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 is the one place the directory remembers the 28 figures behind the modern work who have died, 23 of whom also carry a rank in this site's ranked pool.

This is a curated list, not a computed one. Who appears here is an editorial judgement: a person is listed because their work matters to this problem, and every entry is hand-checked. The Rank column shows the site's composite ranked-pool rank for those who carry one, so the quantitative signal stays visible, but it is a guide to the judgement rather than the thing that decides it. A dash means the person is not in the ranked pool at all, which is the normal case for careers that predate the arXiv and OpenAlex record the pipeline reads from. Sort any column; dashes always sort to the bottom.

Contributions

• Jean Bourgain (1954-2018): Fields Medalist; with Demeter and Guth proved the main conjecture in Vinogradov's mean value theorem (2016), sharpening the exponential-sum machinery that the circle method uses on Landau's additive prime problems
• Boris Bredikhin (1920-1994): Developed the dispersion method for the Goldbach and Waring problems; the Bredikhin-Linnik theorem on primes of the form a^2+b^2+1
• Jingrun Chen (1933-1996): Chen's theorem; also proved that infinitely many n give n^2+1 a prime or a product of two primes
• J. G. van der Corput (1890-1975): Van der Corput's method for exponential sums, foundational for the circle method and prime-distribution estimates
• Harold Davenport (1907-1969): Multiplicative Number Theory and major advances in the Hardy-Littlewood circle method for additive prime problems; his Cambridge school trained much of the modern analytic attack on Landau's problems
• Theodor Estermann (1902-1991): The Goldbach-Estermann theorem and early progress on the ternary problem; his work on exponential sums and the Estermann zeta-function is part of the standard toolkit for Landau's problems
• Patrick X. Gallagher (1935-2019): Pioneered large sieve theory and invented the larger sieve; his 1976 short-interval work turned the Hardy-Littlewood prime-tuple heuristics into the Poisson model used for prime gaps and Legendre's conjecture
• Heini Halberstam (1926-2014): Co-author of the standard monograph Sieve Methods (with Richert); the Elliott-Halberstam conjecture is central to modern work on prime gaps
• G. H. Hardy (1877-1947): With Littlewood created the circle method and the Hardy-Littlewood prime-tuple conjectures, the analytic machinery and the quantitative predictions that all four of Landau's problems are attacked with today
• 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, and his Applications of Sieve Methods is a standard reference for Landau's problems
• Anatoly Karatsuba (1937-2008): Analytic number theory, exponential sums, and the distribution of primes in short intervals; founder of a major Russian school
• 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): The large sieve, the dispersion method, and Linnik's theorem on the least prime in an arithmetic progression
• Ming-Chit Liu (1937-2023): Set an effective record on the ternary Goldbach problem (with Tianze Wang, 2002); analytic number theory at HKU
• Hua Loo-Keng (1910-1985): Hua's lemma; founded the Chinese school of analytic number theory
• Shituo Lou (1941-2015): With Qi Yao proved a Chebyshev-type prime number theorem in short intervals of length x^theta for theta greater than 11/20 (1993), one of the sharpest unconditional results on the interval lengths that Legendre's conjecture asks about
• Chengdong Pan (1934-1997): Proved the (1,5) case toward Goldbach's conjecture (1962) and the (1,4) case (1963, independently and with Barban and Wang Yuan); founder of the Shandong University school of analytic number theory and an academician of the Chinese Academy of Sciences
• Karl Prachar (1925-1994): Primzahlverteilung (1957), the standard reference on the distribution of primes for two generations and the source most work on Legendre's conjecture and prime gaps cites for its background
• 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
• Andrzej Schinzel (1937-2021): Schinzel's Hypothesis H, the general conjecture on simultaneous prime values of polynomials that contains the twin-prime conjecture and the n^2+1 problem as special cases
• Wolfgang Schwarz (1934-2013): Mean-value theorems for arithmetic functions and Ramanujan expansions; co-organizer of the Oberwolfach analytic number theory meetings
• Askold Ivanovich Vinogradov (1929-2005): The Bombieri-Vinogradov theorem on the distribution of primes in arithmetic progressions on average
• Ivan Matveyevich Vinogradov (1891-1983): Proved the ternary Goldbach conjecture for sufficiently large odd integers (1937); the Vinogradov method of exponential sums
• Arnold Walfisz (1892-1962): The Siegel-Walfisz theorem on primes in arithmetic progressions, the uniform prime-counting estimate that every sieve and circle-method attack on Landau's problems is built on
• Yuan Wang (1930-2021): The Wang (1+4) result and major contributions to the circle method and sieve theory for additive prime problems
• 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