Brian Conrey

John Brian Conrey (born June 23, 1955) is an American mathematician, known for his research in analytic number theory, involving L-functions, the Riemann zeta function, and questions related to the Riemann Hypothesis (RH). He was elected a Fellow of the American Mathematical Society in 2015.

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In 1972 H. L. Montgomery announced a remarkable connection between the distribution of the zeros of the Riemann zeta-function and the distribution of eigenvalues of large random Hermitian matrices. Since then a number of startling developments have occurred making this connection more profound. In particular, random matrix theory has been found to be an extremely useful predictive tool in the theory of L-functions.
- "Chapter. L-Functions and Random Matrices by Brian Conrey". Mathematics Unlimited — 2001 and Beyond. Springer. pp. 331–352. doi:10.1007/978-3-642-56478-9_14. (edited by B. Engquist and W. Schmid)

A major difficulty in trying to construct a proof of RH through analysis is that the zeros of L-functions behave so much differently from zeros of many of the special functions we are used to seeing in mathematics and mathematical physics. For example, it is known that the zeta-function does not satisfy any differential equation. The functions which do arise as solutions of some of the classical differential equations, such as Bessel functions, hypergeometric functions, etc., have zeros which are fairly regularly spaced. A similar remark holds for the zeros of solutions of classical differential equations regarded as a function of a parameter in the differential equation.
- (2003). "The Riemann Hypothesis". Notices of the American Mathematical Society 50 (3): 341–353. ISSN 0002-9920. (quote from pages 352–353)

The Riemann Hypothesis is a statement about a deep connection between addition and multiplication that we do not yet understand.
- (March 12, 2020)"Math Encounters - Primes and Zeros: A Million-Dollar Mystery". National Museum of Mathematics, YouTube. (quote at 59:05 of 1:18:02)