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 39 figures behind the modern work who have died, 30 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.

The work listed here is the bedrock on which modern Goldbach research is built; every modern paper in this directory ultimately rests on the circle method (Hardy-Littlewood, Vinogradov, van der Corput), the sieve toolkit (Halberstam-Richert, Linnik), and the breakthroughs of Jingrun Chen, Yuan Wang, and Hua Loo-Keng.

Contributions

• Gennadii Ivanovich Arkhipov (1945-2013): Sharpened the estimate for Vinogradov's integral with Karatsuba (1979), the engine of the circle method for Goldbach, then proved a run of bounds on the exceptional set in binary Goldbach-type problems (1997, 1999, 2002, 2003) and on the number of summands in Vinogradov's additive problem
• Mark Borisovich Barban (1935-1968): The Barban-Davenport-Halberstam mean-square theorem on primes in arithmetic progressions, the large-sieve input that major-arc and exceptional-set arguments for the binary Goldbach problem rest on; his 1960 paper on the elementary method in the binary Goldbach problem and his 1963 L-function density theorems attacked the sum of a prime and an almost prime directly
• 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 Vinogradov's method uses on the ternary Goldbach problem
• 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
• Alexander Buchstab (1905-1990): The Buchstab function and Buchstab identity, foundational tools in sieve theory
• Jingrun Chen (1933-1996): Chen's theorem: every sufficiently large even integer is the sum of a prime and a product of at most two primes, the strongest known partial result toward Goldbach
• Nikolai Chudakov (1904-1986): Work on the ternary Goldbach problem, prime gaps, and the zeros of Dirichlet L-functions (published as N. G. Tchudakoff)
• J. G. van der Corput (1890-1975): Van der Corput's method for exponential sums; foundational for the circle method
• Harold Davenport (1907-1969): Multiplicative Number Theory and major advances in the Hardy-Littlewood circle method for additive prime problems
• Paul Erdős (1913-1996): Foundational and prolific contributor to additive and combinatorial number theory; posed and funded many of the prize problems that drive modern work on representing integers as sums of primes
• Theodor Estermann (1902-1991): Goldbach-Estermann theorem; early progress on the ternary problem
• George Greaves (1941-2008): Author of Sieves in Number Theory (Springer, 2001); his weighted sieve results bear directly on almost-prime values of polynomials
• Emil Grosswald (1912-1989): Analytic number theorist and Rademacher's student; author of Topics from the Theory of Numbers and Representations of Integers as Sums of Squares
• 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 conjectures underlying modern work on the Goldbach and prime-tuple problems
• 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
• Matti Jutila (1943-2026): His variant of the circle method, with overlapping intervals, is named after him and used without explanation; his work repeatedly lowered the upper bound for Linnik's constant
• Anatoly A. Karatsuba (1937-2008): Analytic number theory, exponential sums, and the Karatsuba multiplication algorithm; advisor to 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
• Yu. V. Linnik (1915-1972): Linnik's theorem, the dispersion method, and the Linnik constant
• Ming-Chit Liu (1937-2023): Set a record on the ternary Goldbach problem with an effective bound (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
• Florian Luca (1969-2026): Prolific number theorist whose work reached the Goldbach circle of ideas through additive problems and Diophantine equations; on this board at the time of his death in late July 2026
• 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 prime distribution for two generations
• Hans Rademacher (1892-1969): Rademacher's exact convergent series for the partition function; a foundational figure in analytic number theory
• Kanakanahalli Ramachandra (1933-2011): Founded the Hardy-Ramanujan Journal; mean value and omega theorems for the Riemann zeta-function, and the six exponentials theorem
• Hans-Egon Richert (1924-1993): Sieve Methods (with Halberstam); the standard reference
• Georg Johann Rieger (1931-2021): Additive number theory, the Goldbach and Waring problems, and the distribution of squarefree numbers
• Nikolai Pavlovich Romanov (1907-1972): Romanov's theorem (1934): the integers representable as a prime plus a perfect power p + a^k have positive lower density, the first density theorem of its kind in the additive theory of primes and a direct extension of Schnirelmann's route to Goldbach
• Wolfgang Schwarz (1934-2013): Mean-value theorems for arithmetic functions and Ramanujan expansions; co-organizer of the Oberwolfach analytic number theory meetings
• Wacław Sierpiński (1882-1969): Founder of the Polish school of number theory and set theory; Sierpinski numbers and extensive work on elementary number theory
• Askold Ivanovich Vinogradov (1929-2005): Bombieri-Vinogradov theorem on average prime distribution
• Ivan Matveyevich Vinogradov (1891-1983): Proved the ternary Goldbach conjecture for sufficiently large odd integers (1937)
• Sergei Voronin (1946-1997): Proved the universality theorem for the Riemann zeta-function and its value distribution
• Arnold Walfisz (1892-1962): Siegel-Walfisz theorem on primes in arithmetic progressions
• Yuan Wang (1930-2021): Wang (1+4) result; key contributor to the Chinese school of additive prime number theory
• Dieter Wolke (1942-2015): Freiburg analytic number theorist whose research group page named the Goldbach and twin prime problems as its subject; doctoral advisor of Claus Bauer