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The Riemann Hypothesis pp 93–160Cite as

Expert Witnesses

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Abstract

This chapter contains four expository papers on the Riemann hypothesis. These are our “expert witnesses”, and they provide the perspective of specialists in the fields of number theory and complex analysis. The first two papers were commissioned by the Clay Mathematics Institute to serve as official prize descriptions. They give a thorough description of the problem, the surrounding theory, and probable avenues of attack. In the third paper, Conrey gives an account of recent approaches to the Riemann hypothesis, highlighting the connection to random matrix theory. The last paper outlines reasons why mathematicians should remain skeptical of the hypothesis, and possible sources of disproof.

Hilbert included the problem of proving the Riemann hypothesis in his list of the most important unsolved problems which confronted mathematics in 1900, and the attempt to solve this problem has occupied the best efforts of many of the best mathematicians of the twentieth century. It is now unquestionably the most celebrated problem in mathematics and it continues to attract the attention of the best mathematicians, not only because it has gone unsolved for so long but also because it appears tantalizingly vulnerable and because its solution would probably bring to light new techniques of far-reaching importance [51].

H. M. Edwards

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  1. Department of Mathematics & Statistics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada

    Peter Borwein & Stephen Choi

  2. Simon Fraser University, 9161 Tenth Avenue, Burnaby, BC, V3N 2T2, Canada

    Brendan Rooney

  3. University of Western Ontario, 727 Windsor Street, Fredericton, ON, E2B 4G3, Canada

    Andrea Weirathmueller

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  1. Peter Borwein
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  1. Department of Mathematics & Statistics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada

    Peter Borwein  & Stephen Choi  & 

  2. Simon Fraser University, 9161 Tenth Avenue, Burnaby, BC, V3N 2T2, Canada

    Brendan Rooney

  3. University of Western Ontario, 727 Windsor Street, Fredericton, ON, E2B 4G3, Canada

    Andrea Weirathmueller

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Borwein, P., Choi, S., Rooney, B., Weirathmueller, A. (2008). Expert Witnesses. In: Borwein, P., Choi, S., Rooney, B., Weirathmueller, A. (eds) The Riemann Hypothesis. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-72126-2_11

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