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
| Source | What it gives | Limitations |
|---|---|---|
| arXiv (math.NT, math.CO) | Preprint-level: titles, abstracts, authors, dates, co-author graph | Biased toward people who post preprints. Senior figures who publish only in journals are undercounted. |
| OpenAlex | Author-level: paper count, citations, affiliations, country | Concept tagging is noisy in math; surname-only matching can misidentify. |
| zbMATH Open | Curated math review database using MSC classes 11N05, 11N35, 11N36 | Coverage of older non-Western mathematicians is the best of the three sources. |
| Math Genealogy Project | Advisor-student trees | Dissertation-era affiliations only; gaps for some non-Western mathematicians. |
| Citation influence, built from OpenAlex and zbMATH | How many works in the literature on this problem cite a researcher, by reference or by name | Many works carry no machine-readable reference list. |
The citation-influence source
The Top 100 combines four ranked sources. arXiv, OpenAlex and zbMATH Open measure research activity, the papers a researcher writes on the topic. The fourth measures influence: the number of works in the literature on the twin prime conjecture that cite a researcher, counting each work once, by a linked reference, by an unlinked reference identified from the author names, or by naming them as the source of a result. Self-citations never count, a citing work counts only if zbMATH reviewed it, someone cited it, or it carries a reference list, and a researcher needs at least 3 citing works. The four ranks enter the same weighted order statistic, 70/20/10 on the best three. The same source is used on the sister Riemann hypothesis, abc conjecture and Goldbach sites.
For twin primes the literature is every work in zbMATH Open, or in OpenAlex with a Mathematics primary topic, that names twin primes or bounded gaps between primes: 3,059 works in the September 2026 build. The Mathematics restriction matters because twin prime editing is also a genome-editing technique, and coding-theory papers on twin-prime sequences and difference sets are excluded for the same reason. This source is why Yitang Zhang, whose 2013 bounded-gaps theorem set off the modern work, now ranks near the top.
Pipeline
- arXiv pull: 17 search terms restricted to the math.NT and math.CO categories. Title-weighting: a match in the paper title counts at full weight, abstract-only at half.
- OpenAlex pull: phrase queries, author cap of 10 per work to remove physics megapapers. Title-weighting applied.
- zbMATH pull: documents tagged with the MSC classes 11N05, 11N35, 11N36.
- Merge and scoring: weighted order statistic with 70/20/10 on the best, middle, and worst of each researcher's three ranks. Lower combined score ranks higher.
- Estimating a missing rank: missing ranks are interpolated from the nearest ranked neighbours and shown in [square brackets].
What's not in this list
- Researchers without an OpenAlex profile. The list is biased toward digitally-indexed publication output.
- Subjective importance. We rank by output, not by depth.