Any regularity you can show about primes is beguiling," says Harvard University

number theorist Barry Mazur.

Given Lagrange's result,

number theorists asked whether there are other such expressions, called quadratic forms, that also repre sent all positive integers.

In the late 1990s, Bruce Berndt, a

number theorist at the University of Illinois at Urbana-Champaign, asked Ono to help him edit for publication a section of the notebook about partitions.

Give

number theorists a year with this algorithm, and it should be much clearer what its future is," Caldwell says.

Last year, working independently,

number theorist Don Zagier of the Max Planck Institute for Mathematics in Bonn, Germany, used a modular-forms approach to provide a significantly shorter proof of the Kac-Wakimoto conjectures.

This was really quite unexpected," says

number theorist Ono, who holds positions at both Penn State and the University of Wisconsin-Madison.

It was this book that introduced

number theorist Noam D.

Spanish

number theorists gather once more to maintain contacts, exchange ideas, and gather information.

Number theorists, like Philolaus, could account for unity and difference by analogy with the principle by which particular numbers, and their instantiated quantities in the world, participate necessarily in higher order mathematical properties (odd or even) which necessarily exclude opposed properties.

That's an open question best left to scientists,

number theorists, and idle afternoons.

Great arithmeticians and

number theorists include Diophantus of Mexandria, Pierre de Fermat, and Kurt Godel.

Various probability-based arguments I carried out suggested that it was close to the finite-vs-infinite boundary, a property which often attracts the attention of academic

number theorists (the series of perfect numbers 6, 28, 496, 8128, 33550336 .

Septimus (or 'seventh') is a name with great resonance for

number theorists.

Suitable for advanced undergraduates or beginning graduate students, this introduction to Ramanujan's work in q-series and theta functions also sets this greatest of

number theorists within the context of his world in and out of mathematics.

In this sense, the students working on this problem evolve from marble mayhem sleuths to mathematical

number theorists.