in the audience and realised that I was in for trouble at the last part of my speech dealing with the age of the earth, where my views conflicted with his. To my relief, Kelvin fell fast asleep, but as I came to the important point, I saw the old bird sit up, open an eye and cock a baleful glance at me! Then a sudden inspiration came, and I said Lord Kelvin had limited the age of the earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium! Behold! the old boy beamed upon me.
         Ernest Rutherford

In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life.
         Atiyah (NAMS Jan 2010 p.8).

I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, "Well, I have done one thing you could never have have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms."
         Hardy, Apology, Sect. 29.

The problem with the global village is all the global-village idiots.
         Attributed to Sidney Coleman in arXiv:1108.2700.

Arithmetic has a well-known liberal bias. [or worse]
         Paul Krugman, blog April 8 2011.

Now, people ask me all the time how we got four surplus budgets in a row. What new ideas did we bring to Washington? I always give a one-word answer: Arithmetic. (Sustained cheers, applause.)
         Bill Clinton (Sept. 6, 2012).

Do not work within two hours of a substantial meal; blood cannot be in two places at once.
         J.E. Littlewood, in Littlewood's miscellany, p199.

Certainly the best times were when I was alone with mathematics, free of ambition and pretense, and indifferent to the world.
        Langlands, in Mathematicians: An Outer View of the Inner World, p142.

Mathematics has been for me, not only a profession, but also my preferred hobby. ... Again and again I have been guided by a sense of the architecture of this edifice, to which we continue to add new wings and new floors while renovating the parts already constructed, into feeling that certain problems had priority as opening new perspectives or establishing a new foundation for future constructions. This is the professional point of view, but happily these problems were those that attracted me the most. In other instances I was not guided by such motives, being attracted only by curiosity, by the need to know the answer to an enigma, without reference to its importance in a general context. Borel, Œuvres IV, p376.