Methodology

How the rankings are built

This page documents how the Top 100 list is constructed, what is in the data, and what is deliberately left out. The abc ranking combines four ranked sources. Three measure research activity, the papers a person writes on the topic: arXiv, OpenAlex and zbMATH Open, the same three the sister sites use. The fourth measures influence: how often the abc literature itself cites a person. Nobody on this list is placed by hand.

Why a fourth source

Counting a person's own papers measures output. It cannot see a founder who wrote one or two papers that everybody else builds on. David Masser and Joseph Oesterlé formulated the abc conjecture in 1985, and between them they have written only a handful of papers about it, so the three activity sources ranked neither of them. A specialist in the field pointed this out in September 2026, and he was right. The citation-influence source fixes that with a rule applied to everyone, rather than by adding their names to the list.

Data sources

The three activity sources

The arXiv and OpenAlex pulls use 14 search terms: abc conjecture, Szpiro conjecture, Vojta conjecture, S-unit equation, height inequality, Belyi map, Wieferich prime, Thue equation, inter-universal Teichmuller, Nevanlinna theory arithmetic, integral points on curves, effective Mordell, radical of integers, and Mason-Stothers theorem. A match in a paper's title counts at full weight; a match only in its abstract counts half. Recent work weighs more than old work.

1. arXiv: an author qualifies with at least 3 topical papers, and is ranked by weighted paper count, then by co-author connections.
2. OpenAlex: an author qualifies with at least 2 topical works, and is ranked by weighted works, then by weighted citations. Someone found only in OpenAlex also needs an established record, at least 4 works and 30 citations, and a mathematics profile.
3. zbMATH Open: an author qualifies with at least 3 documents in the three MSC classes, ranked by weighted document count.
4. Topic gate: the search terms reach well beyond abc, into Thue equations, S-unit equations and heights generally. To stay on topic, a researcher counts only with at least one work that is actually about abc or a proven equivalent, judged from its title and abstract, or with a strong citation-influence record.

The citation-influence source

The abc literature is every work in OpenAlex or zbMATH Open whose title, abstract or review names the conjecture: "abc conjecture", "Masser-Oesterlé conjecture" or "Oesterlé-Masser conjecture". In the September 2026 build that is 1,388 works. A person's influence is the number of those works that cite them. A work counts once per person, however many times it cites them, and it can cite them in any of three ways:

1. A linked reference to a paper they wrote, from OpenAlex reference lists or zbMATH reference lists.
2. An unlinked reference: a zbMATH reference to a paper no database indexes, identified from the author names in the reference text. Masser's 1985 note "Open problems", where the conjecture first appeared, is indexed nowhere, but it is still counted this way.
3. A citation by name: the work names them as the source of a result, as in "the Masser-Oesterlé conjecture", "Mason's theorem" or "a result of Stewart and Yu". A foundational result is often cited by name alone, so a name counts as a citation. A surname shared by several researchers counts only when one of them clearly dominates that surname's formal citations. Surnames that the literature also uses as ordinary words or first names are ignored.

Self-citations never count. To keep out crank proof announcements, a citing work counts only if zbMATH reviewed it, someone has cited it, or it carries a reference list; the site's list of crank title phrases applies here too. A person needs at least 3 citing works to be ranked on this source.

Merge and scoring

Each researcher has up to four ranks, one per source. The three activity ranks, arXiv, OpenAlex and zbMATH Open, are sorted and combined into an activity score with a weighted order statistic: 0.70 on the best, 0.20 on the next and 0.10 on the third, the 0.70 weight only ever on a measured rank. The influence rank counts only when at least 10 works cite the researcher; with fewer, or none, it is set to one place below the lowest measured influence rank, never estimated, and shows in [square brackets]. The final score is the geometric mean of the two, the square root of influence rank times activity score. Lower is better. A researcher needs both to finish near the top, so neither a long publication list nor a famous name is enough alone. The previous merge sorted all four ranks together and kept the best three, which let the three activity sources outvote the single influence source; that is why the founders sat lower than they should.

On-topic floor: a researcher is eligible for the top of the list with at least one paper of their own whose title is about the abc conjecture or a proven equivalent, or with at least 5 works citing them whose own titles are. Everyone eligible is listed ahead of everyone who is not; the floor removes nobody. The same merge and floor are used on the Riemann hypothesis, Goldbach and twin prime sites.

Estimating a missing rank, by interpolation: when a researcher has no rank in a source, it is estimated from the researchers ranked near them in the sources where they do appear, using the median of those neighbours. Estimated ranks show in [square brackets]; measured ranks show plain.

Living researchers only: the Top 100 lists living researchers. Anyone with a verified date of death is listed in In Memoriam instead, which is why historical figures cited by the literature, such as Siegel, Roth and Szpiro, do not appear on the Top 100.

Hand-curated edits: an exclusions file removes people the pipeline surfaced in error, such as non-mathematicians. No one is added or placed by hand.

The Mochizuki IUT literature

Shinichi Mochizuki announced a claimed proof of the abc conjecture via Inter-universal Teichmuller theory in 2012. As of 2026 the proof has not been accepted by the broader mathematical community. The pipeline treats Mochizuki as one researcher among many, and ranks him by his activity and by how often the reviewed or cited literature cites him, not by the proof claim.

What is not in this list

• A verdict on importance. Citation influence gets closer to what specialists would name than counting papers does, but it is still a count, not a judgment. Use the directory as a map.
• Complete reference data. About two thirds of the works in the abc literature have no machine-readable reference list. Citations by name recover much of what is lost, but not all of it.

Sources of error

• The abc field is not a single cluster. Researchers on Thue equations, Belyi maps, S-unit equations and the Vojta conjecture form somewhat separate communities, and the activity sources capture all of them.
• Surname matching is fragile. Researchers are identified by surname and first initial, so two people can collide. The worst cases are split by hand with verified records, but misses are possible.
• Citation by name depends on wording. A work that uses a result without naming its author, and without a reference list, is invisible to the influence source.
• 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.