About
Why this site exists
At the 1912 International Congress of Mathematicians in Cambridge, Edmund Landau presented four specific problems about prime numbers that he regarded as inaccessible to current methods. They have remained unsolved for more than 110 years. The four problems, Goldbach's conjecture, the twin prime conjecture, Legendre's conjecture, and the conjecture that infinitely many primes of the form n2+1 exist, share analytic methods and a common research community. Significant advances on any one of them typically use techniques (sieve theory, the circle method, exponential sums, and Fourier-analytic tools on primes) that advance the others as well.
This site is a starting point for anyone wanting to know who is working on this family of problems today, where they are, and what they have been writing recently. The ranking covers the whole Landau-problems family at once. Individual problem sites linked from this page provide narrower, problem-specific rankings.
The four problems
- Goldbach conjecture: every even integer greater than 2 is the sum of two primes. Directory: wwigr.org.
- Twin prime conjecture: there are infinitely many pairs of primes differing by 2. Directory: wwitp.org.
- Legendre's conjecture: for every positive integer n, there is a prime between n2 and (n+1)2. Directory: wwileg.org.
- Primes of the form n2+1: there are infinitely many primes of this polynomial form. Directory: wwin2p1.org.
Who built it
Steve Hubbard built this as part of the Who's Who in Mathematics Research network, alongside Who's Who in Goldbach Research, Who's Who in Twin Prime Research, and Who's Who in Riemann Hypothesis Research, using the same open pipeline and documented methodology. Suggestions, corrections, and additions are welcome.
Contact
Questions, corrections, or additions: admin@wwilp.org.
Sources of error
- Surname matching is fragile. Mathematicians with common surnames may be conflated. The pipeline handles the worst cases but misses are possible.
- The umbrella scope is wide. Terms like "circle method" and "exceptional set" pull in researchers whose primary focus is adjacent (for example, Waring's problem or additive combinatorics) rather than any of the four Landau problems directly. Title-weighting reduces but does not eliminate this.
- Single breakthrough papers do not score well. The ranking measures sustained output. A researcher whose contribution to the field is one landmark paper will rank lower than a productive researcher with many related papers.
- The Top 100 is not a verdict. It is a starting point. Use it alongside MathSciNet, your advisor, and your own reading.
Acknowledgments
Data sources: arXiv, OpenAlex, zbMATH Open.
License and reuse
The data on this site is built from public sources (arXiv, OpenAlex, zbMATH) under their respective license terms. The compiled list and methodology are released under CC-BY 4.0: feel free to reuse with attribution.
Methodology and data
How the rankings are built, what is in the data, and what is deliberately left out is documented on the Methodology page. The full Top 100 is published as an open, downloadable dataset on the Data and citation page.
Contact and corrections
This is an independent, non-commercial directory built from public data, so some entries carry errors. To fix a profile, suggest someone missing, or ask not to be listed, see the Corrections and removal page, or email admin@wwilp.org. Every message is read and acted on by a person.