I am getting up in age and am often tired and discouraged about how little I know after all these years and how unlikely it is I will ever master even the foundations of my own subject before I retire.(adsbygoogle = window.adsbygoogle || []).push({});

However I heard a talk Tuesday by the great Jean Pierre Serre that somewhat rejuvenated me.

In a colloquium at Emory, he surveyed the whole panorama of topics surrounding the number of solutions of equations over finite fields, and the relationship this reveals between prime numbers and solutions of equations in integers.

He brought in polynomials, power series, Fourier series, Dirchlet series, algebraic varieties, algebraic topology, group representations, eigenvalues, frobenius endomorphisms, etale and l - adic cohomology, Weil conjectures, Mordell conjecture, modularity of elliptic curves and of representations, Langlands program,.... all to illuminate the fundamental study of prime numbers, and solutions of simple equations like x^2 - x - 1. and he did it without even defining any of these things.

I thought it was the most enjoyable talk I had ever heard in my life, and I have heard some good ones.

It inspired me and made me feel I simply could not afford to continue to avoid learning about more of these tools, especially group representations, if I was interested in understanding the basic phenomena in number theory. It also helped that he was 79 years old and still going strong.

This kind of experience cannot be had from books, nor self study, nor research on the internet. We could even ask him questions.

One must have some exposure to and contact with real live vibrant practitioners of mathematics to feel and appreciate the essence of what they do, the unity of it, the scope, and the excitement.

Even on a momentous occasion like this, there were fewer than 100 people in the auditorium, plenty of empty seats, and the next day in his seminar there were only 15 of us.

I urge you all to go listen to talks by good scientists when you have a chance, and ask them questions. These opportunities arise at every university from time to time. Seize them.

best wishes,

mathwonk.

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