About

Why this site exists

The abc conjecture has been open since 1985. It sits at the intersection of Diophantine approximation, arithmetic geometry, and the theory of heights, and implies a remarkable breadth of consequences in number theory. The community working on it and on the surrounding problems (Szpiro, Vojta, S-unit equations, Thue equations, Belyi maps) is spread across several research areas. This site is a starting point for anyone wanting to know who is active on these topics today, where they are, and what they have been writing.

Who built it

Steve Hubbard built this as a sister project to Who's Who in Goldbach 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@wwiabc.org.

Sources of error

• The abc conjecture field is not a single cluster. Researchers on Thue equations, Belyi maps, S-unit equations, and the Vojta conjecture each form somewhat separate communities. The pipeline captures all of them, but a specialist in one area may rank higher than a generalist who has contributed to several. Use the directory as a map, not a verdict.
• Surname matching is fragile. Mathematicians with common surnames may be conflated. The pipeline handles the worst cases but misses are possible.
• Coverage is biased toward digital publishing. The abc conjecture has a significant arXiv presence, but some senior researchers who publish mainly in journals are undercounted until the zbMATH MSC layer is fully integrated.
• The Mochizuki IUT literature is specialized. The claimed proof via Inter-universal Teichmuller theory uses terminology (IUT, IUTT, anabelian geometry, Hodge theaters) that does not overlap with the standard abc/Szpiro/Vojta search terms. Mochizuki and his direct collaborators may rank lower than their publication output warrants.
• 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.