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 out. This site is an umbrella directory, and its ranking is a consolidation of the four member directories rather than a separate classification of papers. The four members are Goldbach, twin primes, Legendre's conjecture, and n2+1 primes. Each member site ranks researchers on its own problem from arXiv preprint output, OpenAlex topical citations, and zbMATH MSC classifications. This site fuses those four rankings into one.
The consolidation
The input is the served roster of each member directory, meaning its Top 100 plus its published next 100. The four rosters are fused by reciprocal rank fusion. For each researcher, summed over the member problems whose roster lists them:
score = sum of 1 / (10 + rank on that member list)
A higher score ranks higher. Ties break on the researcher's best single member rank, then on name, so an identical set of member rosters always produces an identical umbrella order.
Two properties follow by construction. First, nobody appears here who is not served on at least one member problem: every person on this list has already passed a member site's relevance gate, its identity resolution, its roster curation, and its quality-assurance suite. Second, breadth counts but does not dominate: a researcher on three or four member lists gains ground on a researcher of similar standing on one, while a genuine single-problem specialist ranked near the top of that problem still ranks highly here.
Why the constant is 10
The constant added to each rank sets how much a second, third or fourth member listing is worth against one strong listing. It was chosen by measurement, not by taste. At 10, the top of the list follows the member evidence, every canonical figure of the four problems stays inside the top 100, 16 single-problem specialists still hold top-100 places, and 84 of the top 100 appear on two or more member lists. The safe band runs from about 5 to about 20. Push the constant to 45 and the ordering at the very top flips to a breadth-only result; by 60 the single-problem share of the top 100 collapses toward zero, which would wrongly exclude a researcher who is first on one problem and absent from the other three. That failure mode is the reason the value is a deliberate, documented choice.
What the columns mean
The Top 100 table shows one column per member problem, labelled with the member site's
abbreviation and ordered alphabetically, the same order as the sister-site bar: gb
(Goldbach, wwigb.org), leg (Legendre's conjecture, wwileg.org), n2p1
(n2+1 primes, wwin2p1.org), and tp (twin primes, wwitp.org).
The cell holds the researcher's rank on that member directory.
A dash is a fact, not a gap: that member directory does not list the researcher. The
Source column names the member problems the researcher appears on, using the same
abbreviations in the same order, joined with + (for example gb+leg+tp).
Because this site does not classify papers itself, it publishes no arXiv, OpenAlex or zbMATH rank of its own;
those ranks live on the four member sites, where they are measured.
The remaining facts on a profile page (institution, country, active years, h-index, PhD year, topical work and citation counts) come from the same verified people store the member sites use. Where a topical count is shown, it is the count measured on the member problem on which the researcher ranks highest.
Data sources
| Source | What it gives | Limitations |
|---|---|---|
| wwigb.org (Goldbach) | The served Goldbach roster and each researcher's rank on it | Inherits the Goldbach site's own coverage limits. |
| wwileg.org (Legendre) | The served Legendre roster and ranks | A smaller roster, so a Legendre rank is a coarser signal than a Goldbach rank. |
| wwin2p1.org (n2+1) | The served n2+1 roster and ranks | Inherits the n2+1 site's own coverage limits. |
| wwitp.org (twin primes) | The served twin-primes roster and ranks | Inherits the twin-primes site's own coverage limits. |
| Math Genealogy Project | Advisor-student trees, PhD year | Dissertation-era affiliations only; gaps for some non-Western mathematicians. |
Each member site's own pipeline (title-weighted arXiv term search, OpenAlex phrase queries with an author cap, zbMATH MSC classes, a core-relevance gate, and a weighted order statistic over the three source ranks) is documented on that site's methodology page. This site adds no new classification step.
What is not in this list
- Researchers not served on any of the four member problems. This is the cost of consolidation, and it is deliberate. A researcher whose work is adjacent to the family (Waring's problem, primes in arithmetic progressions, additive combinatorics) but who does not reach a member roster no longer appears here, even where the earlier union-of-terms ranking surfaced them.
- Single-breakthrough authors. The member rankings measure sustained output, and the consolidation inherits that.
- Subjective importance. We rank by measured output and breadth across the family, not by depth of insight.
Sources of error
- Every member-site error propagates. A misidentified researcher or a stale affiliation on a member site arrives here unchanged. The corresponding upside is that a correction on a member site propagates here too.
- Roster sizes differ. The four member rosters are not the same length, so rank 60 does not mean the same thing on each list. Reciprocal rank fusion weights the top of every list most heavily, which limits but does not remove the effect.
- Breadth is not depth. A researcher who has written once on each of the four problems can outrank a specialist. The member-rank columns are shown precisely so a reader can see which case they are looking at.
- The Top 100 is not a verdict. It is a starting point. Use it alongside MathSciNet, your advisor, and your own reading.
Acknowledgments
Member directories: wwigb.org, wwitp.org, wwileg.org, wwin2p1.org. Underlying data sources: arXiv, OpenAlex, zbMATH Open, Mathematics Genealogy Project.