In Memoriam

Researchers in this directory who are no longer with us

The Top 100 and the regional pages list living researchers only, so the directory stays accurate for anyone using it to make contact. This page remembers the 1 key figures from the ranked pool who have passed away (the most highly ranked of the deceased), plus a separate listing of foundational figures whose careers predate the digital publication record our pipeline reads from.

Foundational figures

The pipeline behind this site ranks researchers whose work appears on arXiv or in OpenAlex, which mostly means careers active from the mid-1990s onward. The names below predate that coverage. Their work is the bedrock on which modern research is built. They are listed by last name; each contribution is noted at the bottom of the page.

Foundational figures: contributions

• Viggo Brun (1885-1978): Created the modern sieve (Brun's sieve) and proved the sum of reciprocals of twin primes converges; Brun's constant is named for him
• Jingrun Chen (1933-1996): Proved Chen's theorem
• Paul Erdős (1913-1996): Pioneering results on gaps between consecutive primes; the Erdős prize on prime gaps spurred the bounded-gaps breakthroughs
• Patrick X. Gallagher (1935-2019): Pioneered large sieve theory and invented the larger sieve; his singular-series work underlies the Hardy-Littlewood prime-tuple heuristics
• Heini Halberstam (1926-2014): Co-author of the standard monograph Sieve Methods; the Elliott-Halberstam conjecture is central to bounded prime gaps
• Christopher Hooley (1928-2018): Hooley's theorem on Artin's conjecture under GRH; a leading figure in applying the Selberg sieve to problems on primes
• Anatoly A. Karatsuba (1937-2008): Deep contributions to analytic number theory and the distribution of primes in short intervals
• Stanisław Knapowski (1931-1967): With Turan developed comparative prime number theory and studied sign changes of pi(x) - li(x)
• Edmund Landau (1877-1938): Posed the four problems on primes (Goldbach, twin primes, Legendre's conjecture, and n^2+1 primes) as unattackable at the 1912 International Congress of Mathematicians; foundational figure in analytic number theory
• Aleksandr Fedorovich Lavrik (1927-2010): Approximate functional equations for L-functions and work on the ternary Goldbach problem and primes in short intervals
• Yuri Linnik (1915-1972): Invented the large sieve and the dispersion method
• Hans-Egon Richert (1924-1993): Co-author of the standard monograph Sieve Methods (with Halberstam), the foundational reference for work on prime gaps
• Georg Johann Rieger (1931-2021): Additive number theory, the Goldbach and Waring problems, and the distribution of squarefree numbers
• Wolfgang Schwarz (1934-2013): Mean-value theorems for arithmetic functions and Ramanujan expansions; co-organizer of the Oberwolfach analytic number theory meetings
• Atle Selberg (1917-2007): Fields Medalist; the Selberg sieve is a foundational tool in all modern work on gaps between primes
• Pál Turán (1910-1976): Created the power-sum (Turan) method and applied it to the zeros of the zeta-function and to comparative prime number theory
• Yuan Wang (1930-2021): Major contributions to the circle method and sieve theory for problems on primes
• John W. Wrench (1911-2009): Computed the twin-prime constant and Artin's constant to high precision (1961), early machine work on the constants in the Hardy-Littlewood conjectures

Key figures from ranked pool