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The Italian school of differential geometry was a loose association of Italian mathematicians active in the late nineteenth and early 20th century in the closely related mathematical subjects of differential geometry and tensor analysis. Notable members include Beltrami, Ricci-Cubastro, Levi-Civita and Bianchi. Their work was mostly contemporary with the more famed (and much larger) Italian school of algebraic geometry, to which some of them also had close ties to, were influenced by, or were even considered members of, such as Ricci and Beltrami.
Beltrami's work influenced that of Ricci,[1] who in turn created the "Absolute Differential Calculus" with his student Levi-Civta. Other Italians active in the field around this time were Burali-Forte, Marcolongo, Codazzi and Fubini. Vector calculus (today largely subsumed by tensor calculus) due to the efforts of the former,[2] was known for a time in some circles as Italian notation.
The work of the Italians was built largely on Riemann's theories[3] and ran parallel to the efforts of other important differential geometers such as Darboux and later Elie Cartan in France; Grassmann, Weingarten, Killing and Christoffel of Germany, the Norwegian Lie and British Clifford.
It was this group (along with the theories of Riemann) than most directly influenced the early work of Einstein and Grossman in general relativity and subsequently tensor analysis. Einstein later corresponded, even became good friends with Levi-Civita.[4][a][b]
See also edit
Notes edit
- ^ Einstein once wrote to Levi-Civita in a letter : "I admire the elegance of your method of computation; it must be nice to ride through these fields upon the horse of true mathematics while the like of us have to make our way laboriously on foot".
- ^ Later on, when asked what he liked best about Italy, Einstein said: "spaghetti and Levi-Civita".
Suggested Reading edit
- Angelo Guerraggio, Pietro Nastasi (7 December 2005). Italian Mathematics Between the Two World Wars. Springer. ISBN 9783764365554.
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References edit
- ^ Dirk Jan Struik, Concise History of Mathematics, pg 184. Series:Dover histories, biographies and classics of mathematics and the physical sciences, Dover Books on Mathematics Series, Dover series in mathematics & physics, Volume 255 of Dover books, Dover books on advanced mathematics, Dover classics of science and mathematics. Edition 3, illustrated, revised, reprint; Courier Dover Publications, 1967. ISBN 0486138887, ISBN 9780486138886; Length 195 pages.
- ^ Mac Tutuor, St Andrews University: Cesare Burali-Forti biography.
- ^ D. M. Bressoud, Second Year Calculus: From Celestial Mechanics to Special Relativity, ch .4 p. 78, illustrated edition. Series: Undergraduate Texts in Mathematics / Readings in Mathematics Series, Springer Undergraduate Texts in Mathematics and Technology, Applied Mathematical Sciences, Readings in mathematics.Springer, 1991. ISBN 038797606X, 9780387976068. Length 386 pages.
- ^ Jackson, Allyn (1996). "Celebrating the 100th Annual Meeting of the AMS". In Case, Bettye Anne (ed.). A Century of Mathematical Meetings. Providence, RI: American Mathematical Society. pp. 10–18. ISBN 0-8218-0465-0.