Methodology

How the rankings are built

This page documents how the Top 100 list is constructed, what's in the data, and what's deliberately out. The Riemann-hypothesis ranking combines four ranked sources. Three measure research activity, the papers a person writes on the topic: arXiv, OpenAlex and zbMATH Open. The fourth measures influence: how often the Riemann hypothesis literature itself cites a person. The same four sources are used on the sister abc conjecture site.

Data sources

The citation-influence source

Counting a person's own papers measures output, and it cannot see a senior figure whose few papers everyone else builds on. The fourth source counts influence instead. The Riemann hypothesis literature is every work in OpenAlex or zbMATH Open whose title, abstract or review says "Riemann hypothesis": 21,172 works in the September 2026 build. A person's influence is the number of those works that cite them, counting each work once per person, by a linked reference to a paper they wrote, by an unlinked reference identified from the author names in the reference text, or by naming them as the source of a result, as in "Montgomery's pair correlation conjecture".

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. A person needs at least 3 citing works to be ranked on this source. This source is why senior figures such as Montgomery, Iwaniec, Odlyzko, Sarnak and Bombieri now rank near the researchers most active today.

Pipeline

Title-weighting. A paper can mention the Riemann hypothesis without being about it, for example a paper that cites it in its introduction as a famous open problem. To separate genuine work from passing mentions, the arXiv and OpenAlex pipelines weight a keyword match by where it appears: a match in the paper title counts at full weight, and a match only in the abstract counts at half (a factor of 0.5). zbMATH is not title-weighted, because its documents are classified by human editors, so the subject class itself is the relevance signal.

1. arXiv pull: 15 search terms (Riemann hypothesis, Riemann zeta function, Dirichlet L-functions, critical line, critical strip, pair correlation, zero-density, zeros of the zeta function, nontrivial zeros, Selberg class, Mertens function, moments of the zeta function, Lindelof, Beurling-Nyman, and random matrix) restricted to the math.NT category. Each paper's contribution to an author is title-weighted as above. A co-authorship graph is built and eigenvector centrality is the second factor in an arXiv composite of 0.60 * pr(weighted papers) + 0.40 * pr(eigen). Authors with at least 3 topical papers qualify.
2. OpenAlex pull: 14 phrase queries (the arXiv terms minus random matrix, which without a category guard floods the results with wireless and random-matrix-theory engineers), with an author cap of 10 per work to remove physics megapapers. Works and their citations are title-weighted as above. Composite: 0.60 * pr(weighted works) + 0.40 * pr(weighted citations). Result: 137 qualifying authors. Because the Riemann hypothesis is so strongly an arXiv-preprint field, OpenAlex overlaps with only a handful of the top-ranked researchers directly; the others are carried by their arXiv signal.
3. zbMATH pull: documents tagged with either of the two Riemann-hypothesis-core MSC classes, 11M26 (zeros of zeta and L-functions and the Riemann hypothesis) or 11M50 (relations of the zeta function with random matrices and physics). The editor-assigned MSC classes correct a systematic gap in the other sources: pre-1995 number theorists and specialists who publish in journals with sparse arXiv presence. This pull is in progress and is being folded into the merged ranking.
4. Merge and scoring: the rankings are surname-deduplicated and joined. Each researcher first gets an activity score from the three activity sources, arXiv, OpenAlex and zbMATH Open: their three ranks are sorted and weighted 0.70 on the best, 0.20 on the middle and 0.10 on the worst, and the 0.70 weight only ever lands on a measured rank. Their influence rank comes from the citation-influence source and counts only when at least 10 works in the literature cite them; with fewer, or none, it is set to one place below the lowest measured influence rank, never estimated from neighbours, and the Top 100 table shows that placeholder in [square brackets]. The final score is the geometric mean of the two, the square root of influence rank times activity score, and lower is better. A researcher needs both to finish near the top. The previous merge sorted all four ranks together and kept the best three, so the three activity sources could outvote the single influence source and a heavily cited founder lost to a prolific author; the geometric mean gives influence and activity equal say.
5. 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 Riemann hypothesis or the zeros of zeta and L-functions, judged by the site's core vocabulary, or with at least 5 works citing them whose own titles are about the Riemann hypothesis or the zeros of zeta and L-functions. Everyone eligible is listed ahead of everyone who is not. The floor removes nobody; it only orders the list. The same merge and the same floor are used on the Riemann hypothesis, Goldbach, twin prime and abc sites, and nobody is placed by hand.
6. Estimating a missing rank (interpolation): a researcher ranked by only one of the pipelines is not given a flat penalty. To estimate a missing rank, we order the whole pool by a pipeline the researcher does appear in, then walk outward to the two nearest researchers above and the two nearest below who carry a real rank in the missing pipeline, and average those (up to four) values. One rule protects the scoring: the 0.70 top weight may only land on a measured rank, so an estimate can support a researcher's score but can never be their headline signal. Estimated ranks show in [square brackets] on the Top 100 table; measured ranks show plain.
7. Recency weighting: each paper is weighted by how recent it is, so currently active researchers are favoured over those long inactive, with no hard cutoff. Relative to the current year, a paper from the last five years counts at full weight, one six to ten years old counts at 0.6, one eleven to twenty years old counts at 0.3, and anything older still counts, at 0.1. The weight is applied to each source signal before ranks are formed: the arXiv paper count, the OpenAlex work and citation counts, and the zbMATH document count. Older work is never discarded; it simply contributes less. A paper still counts toward whether a researcher qualifies for a pipeline; recency only changes the order. The arXiv and OpenAlex layers carry a year for every paper, so recency applies in full there. The zbMATH layer does not yet record a per-document year, so its documents are all weighted equally until that field is added.
8. Hand-curated edits: an exclusions file removes researchers the automated pipeline surfaced in error (see Audit decisions). The merge does not hand-place any researcher; everyone earns their rank from the pipeline scores.

Audit decisions

Excluded

A small number of authors surfaced by the automated pipeline are removed by hand. Some work in unrelated fields, for example signal processing, wireless communications, or coding theory, and were pulled in by surname collisions or by the noisy random matrix topic before it was dropped from the OpenAlex queries. A few others are self-published authors whose output is not part of mainstream research. The specific names are kept internal: listing them here would only give them visibility, which is the opposite of the point.

What's not in this list

• Researchers without a strong digital footprint. The pipeline indexes arXiv well and OpenAlex moderately, so figures who publish mainly in journals are undercounted until the zbMATH MSC layer is fully integrated.
• A verdict on importance. The citation-influence source brings the list closer to what specialists would name than counting papers alone, but it is still a count, not a judgment.
• Adjacent topics. The list covers the Riemann hypothesis and adjacent problems, so some of the 100 work mainly on related questions (pair correlation of zeros, moments of the zeta function, Dirichlet L-functions, the Selberg class, the random-matrix connection) rather than on the Riemann hypothesis directly. Title-weighting reduces, but does not eliminate, the appearance of researchers whose connection to the hypothesis itself is incidental.

Sources of error

• Surname matching is fragile. Mathematicians with common surnames may be conflated. The pipeline handles the worst cases but misses are possible.
• Citation counts are influenced by adjacent fields. Riemann-hypothesis work overlaps with random matrix theory, analytic number theory, and mathematical physics, so a researcher whose work bridges those fields may rank higher purely because those fields cite more. The OpenAlex term random matrix in particular pulls in wireless and signal-processing engineers, so it is excluded from the OpenAlex queries.
• Coverage is biased toward digital publishing. The Riemann hypothesis is a heavily arXiv-based field, which the pipeline indexes well, but some senior figures who publish mainly in journals are undercounted, and the zbMATH MSC layer that corrects for this is still being integrated.
• 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.