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Gerry Myerson
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The Selberg intervalintegral was proved in a 1944 paper of Selberg, after being stated without proof in a 1941 paper. The paper was in Norwegian, and was also in a journal that would have been of little interest to the research community:

This paper was published with some hesitation, and in Norwegian, since I was rather doubtful that the results were new. The journal is one which is read by mathematics-teachers in the gymnasium

This result was little-used, being used in one paper in 1953.

A closely related integral then appeared in random matrix theory. Mehta and Dyson gave a conjectural value for this integral, publicizing this conjecture as an open problem in a paper in 1963, a textbook in 1967, and the SIAM Review in 1974. However, no one remembered Selberg's work and thought to apply it.

Finally in 1976 Bombieri came across another similar integral when studying a different topic (prime numbers). He went to discuss his overall work on the distribution of prime numbers with Selberg, because of Selberg's expertise in number theory, and Selberg then mentioned his integral, which Bombieri used to solve his problem.

This was after Bombieri was informed by Spencer about the relationship of his integral to a third topic (the Coulomb gas), motivating him to ask Dyson about it, at which point Dyson explained the connection to random matrices, and thus Bombieri was able to prove the conjecture in random matrix theory as well.

Since then, the result has found further use and development, and is now widely-known.

My source for all these details is the paper The importance of the Selberg integral by Peter J. Forrester and S. Ole Warnaar

The Selberg interval was proved in a 1944 paper of Selberg, after being stated without proof in a 1941 paper. The paper was in Norwegian, and was also in a journal that would have been of little interest to the research community:

This paper was published with some hesitation, and in Norwegian, since I was rather doubtful that the results were new. The journal is one which is read by mathematics-teachers in the gymnasium

This result was little-used, being used in one paper in 1953.

A closely related integral then appeared in random matrix theory. Mehta and Dyson gave a conjectural value for this integral, publicizing this conjecture as an open problem in a paper in 1963, a textbook in 1967, and the SIAM Review in 1974. However, no one remembered Selberg's work and thought to apply it.

Finally in 1976 Bombieri came across another similar integral when studying a different topic (prime numbers). He went to discuss his overall work on the distribution of prime numbers with Selberg, because of Selberg's expertise in number theory, and Selberg then mentioned his integral, which Bombieri used to solve his problem.

This was after Bombieri was informed by Spencer about the relationship of his integral to a third topic (the Coulomb gas), motivating him to ask Dyson about it, at which point Dyson explained the connection to random matrices, and thus Bombieri was able to prove the conjecture in random matrix theory as well.

Since then, the result has found further use and development, and is now widely-known.

My source for all these details is the paper The importance of the Selberg integral by Peter J. Forrester and S. Ole Warnaar

The Selberg integral was proved in a 1944 paper of Selberg, after being stated without proof in a 1941 paper. The paper was in Norwegian, and was also in a journal that would have been of little interest to the research community:

This paper was published with some hesitation, and in Norwegian, since I was rather doubtful that the results were new. The journal is one which is read by mathematics-teachers in the gymnasium

This result was little-used, being used in one paper in 1953.

A closely related integral then appeared in random matrix theory. Mehta and Dyson gave a conjectural value for this integral, publicizing this conjecture as an open problem in a paper in 1963, a textbook in 1967, and the SIAM Review in 1974. However, no one remembered Selberg's work and thought to apply it.

Finally in 1976 Bombieri came across another similar integral when studying a different topic (prime numbers). He went to discuss his overall work on the distribution of prime numbers with Selberg, because of Selberg's expertise in number theory, and Selberg then mentioned his integral, which Bombieri used to solve his problem.

This was after Bombieri was informed by Spencer about the relationship of his integral to a third topic (the Coulomb gas), motivating him to ask Dyson about it, at which point Dyson explained the connection to random matrices, and thus Bombieri was able to prove the conjecture in random matrix theory as well.

Since then, the result has found further use and development, and is now widely-known.

My source for all these details is the paper The importance of the Selberg integral by Peter J. Forrester and S. Ole Warnaar

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Will Sawin
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The Selberg interval was proved in a 1944 paper of Selberg, after being stated without proof in a 1941 paper. The paper was in Norwegian, and was also in a journal that would have been of little interest to the research community:

This paper was published with some hesitation, and in Norwegian, since I was rather doubtful that the results were new. The journal is one which is read by mathematics-teachers in the gymnasium

This result was little-used, being used in one paper in 1953.

A closely related integral then appeared in random matrix theory. Mehta and Dyson gave a conjectural value for this integral, publicizing this conjecture as an open problem in a paper in 1963, a textbook in 1967, and the SIAM Review in 1974. However, no one remembered Selberg's work and thought to apply it.

Finally in 1976 Bombieri came across another similar integral when studying a different topic (prime numbers). He went to discuss his overall work on the distribution of prime numbers with Selberg, because of Selberg's expertise in number theory, and Selberg then mentioned his integral, which Bombieri used to solve his problem.

This was after Bombieri was informed by Spencer about the relationship of his integral to a third topic (the Coulomb gas), motivating him to ask Dyson about it, at which point Dyson explained the connection to random matrices, and thus Bombieri was able to prove the conjecture in random matrix theory as well.

Since then, the result has found further use and development, and is now widely-known.

My source for all these details is the paper The importance of the Selberg integral by Peter J. Forrester and S. Ole Warnaar