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Alfred Clebsch’s “geometrical clothing” of the theory of the quintic equation. (English) Zbl 1360.01025
Let us start with the author’s summary: “This paper describes A. Clebsch’s article [Math. Ann. 4, 284–345 (1871; JFM 03.0031.01)] that gave a geometrical interpretation of elements of the theory of the general algebraic equation of degree 5. Clebsch’s approach is used here to illuminate the relations between geometry, intuition, figures, and visualization at the time. In this paper, we try to delineate clearly what he perceived as geometric in his approach, and to show that Clebsch’s use of geometrical objects and techniques is not intended to aid visualization matters, but rather is a way of directing algebraic calculations. We also discuss the possible reasons why the article of Clebsch has been eventually completely forgotten by the historiography.”
As a reviewer, I am able to admit that the author did do a perfect job in fulfilling his aims. The paper brings to light many not so commonly things regarding the history of the quintic equation. Also, much has been revealed of Alfred Clebsch as a scientist in his time, and about all the work he did and also his contemporaries in treating the quintic equation. In short, highly recommended, a very good historical account from which one can learn and read a lot.

MSC:
01A55 History of mathematics in the 19th century
01A70 Biographies, obituaries, personalia, bibliographies
11-03 History of number theory
11D41 Higher degree equations; Fermat’s equation
11E99 Forms and linear algebraic groups
11F03 Modular and automorphic functions
01A85 Historiography
Biographic References:
Clebsch, Alfred
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