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. 2 Notable WorkThe Theory and Applications of Harmonic Integrals (1941); Methods of Algebraic Geometry, three volumes with Daniel Pedoe (from 1941) 1 AwardFellow of the Royal Society (1938); Adams Prize (1937); Royal Medal (1957); Knighted (1959); De Morgan Medal (1959); Copley Medal (1974) 1 Cross-Tradition Connections
Sources
1. 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.
2. 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.
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.
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