Scottish mathematician who worked in algebraic and differential geometry. His 1930 paper on multiple integrals attached to an algebraic variety brought him international recognition, and his theory of harmonic integrals was described by Hermann Weyl as one of the great landmarks in the history of science of the twentieth century. At the 1950 International Congress of Mathematicians he posed the Hodge conjecture, relating the topology of a complex algebraic variety to its algebraic subvarieties. He served as Lowndean Professor of Astronomy and Geometry at Cambridge from 1936 and as Master of Pembroke College, Cambridge.
Facts
Nationality / Culture Defining ContributionPosed the Hodge conjecture at the 1950 International Congress of Mathematicians, and developed the theory of harmonic integrals in algebraic geometry. 1 Notable WorkThe Theory and Applications of Harmonic Integrals (1941); Methods of Algebraic Geometry, three volumes with Daniel Pedoe (from 1941) 2 AwardFellow of the Royal Society (1938); Adams Prize (1937); Royal Medal (1957); Knighted (1959); De Morgan Medal (1959); Copley Medal (1974) 2 William Vallance Douglas Hodge
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Connections
Conjectures Posed
Source Wolfram MathWorld
In Branch
Mentored
Source Roger Penrose (Wikipedia)
Proofs Credited
Source Hodge index theorem, Wikipedia
In the Other Atlases
Nationality
Also in Geography Atlas: the nationality of this subject.
Source Wikidata: William Vallance Douglas Hodge
Sources
1. Clay Mathematics Institute
Clay Mathematics Institutehttps://www.claymath.org/millennium-problems/, Hodge Conjecture section (unsolved problems)Quote, https://www.claymath.org/millennium-problems/, Hodge Conjecture section (unsolved problems)
The answer to this conjecture determines how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations.
2. MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and Statisticshttps://mathshistory.st-andrews.ac.uk/Biographies/Hodge/Quote, https://mathshistory.st-andrews.ac.uk/Biographies/Hodge/
William Hodge was Lowndean Professor of Astronomy and Geometry at Cambridge. His main interests were in Algebraic Geometry and Differential Geometry.
Wikidata: William Vallance Douglas Hodge
Wikidata Q1356359, class allow-list match (w-wdresolver-0926)View the Source Wolfram MathWorld
Wolfram Research, Inc.Conjectures Posed: Hodge Conjecture, References section, Hodge W.V.D. 1952 entryQuote, Conjectures Posed: Hodge Conjecture, References section, Hodge W.V.D. 1952 entry
Hodge, W. V. D. The Topological Invariants of Algebraic Varieties. Proc. Internat. Congress Math., Cambridge, Mass., 1950, Vol. 1. Providence, RI: Amer. Math. Soc., pp. 182-192, 1952.
Roger Penrose (Wikipedia)
Mentored: Roger Penrose, Infobox, doctoral advisor or academic advisorsView the Source Hodge index theorem, Wikipedia
Proofs Credited: Hodge Index Theorem, LeadQuote, Proofs Credited: Hodge Index Theorem, Lead
This result was proved in the 1930s by W. V. D. Hodge, for varieties over the complex numbers, after it had been a conjecture for some time of the Italian school of algebraic geometry (in particular, Francesco Severi, who in this case showed that ρ < ∞).
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