The Riemann hypothesis: The great pending mathematical challenge

Authors

  • Pilar Bayer University of Barcelona (Spain).

DOI:

https://doi.org/10.7203/metode.0.8903

Keywords:

prime numbers, zeta function, L-function, Riemann hypothesis, millennium problems

Abstract

The Riemann hypothesis is an unproven statement referring to the zeros of the Riemann zeta function. Bernhard Riemann calculated the first six non-trivial zeros of the function and observed that they were all on the same straight line. In a report published in 1859, Riemann stated that this might very well be a general fact. The Riemann hypothesis claims that all non-trivial zeros of the zeta function are on the the line x = 1/2. The more than ten billion zeroes calculated to date, all of them lying on the critical line, coincide with Riemann’s suspicion, but no one has yet been able to prove that the zeta function does not have non-trivial zeroes outside of this line.

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Author Biography

Pilar Bayer, University of Barcelona (Spain).

Specialist in number theory. Her academic career is tied to the University of Regensburg (Germany), the Autonomous University of Barcelona, the University of Santander, and the University of Barcelona (the latter three in Spain), where she has resided as a professor since 1982. Her research includes, among other themes, publications on zeta functions, Diophantine equations, elliptic curves, modular forms, and Shimura curves. In the 1980s, she founded the Barcelona Number Theory Seminar, which is still an ongoing program. She has directed fifteen PhD dissertations and is a tenured member of the Royal Spanish Academy of Exact, Physical, and Natural Sciences, the Royal Academy of Sciences and Arts, and the Royal European Academy of Doctors, and is member of the Institute for Catalan Studies. In 2015, she was awarded the Vives University Network Medal of Honour.

References

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Published

2018-06-05

How to Cite

Bayer, P. (2018). The Riemann hypothesis: The great pending mathematical challenge. Metode Science Studies Journal, (8), 35–41. https://doi.org/10.7203/metode.0.8903
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Issue

Making science: A multitude of perspectives (2018)

Section

The millennium problems. Challenges to further mathematics

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