Louis Joel Mordell ( Eng. Louis Joel Mordell ; January 28, 1888 , Philadelphia , USA - March 12, 1972 , Cambridge , UK ) - English mathematician.
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| Awards and prizes | member of the Royal Society of London de Morgan Medal ( 1941 ) [d] |
Author of works on algebra , the theory of Diophantine equations , trigonometric series . He substantiated the problem for functional fields named after him. He proved Einstein's formulas in the field of the theory of quadratic forms (1918).
His name is associated with the analysis of the Diophantine equation
Where Is an integer. The corresponding elliptic curve is now called the Mordell curve . [four]
In 1922, L. Mordell connected many solutions of the Diophantine algebraic equation with the geometric genus of the curve defined by this equation. He came to the conclusion that if the degree of the equation is sufficiently large (more than two), then the dimension of the solution space is expressed in terms of the genus of the curve, and therefore this dimension is finite . For smaller degrees, this may not be the case - the Pythagorean equation of degree 2 has an infinite family of solutions. This hypothesis was proved only in 1983 by the German mathematician Faltinges .
Outstanding success L. Mordell achieved in geometry. For example, in 1937, he proved the Erdшаs – Mordell inequality , which states that for any point M inside a given triangle, the sum of the distances from it to the vertices is at least twice the sum of the distances from the point to the sides of the triangle, and equality holds if and only if the triangle equilateral and point M is its center .
In 1956, L. Mordell found a beautiful particular solution to the problem of four cubes . [5]
Mordell is the author of 270 publications. His main monograph is Diophantine Equations ( 1969 ).
In 1971, Mordell participated in a theoretical conference in Moscow and was then invited to Leningrad to give lectures.
Rewards
- Medal de Morgan (1941)
- Sylvester Medal (1949)
Notes
- ↑ 1 2 German National Library , Berlin State Library , Bavarian State Library , etc. Record # 117713155 // General regulatory control (GND) - 2012—2016.
- ↑ 1 2 Archive for the history of mathematics MacTyutor
- ↑ 1 2 SNAC - 2010.
- ↑ Weisstein, Eric W. Mordell Curve on Wolfram MathWorld .
- ↑ The Four Cubes Problem (Inaccessible link) . Date of treatment July 11, 2007. Archived July 14, 2007.
Links
- John J. O'Connor and Edmund F. Robertson . Mordell, Louis Joel (English) - biography in the MacTutor archive.
- Pell equation and equation y 2 + 1 = 2x 4