Gerd Faltings
Faltings in 2005
Born (1954-07-28) 28 July 1954 (age 71)
Gelsenkirchen-Buer, North Rhine-Westphalia, West Germany
Education University of Münster (Dip, Dr. rer. nat.)
Known for
  • Almost ring
  • Faltings height
  • Faltings' annihilator theorem
  • Faltings' theorem
  • Faltings' product theorem
Spouse
Angelika Tschimmel
​
​
(m. 1984; died 2011)​
Awards
  • Dannie Heineman Prize (1983)
  • Fields Medal (1986)
  • ICM Speaker (1986, 1994)
  • Guggenheim Fellowship (1988)
  • Leibniz Prize (1996)
  • Von Staudt Prize (2008)
  • Heinz Gumin Prize (2010)
  • King Faisal International Prize (2014)
  • Shaw Prize (2015)
  • ForMemRS (2016)
  • Cantor Medal (2017)
  • Pour le Mérite (2024)
  • Abel Prize (2026)
Scientific career
Fields Mathematics
Institutions
  • Max Planck Institute for Mathematics
  • University of Bonn
  • Princeton University
  • University of Wuppertal
Theses
Doctoral advisor Hans-Joachim Nastold
Doctoral students
  • Michael J. Larsen
  • Shinichi Mochizuki[1]
  • Wiesława Nizioł[2]
  • Nikolai Durov

Gerd Faltings ( German pronunciation: [ɡɛʁt ˈfaltɪŋs] ⓘ; born 28 July 1954) is a German mathematician known for his work in arithmetic geometry.[3][4] He was awarded the Fields Medal in 1986 for his proofs of the Mordell conjecture and several related conjectures.[5][6] He won the Abel Prize in 2026 for these achievements.[7][8][9]

Education

Faltings was born on 28 July 1954 in Gelsenkirchen-Buer, West Germany.[10] From 1972 to 1978, Faltings studied mathematics and physics at the University of Münster. Interrupted by 15 months of obligatory military service, he received his Dr. rer. nat. in mathematics in 1978.[4][11][12]

Career and research

In 1981, he obtained the venia legendi (Habilitation) in mathematics, from the University of Münster. During this time he was an assistant professor at the University of Münster. From 1982 to 1984, he was professor at the University of Wuppertal.[13]

From 1985 to 1994, he was professor at Princeton University. In autumn of 1988 and in the academic year 1992–1993 he was a visiting scholar at the Institute for Advanced Study.[14]

He was awarded the Fields Medal in 1986[15] for proving the Tate conjecture for Abelian varieties over number fields, the Shafarevich conjecture for Abelian varieties over number fields and the Mordell conjecture,[16][17] which states that any non-singular projective curve of genus g > 1 defined over a number field K contains only finitely many K-rational points.[18]

In 1994, as an invited speaker at the International Congress of Mathematicians he gave a talk Mumford-Stabilität in der algebraischen Geometrie lit. 'Mumford stability in algebraic geometry'. Extending methods of Paul Vojta, he proved the Mordell–Lang conjecture,[19] which is a generalization of the Mordell conjecture. Together with Gisbert Wüstholz,[20] he re-proved Roth's theorem, for which Roth had been awarded the Fields medal in 1958.[21]

He returned to Germany the same year, and from 1994 to 2018, he was a director of the Max Planck Institute for Mathematics in Bonn.[7] In 1996, he received the Gottfried Wilhelm Leibniz Prize of the Deutsche Forschungsgemeinschaft.[7]

Faltings has been the formal supervisor of over a dozen PhD students, including Shinichi Mochizuki,[1] Wiesława Nizioł,[2] and Nikolai Durov.[22]

On 19 March 2026, the Norwegian Academy of Science and Letters announced Faltings as the winner of the Abel Prize, "for introducing powerful tools in arithmetic geometry and resolving long-standing diophantine conjectures of Mordell and Lang."[7] He is the first German mathematician to have received both the Fields Medal and the Abel Prize.[23]

Personal life

Faltings married Angelika Tschimmel in 1984; she died in 2011.[24]

Awards and honours

  • Dannie Heineman Prize (1983)[7]
  • Fields Medal (1986)[7]
  • Guggenheim Fellowship (1988/89)[25]
  • Gottfried Wilhelm Leibniz Prize (1996)[7]
  • von Staudt Prize (2008)[26]
  • Heinz Gumin Prize (2010)[27]
  • King Faisal International Prize (2014)[7]
  • Shaw Prize (2015)[28]
  • Foreign Member of the Royal Society (2016)[29]
  • Cantor Medal (2017)[30]
  • National Academy of Sciences International Member (2018)[31]
  • Pour le Mérite for Sciences and Arts (2024)[32]
  • Abel Prize (2026)[33]

References

  1. ^ a b Castelvecchi, Davide (7 October 2015). "The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof". Nature. 526 (7572): 178–181. Bibcode:2015Natur.526..178C. doi:10.1038/526178a. PMID 26450038.
  2. ^ a b Gerd Faltings at the Mathematics Genealogy Project
  3. ^ O'Connor, John J.; Robertson, Edmund F., "Gerd Faltings", MacTutor History of Mathematics Archive, University of St Andrews
  4. ^ a b Gerd Faltings at the Mathematics Genealogy Project
  5. ^ "Autobiography of Gerd Faltings". The Shaw Prize.
  6. ^ "Fields Medals 1986". international math union.
  7. ^ a b c d e f g h "Gerd Faltings awarded the 2026 Abel Prize", abelprize.no, The Norwegian Academy of Science and Letters, 2026
  8. ^ Howlett, Joseph. "Gerd Faltings, mathematician who proved the Mordell conjecture, wins the Abel Prize at age 71". Scientific American. Retrieved 28 March 2026.
  9. ^ Chang, Kenneth (19 March 2026). "German Mathematician Wins Abel Prize for Number Theory Work". The New York Times. ISSN 0362-4331. Retrieved 28 March 2026.
  10. ^ "Gerd Falting". Encyclopædia Britannica. Retrieved 21 March 2026.
  11. ^ Faltings, Gerd (1 June 1978). "Über Macaulayfizierung". Mathematische Annalen (in German). 238 (2): 175–192. doi:10.1007/BF01424774. ISSN 1432-1807.
  12. ^ "Gerd Faltings". The Shaw Prize. Retrieved 18 January 2025.
  13. ^ Kirbach, Roland (8 June 1984). "Gerd Faltings: Genie ist für ihn normal" [Gerd Faltings: For him, genius is the norm]. Die Zeit (in German). Retrieved 14 May 2013.
  14. ^ "Gerd Faltings". Institute for Advanced Study. 9 December 2019.
  15. ^ "Fields Medals 1986 – Donaldson, Faltings, Freedman Achievements". www.mathunion.org. Retrieved 19 March 2026.
  16. ^ Faltings, Gerd (1983). "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern" [Finiteness theorems for abelian varieties over number fields]. Inventiones Mathematicae (in German). 73 (3): 349–366. Bibcode:1983InMat..73..349F. doi:10.1007/BF01388432. MR 0718935.
  17. ^ Faltings, Gerd (1984). "Erratum: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern". Inventiones Mathematicae (in German). 75 (2): 381. doi:10.1007/BF01388572. MR 0732554.
  18. ^ Hazewinkel, M. (1 December 2013), Encyclopaedia of Mathematics: Monge—Ampère Equation — Rings and Algebras, Springer, p. 19, ISBN 978-1-4899-3791-9
  19. ^ Faltings, Gerd (1994). "The general case of S. Lang's conjecture". In Cristante, Valentino; Messing, William (eds.). Barsotti Symposium in Algebraic Geometry. San Diego: Academic Press. pp. 175–182. ISBN 978-0-12-197270-7.
  20. ^ Faltings, Gerd; Wüstholz, Gisbert (1994). "Diophantine approximations on projective spaces". Inventiones Mathematicae. 116 (1): 109–138. Bibcode:1994InMat.116..109F. doi:10.1007/BF01231559. MR 1253191. S2CID 120642283.
  21. ^ "Citation from The Abel Prize Committee – Gerd Faltings", abelprize.no, The Norwegian Academy of Science and Letters, 2026
  22. ^ "PhD Students of Gerd Faltings". www.hcm.uni-bonn.de. Archived from the original on 19 July 2011.
  23. ^ Castelvecchi, Davide (19 March 2026). "Mathematician who reshaped number theory wins prestigious Abel prize". Nature. Retrieved 21 March 2026.
  24. ^ "Gerd Faltings". The Shaw Prize. 16 August 2023. Retrieved 25 September 2025.
  25. ^ "John Simon Guggenheim Foundation | Gerd Faltings". Archived from the original on 14 December 2019. Retrieved 14 December 2019.
  26. ^ "Gerd Faltings". Retrieved 13 December 2024.
  27. ^ "Oberwolfach Photo Collection". Retrieved 9 December 2024.
  28. ^ "The Shaw Prize – Top prizes for astronomy, life science and mathematics". www.shawprize.org. Archived from the original on 21 October 2019. Retrieved 1 June 2015.
  29. ^ "Gerd Faltings | Royal Society". royalsociety.org.
  30. ^ "Presseinformationen". www.mathematik.de.
  31. ^ "Gerd Faltings". National Academy of Sciences. 10 June 2021. Retrieved 9 September 2022.
  32. ^ "Faltings". ORDEN POUR LE MÉRITE (in German). Retrieved 26 November 2024.
  33. ^ "Prize winner 2026". Norwegian Academy of Science and Letters. Retrieved 19 March 2026.