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.

Data sources

The citation-influence source

The Top 100 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 Goldbach literature itself cites a person. The same four sources are used on the sister Riemann hypothesis and abc conjecture sites.

The literature is every work in OpenAlex or zbMATH Open whose title, abstract or review names Goldbach: 7,196 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. Self-citations never count. A citing work counts only if zbMATH reviewed it, someone has cited it, or it carries a reference list, which keeps out crank proof announcements. A person needs at least 3 citing works to be ranked on this source. Hardy, Vaughan, Vinogradov and Hua lead that count, and it is why Iwaniec, Friedlander, Montgomery and Bombieri now rank alongside the researchers most active today, and why the computational verifiers of the conjecture, Oliveira e Silva, Herzog and Pardi, appear on the list.

Influence and activity are combined as described below: the score is the geometric mean of the influence rank and the activity score, and researchers with on-topic work or on-topic citations are listed first. Historical figures the literature cites heavily are listed in In Memoriam rather than the Top 100.

Pipeline

Title-weighting. A paper can mention the Goldbach conjecture without being about it, for example a paper that cites Goldbach 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: 17 search terms (Goldbach, prime gap, twin prime, Vinogradov, Hardy-Littlewood, sum of two primes, and others) restricted to the math.NT and math.CO categories. 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. Result: 137 names.
2. OpenAlex pull: 13 phrase queries (Goldbach conjecture, Goldbach problem, Goldbach's conjecture, and adjacent additive-prime phrases), 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: 572 ranked authors.
3. zbMATH pull: documents tagged with any of the three Goldbach-core MSC classes, 11P32 (Goldbach-type additive problems), 11P55 (Hardy-Littlewood circle method), or 11N36 (applications of sieve methods). The broader distribution classes 11N05 (distribution of primes) and 11N13 (primes in arithmetic progressions) were tested and dropped: they pulled in general analytic and multiplicative number theorists whose connection to Goldbach is diffuse, while every genuine additive-prime and circle-method specialist survived the narrower set. Composite: 0.60 * pr(papers) + 0.40 * pr(eigen) over the co-authorship graph among authors with at least 3 topical documents. Result: 495 ranked authors. The editor-assigned MSC classes correct two systematic gaps in the other sources: pre-1995 Russian and Chinese number theorists, and specialists who publish in journals with sparse arXiv presence.
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 Goldbach-type sums of primes, judged by the site's core vocabulary, or with at least 5 works citing them whose own titles are about Goldbach-type sums of primes. 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 or two of the three 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. If two pipelines can each supply such a neighbourhood, we compute the estimate from each and average the two, so the two sources count equally. 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. Hand-curated edits: an exclusions file removes researchers the automated pipeline surfaced in error (see Audit decisions). The merge no longer hand-places any researcher: an earlier version floored a few canonical figures editorially, but the scoring below now lets them earn their rank on their own.
8. Genealogy reseeded: the Top 100 becomes the seed list for the Mathematics Genealogy Project graph, and close-relations surface from the network analysis.

Audit decisions

Excluded

A small number of authors surfaced by the automated pipeline are removed by hand. Some work in unrelated fields, for example chemistry, mathematical demography, or coding theory, and were pulled in by surname collisions or noisy topic tagging. 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.

Name aliases (forced MGP ids)

What's not in this list

• Researchers without an OpenAlex profile. OA missed several Russian and Chinese number theorists from the 1960s-90s era. The genealogy supplement partially covers this gap but the list is biased toward digitally-indexed publication output.
• Subjective importance. A theorist whose entire body of Goldbach work is one influential paper may rank lower than a productive researcher with many adjacent papers. We rank by output, not by depth.
• Adjacent topics. The list covers the Goldbach conjecture and adjacent additive prime number theory, so some of the 100 work mainly on related problems (twin primes, prime gaps, the circle method, sieve theory) rather than on Goldbach directly. Title-weighting reduces, but does not eliminate, the appearance of researchers whose Goldbach connection is incidental.

Sources of error

• Surname matching is fragile. Mathematicians named Liu, Wang, or Pan may be conflated. The pipeline handles the worst cases via the name aliases file but misses are possible.
• Citation counts are influenced by adjacent fields. A researcher whose Goldbach work overlaps with cryptography or computer science may rank higher purely because those fields cite more.
• Coverage is biased toward digital publishing. Some senior mathematicians, especially from the Russian and Chinese schools, are underrepresented because their pre-internet papers aren't well-indexed.
• The Top 100 is not a verdict. It's a starting point. Use it alongside MathSciNet, your advisor, and your own reading.

Acknowledgments

Data sources: arXiv, OpenAlex, zbMATH Open, Mathematics Genealogy Project, Google Maps.

R packages: aRxiv, dplyr, ggplot2, ggmap, ggrepel, igraph, maths.genealogy, patchwork, ragg.