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Academic journal
Documenta Mathematica is a peer-reviewed multidisciplinary mathematical journal by the German Mathematical Society published since 1996. The journal doesn't
Documenta_Mathematica
Ars Mathematica Contemporanea Australasian Journal of Combinatorics Discrete Analysis Discrete Mathematics & Theoretical Computer Science Documenta Mathematica
List_of_open-access_journals
Conjecture on zeros of the zeta function
International Congress of Mathematicians, Vol. I (Berlin, 1998), Documenta Mathematica, pp. 163–186, MR 1648030 Dudek, Adrian W. (2014-08-21), "On the
Riemann_hypothesis
Unsolved problem in computer science
1954–2012". In Grötschel, M. (ed.). Optimization Stories (PDF). Documenta Mathematica. pp. 359–376. ISBN 978-3-936609-58-5. ISSN 1431-0643. Foulds, L
P_versus_NP_problem
Algorithm for finding shortest paths
history of the shortest path problem" (PDF). Optimization Stories. Documenta Mathematica Series. Vol. 6. pp. 155–167. doi:10.4171/dms/6/19. ISBN 978-3-936609-58-5
Dijkstra's_algorithm
Optimization algorithm
method" ( (PDF)). In Grötschel, M. (ed.). Optimization Stories. Documenta Mathematica Series. Vol. 6 (1st ed.). EMS Press. pp. 251–254. doi:10.4171/dms/6/27
Gradient_descent
Japanese mathematician (born 1952)
member at the University of Chicago in 2009. A special volume of Documenta Mathematica was published in honor of his 50th birthday, together with research
Kazuya_Kato
American mathematician
Victor; Williams, Lauren (2008), "Faces of generalized permutohedra", Documenta Mathematica, 13: 207–273, arXiv:math/0609184, Bibcode:2006math......9184P, doi:10
Lauren Williams (mathematician)
Lauren_Williams_(mathematician)
American mathematician
and Artificial Intelligence, Mathematical and Computer Modelling, Documenta Mathematica and others. In 2012 he became a fellow of the American Mathematical
Anil_Nerode
Optimization algorithm for artificial neural networks
Invented the Reverse Mode of Differentiation?". Optimization Stories. Documenta Mathematica, Extra Volume ISMP. pp. 389–400. S2CID 15568746. Griewank, Andreas;
Backpropagation
German mathematician
society. Under her leadership, the society founded the journal Documenta Mathematica. Birth date from German National Library catalog entry, retrieved
Ina_Kersten
Invented the Reverse Mode of Differentiation?". Documenta Mathematica, Extra Volume ISMP. Documenta Mathematica Series. 6: 389–400. doi:10.4171/dms/6/38.
Timeline_of_machine_learning
Japanese mathematician
International Congress of Mathematicians, Vol. II (Berlin, 1998)", Documenta Mathematica: 187–196, ISSN 1431-0635, MR 1648069 Mochizuki, Shinichi (1999)
Shinichi_Mochizuki
Collection of notes
International Congress of Mathematicians, Vol. III (Berlin, 1998). Documenta Mathematica. pp. 799–809. doi:10.4171/dms/1-3/77. MR 1648209. Zbl 0905.01006
Mathematical manuscripts of Karl Marx
Mathematical_manuscripts_of_Karl_Marx
Topological invariant in mathematics
Leinster, Tom (2008). "The Euler characteristic of a category" (PDF). Documenta Mathematica. 13: 21–49. doi:10.4171/dm/240. S2CID 1046313. Archived from the
Euler_characteristic
Smooth manifold with an inner product on each tangent space
geodesic distance on spaces of submanifolds and diffeomorphisms". Documenta Mathematica. 10: 217–245. arXiv:math/0409303. doi:10.4171/dm/187. S2CID 69260
Riemannian_manifold
Algorithm for solving systems of linear equations
variables of a system of linear inequalities, rather than equations. "DOCUMENTA MATHEMATICA, Vol. Extra Volume: Optimization Stories (2012), 9-14". www.emis
Gaussian_elimination
British-American mathematician (born 1959)
S2CID 58095147. Goddard, Peter (1998). "The work of Richard Ewen Borcherds". Documenta Mathematica: 99–108. arXiv:math/9808136. Bibcode:1998math......8136G. ISSN 1431-0635
Richard_Borcherds
South African-born mathematician
Sarnak, Peter (1998). " L {\displaystyle L} -functions" (PDF). Documenta Mathematica Journal der Deutshen Mathematiker-Vereinigung Extra Vol. ICM Berlin
Peter_Sarnak
Study of mathematical algorithms for optimization problems
of linear and mixed-integer programming computation". Documenta Mathematica. Documenta Mathematica Series. 2012: 107–121. doi:10.4171/dms/6/16. Abdulkadirov
Mathematical_optimization
Finding shortest walks through all graph edges
on Mathematical Programming, Berlin, August 19–24, 2012 (PDF), Documenta Mathematica, pp. 43–50, doi:10.4171/dms/6/10, ISBN 978-3-936609-58-5, MR 2991468
Chinese_postman_problem
Theory in number theory
absolute anabelian geometry of canonical curves" (PDF). Documenta Mathematica. Documenta Mathematica Series. Extra Vol., Kazuya Kato's fiftieth birthday:
Anabelian_geometry
Method of quantum computing
as of July 2025 (link) P. Shor (1998). Quantum Computing (PDF). Documenta Mathematica. p. 468. Archived from the original (PDF) on 2022-03-18. Retrieved
One-way_quantum_computer
Branching diagram of evolutionary relationships between organisms
Moulton. 2001. Metric Spaces in Pure and Applied Mathematics. Documenta Mathematica LSU 2001: 121–139 "Tree Formats". Evolution and Genomics. Retrieved
Phylogenetic_tree
How spheres of various dimensions can wrap around each other
of the International Congress of Mathematicians (Berlin, 1998), Documenta Mathematica, Extra Volume, vol. II, pp. 465–472, MR 1648096 Mahowald, Mark (2001)
Homotopy_groups_of_spheres
American mathematician and educator
2020-01-28. "William Karush and the KKT Theorem" by Richard W. Cottle. Documenta Mathematica, 2012 "William Karush". Nuclear Museum. 2026-03-07. Retrieved 2026-03-07
William_Karush
Russian mathematician
cohomology. In 2010 special issues of Journal of K-theory and of Documenta Mathematica have been published in honour of his 60th birthday. He died in July
Andrei_Suslin
differentiation?", in Grötschel, Martin (ed.), Optimization Stories, Documenta Mathematica Series, vol. 6 (1 ed.), EMS Press, pp. 389–400, doi:10.4171/dms/6/38
History of artificial neural networks
History_of_artificial_neural_networks
Russian mathematician
triangulations: ubiquitous Siamese twins". Optimization Stories. Documenta Mathematica Series. Vol. ISMP. pp. 419–431. doi:10.4171/DMS/6/40. ISBN 978-3-936609-58-5
Georgy_Voronoy
Italian mathematician (born 1963)
Matthias (2012), "Modularity of the Consani–Scholten quintic" (PDF), Documenta Mathematica, 17: 953–987, doi:10.4171/dm/386, MR 3007681, S2CID 6475185 Thas
Caterina_Consani
Arrangement of spheres within a space
MathWorld. Sloane, N. J. A. (1998). "The Sphere-Packing Problem". Documenta Mathematica. 3: 387–396. arXiv:math/0207256. Vardy, Alexander (1999). "Density
Sphere_packing
Numerical calculations carrying along derivatives
reverse mode of differentiation?" (PDF). Optimization Stories. Documenta Mathematica Series. Vol. 6. pp. 389–400. doi:10.4171/dms/6/38. ISBN 978-3-936609-58-5
Automatic_differentiation
American mathematician
(1998). "Generic large cardinals: New axioms for mathematics?". Documenta Mathematica (Bielefeld), Extra Volume ICM Berlin. Vol. II. pp. 11–21. "2023
Matthew_Foreman
Israeli mathematician
Jarden and F. Pop, Function fields of one Variable over PAC Fields, Documenta Mathematica 14 (2009) 517–523. M. Jarden, Diamonds in torsion of Abelian varieties
Moshe_Jarden
American mathematician (born 1954)
(2010-08-11), "The geometry of the Seiberg-Witten invariants.", Documenta Mathematica, Universiät Bielefeld, Fakultät für Mathematik: 493–504, ISSN 1431-0643
Clifford_Taubes
Canadian mathematician
pp. 121–186 with C. Cornut CM points and quaternion algebras, Documenta Mathematica, volume 10, 2005 Vatsal is also a published author. His short story
Vinayak_Vatsal
Hungarian-American computer scientist
"Worst-case complexity, average-case complexity and lattice problems". Documenta Mathematica: 421–428. AAAS Members Elected as Fellows, AAAS, 29 November 2012
Miklós_Ajtai
Mathematical society
de l'Institut Henri Poincaré D Commentarii Mathematici Helvetici Documenta Mathematica Elemente der Mathematik EMS Surveys in Mathematical Sciences Groups
European_Mathematical_Society
American mathematician (1935–2020)
Ronald Graham: laying the foundations of online optimization. Documenta Mathematica. pp. 239–245. MR 2991486. Garey, M. R.; Johnson, D. S. (1981). "Approximation
Ronald_Graham
Type of number in combinatorial mathematics and statistics
Zyczkowski, Karol (2013). "Densities of the Raney distributions". Documenta Mathematica. 18: 1593–1596. arXiv:1211.7259. Bibcode:2012arXiv1211.7259M. doi:10
Fuss–Catalan_number
American mathematician
conjecture. With an appendix by Agol, Daniel Groves, and Jason Manning". Documenta Mathematica. 18: 1045–1087. doi:10.4171/dm/421. MR 3104553. S2CID 255586740
Ian_Agol
American historian (born 1944)
Congress of Mathematicians, Berlin 1998, Extra Volume ICM 1998. Documenta Mathematica, Machoover, Moshé (1996) "Review: Joseph Warren Dauben, Abraham
Joseph_Dauben
Mathematics concept
With an appendix by Agol, Daniel Groves, and Jason Manning" (PDF). Documenta Mathematica. 18: 1045–1087. MR 3104553. Archived from the original (PDF) on
Haken_manifold
Finnish mathematician and computer scientist
(2012). "Who Invented the Reverse Mode of Differentiation?" (PDF). Documenta Mathematica, Extra Volume ISMP. pp. 389–400. S2CID 15568746. Archived from the
Seppo_Linnainmaa
Notion in metric geometry
Develin, Mike; Sturmfels, Bernd (2004), "Tropical convexity" (PDF), Documenta Mathematica, 9: 1–27, doi:10.4171/dm/154, S2CID 64471. Develin, Mike; Sturmfels
Tight_span
Chinese mathematician
on Mathematical Programming. Berlin, Germany, 19–24 August 2012, Documenta Mathematica Series, vol. 6, pp. 43–50, doi:10.4171/dms/6/10, ISBN 978-3-936609-58-5
Meigu_Guan
Matrix group
Theorem 7.2. Agol, Ian (2013). "The Virtual Haken Conjecture". Documenta Mathematica. 18: 1045–1087. arXiv:1204.2810. doi:10.4171/dm/421. S2CID 255586740
Congruence_subgroup
Software for inferring bioinformatics split graphs
"Metric spaces in pure and applied mathematics" (PDF). Documenta Mathematica. Documenta Mathematica Series. 2: 121–139. doi:10.4171/dms/2/5. ISBN 978-3-98547-042-6
SplitsTree
Shape bounded by non-intersecting line segments
International Congress of Mathematicians, Vol. III (Berlin, 1998). Documenta Mathematica. pp. 533–542. MR 1648186. Quintas, L. V.; Supnick, Fred (1965).
Simple_polygon
Invariant of algebraic varieties and of more general schemes
"Réalisation ℓ-adique des motifs triangulés géométriques. I". Documenta Mathematica. 12: 607–608. doi:10.4171/dm/237.; Bondarko, Mikhail V. (2009).
Motivic_cohomology
Generalizations of the Riemann zeta function
relations of multiple polylogarithm values at roots of unity". Documenta Mathematica. 15: 1–34. arXiv:0707.1459. doi:10.4171/dm/291. Zhao, Jianqiang
Multiple_zeta_function
Infinite series summing alternating 1 and -1 terms
Leinster, Tom (2008). "The Euler characteristic of a category". Documenta Mathematica. 13: 21–49. arXiv:math/0610260. doi:10.4171/dm/240. Baez, John (2006)
Grandi's_series
German professional society
publishes two scientific journals, the Jahresbericht der DMV and Documenta Mathematica. It also publishes a quarterly magazine for its membership the Mitteilungen
German_Mathematical_Society
Concept in differential geometry
Leinster, Tom (2008). "The Euler characteristic of a category" (PDF). Documenta Mathematica. 13: 21–49. https://mathoverflow.net/questions/51993/euler-char
Euler characteristic of an orbifold
Euler_characteristic_of_an_orbifold
2017-08-07. Borcherds, Richard E. (1998). "What is Moonshine?". Documenta Mathematica. ICM 1: 607–615. arXiv:math/9809110. Bibcode:1998math......9110B
Exceptional_object
Conjecture pertaining to finite covers of 3-manifold subfields
hierarchy (PDF). Agol, Ian (2013). "The virtual Haken conjecture". Documenta Mathematica. 18. With an appendix by Ian Agol, Daniel Groves and Jason Manning:
Virtually_fibered_conjecture
Russian American mathematician (born 1955)
the essential dimension of groups. In 2015 a special volume of Documenta Mathematica was published in honor of Merkurjev's sixtieth birthday. 1998: Max-Albert
Alexander_Merkurjev
Every compact, irreducible 3-manifold with infinite fundamental group is virtually Haken
shortly thereafter in a preprint which was eventually published in Documenta Mathematica. The proof was obtained via a strategy by previous work of Daniel
Virtually_Haken_conjecture
Topological structure in number theory
(2006), "Ring-theoretic properties of Iwasawa algebras: a survey", Documenta Mathematica: 7–33, arXiv:math/0511345, Bibcode:2005math.....11345A, ISSN 1431-0635
Iwasawa_algebra
German mathematician (born 1958)
International Congress of Mathematicians, Vol. I (Berlin, 1998), Documenta Mathematica (Extra Vol. I), pp. 163–186, MR 1648030 Deninger, Christopher (2002)
Christopher_Deninger
American computer scientist
International Congress of Mathematicians, Vol. III (Berlin, 1998) (PDF), Documenta Mathematica, pp. 645–656, MR 1648194, archived from the original (PDF) on 2017-07-13
David_Applegate
Planar graph with convex polygon faces
Rote, Günter (2006), "Strictly convex drawings of planar graphs", Documenta Mathematica, 11: 369–391, arXiv:cs/0507030, doi:10.4171/dm/214, MR 2262937,
Convex_drawing
Favi, Giordano (2003). "Essential dimension: A functorial point of view (after A. Merkurjev)". Documenta Mathematica. 8: 279–330. doi:10.4171/DM/145.
Essential_dimension
Czech-Canadian mathematician
William (1998), "On the Solution of Traveling Salesman Problems", Documenta Mathematica, Extra Volume ICM III, archived from the original on 2020-07-27
Václav_Chvátal
Type of quartic plane curve
Kohn, Kathlén, et al. "Adjoints and canonical forms of polypols." Documenta Mathematica 30.2 (2025): 275-346. Julius Plücker, Theorie der algebraischen
Ampersand_curve
Application of homotopy to algebraic varieties
May 2008 Voevodsky, Vladimir (1998), "A1-homotopy theory" (PDF), Documenta Mathematica, Proceedings of the International Congress of Mathematicians, Vol
A¹_homotopy_theory
Completes the Langlands program for general linear groups over algebraic function fields
Drinfeld et applications" [Drinfelʹd shtukas and applications], Documenta Mathematica (in French), II: 563–570, ISSN 1431-0635, MR 1648105, archived from
Lafforgue's_theorem
American mathematician
he was a Guggenheim Fellow. Since 1995 he has been co-editor of Documenta Mathematica. In 2012 he became a fellow of the American Mathematical Society
Stephen_Lichtenbaum
Russian mathematician
2011-09-20. Fesenko, I. (2003). "Analysis on arithmetic schemes. I". Documenta Mathematica: 261–284. ISBN 978-3-936609-21-9.{{cite journal}}: CS1 maint: periodical
Ivan_Fesenko
American economist
in: Möhring, Rolf H. "D. Ray Fulkerson and Project Scheduling." Documenta Mathematica · Extra Volume ISMP (2012) 211–219 Missiles and Rockets. Vol. 8
Willard_Fazar
German mathematician
International Congress of Mathematicians, 1998, Bd.II, S.691, Documenta Mathematica. with Bethuel, Huisken, Steffen: Variational models for microstructure
Stefan_Müller_(mathematician)
British mathematician
International Congress of Mathematicians, Vol. II (Berlin, 1998). Documenta Mathematica (Extra Vol. II): 121–128. MR 1648062. Jeremy Rickard at the Mathematics
Jeremy_Rickard
in: Möhring, Rolf H. "D. Ray Fulkerson and Project Scheduling." Documenta Mathematica Extra Volume ISMP (2012) 211–219. Desmond L. Cook (1966), Program
United States Navy Special Projects Office
United_States_Navy_Special_Projects_Office
Construction in algebraic geometry
Simon K. (1998). "Lefschetz fibrations in symplectic geometry". Documenta Mathematica (Proceedings of the International Congress of Mathematicians, Vol
Lefschetz_pencil
Russian mathematician (1896-1966)
Archive, University of St Andrews "Extra Vol. ICM III (1998)". Documenta Mathematica: 799–809. J. W. Dauben, Marx, Mao and mathematics: the politics
Sofya_Yanovskaya
innovation", Proceedings of the international congress of mathematicians, Documenta mathematica, vol. Extra Volume ICM 1998, III, Berlin: der Deutschen Mathematiker-Vereinigung
List of probabilistic proofs of non-probabilistic theorems
List_of_probabilistic_proofs_of_non-probabilistic_theorems
S2CID 123298695. Agol, Ian (2013). "The virtual Haken conjecture". Documenta Mathematica. 18. With an appendix by Ian Agol, Daniel Groves, and Jason Manning:
Arithmetic hyperbolic 3-manifold
Arithmetic_hyperbolic_3-manifold
Theorem in Lie theory in mathematics
Vincent (2014). "Hyperbolic manifolds of small volume" (PDF). Documenta Mathematica. 19: 801–814. arXiv:1310.2270. doi:10.4171/dm/464. S2CID 303659
Kazhdan–Margulis_theorem
Mathematical concept
Amnon (2001b). "On the derived category of sheaves on a manifold". Documenta Mathematica. 6: 483–488. doi:10.4171/dm/111. Hall, Jack; Neeman, Amnon; Rydh
Compact_object_(mathematics)
American mathematician
Develin, Mike; Sturmfels, Bernd (2004). "Tropical Convexity". Documenta Mathematica. 9: 1–27. arXiv:math/0308254. doi:10.4171/dm/154. S2CID 64471. "Citations
Mike_Develin
Algebraic hypersurface
Matthias (2012), "Modularity of the Consani–Scholten quintic" (PDF), Documenta Mathematica, 17: 953–987, doi:10.4171/dm/386, MR 3007681 Yui, Noriko (2013)
Consani–Scholten_quintic
American mathematician
Series and the Trace Formula for GL(2) over a Function Field" (PDF). Documenta Mathematica. Birkhäuser Basel, ISBN 978-3-319-31593-5. Springer-Verlag New York
Yuval_Flicker
2010-11-25 de Jong, A. J. (1998), "Barsotti-Tate groups and crystals", Documenta Mathematica, Proceedings of the International Congress of Mathematicians, Vol
Barsotti–Tate_group
American mathematician
"Viscosity Solutions of Elliptic Partial Differential Equations". DOCUMENTA MATHEMATICA, Extra Volume ICM III. pp. 31–38. "Robert Jensen, Publications"
Robert_R._Jensen
German mathematician
Fellowship (2000) and a Humboldt Prize (2021). He is editor for Documenta Mathematica and managing editor for Commentarii Mathematici Universitatis Sancti
Thomas_Geisser
the Museum of Contemporary Art in Ghent. Well known from his exposition Documenta IX (Düsseldorf, 1992), he has been responsible for several expositions
Meanings of minor-planet names: 12001–13000
Meanings_of_minor-planet_names:_12001–13000
Austrian ophthalmologist and historian of science (born 1945)
Universitatis Carolinae – Mathematica et Physica 46, Suppl., 27-140 (2005) [6] "Christoph Scheiner's Eye Studies". In: Documenta Ophthalmologica 81:27-35
Franz_Daxecker
American ophthalmologist and educator
"Personal Recollections of Einstein's Boyhood and Youth", in Scripta Mathematica. He also published an account of Einstein's Theory of Relativity. After
Max_Talmey
Contemporary historiography of the Crusades
Peter in his journey to Rome. (Runciman (1952), p. 74n) Documenta Lipsanographica. Documenta Lipsanographica ad I. bellum sacrum spectantia (Relics of
List of sources for the Crusades
List_of_sources_for_the_Crusades
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