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An open research record on the Riemann Hypothesis.

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EXPLAIN

This section is a way into the Riemann Hypothesis and the mathematics around it. It explains ideas, terminology and historical context encountered elsewhere on Riemann Console, with the aim that a curious reader can leave understanding something they did not know before.

Explain articles are educational companions to the research record. They do not change the scientific status of a research object, milestone or release.

Looking for the mathematicians behind the names? Visit People. Looking for a short definition rather than a full article? Visit Glossary.

Available Explain articles

  1. [..]If the Riemann Hypothesis has worked so far, why do we still need a proof?EXPLAIN · 2026-09-10
  2. [..]What is the Riemann Hypothesis?EXPLAIN · 2026-09-09
  3. [..]What is the Riemann zeta function?EXPLAIN · 2026-09-18
  4. [..]What do the zeros of the zeta function have to do with prime numbers?EXPLAIN · 2026-09-19
  5. [..]What is a computer-assisted proof?EXPLAIN · 2026-09-25
  6. [..]What is the Riemann xi function?EXPLAIN · 2026-09-25
  7. [..]What is the gamma function?EXPLAIN · 2026-09-26
  8. [..]What is analytic continuation?EXPLAIN · 2026-09-27
  9. [..]Why is a counterexample useful?EXPLAIN · 2026-09-09
  10. [..]How are the prime numbers distributed?EXPLAIN · 2026-09-30
  11. [..]What does it mean for a quantity to stay non-negative?EXPLAIN · 2026-09-10
  12. [..]What is positive definiteness?EXPLAIN · 2026-09-10
  13. [..]Beyond Human-First MathematicsEXPLAIN · 2026-09-14
  14. [..]Who was Bernhard Riemann?EXPLAIN · 2026-09-14
  15. [..]Who was Leonhard Euler?EXPLAIN · 2026-09-16