Mathematics
‘None Enters Here Unless He is a Geometer’: Simone Weil on the Immorality of Algebra
Abstract
The French philosopher Simone Weil (1909-1943) thought of geometry and algebra not as complementary modes of mathematical investigation, but rather as constituting morally opposed approaches: whereas geometry is the sine qua non of inquiry leading from ruthless passion to temperate perception, in accord with the human condition, algebra leads in the reverse direction, to excess and oppression. We explore the constituents of this argument, with their roots in classical Greek thought, and also how Simone Weil came to qualify it following her exchange with her brother, the mathematician André Weil.
Axiomathes, vol. 32, no. 2 (July, 2022)
About the Author
Aviad Heifetz is a professor in the Department of Management and Economics at the Open University of Israel.
Action and Contemplation: A Commentary on Vance Morgan’s Weaving the World: Simone Weil on Science, Mathematics, and Love
Inside Issue 3: New and Forthcoming
The Weil Conjectures
Sample: “. . . . Before going further I should make clear that The Weil Conjectures is not a textbook or a scholarly monograph. It is not addressed to an audience of mathematicians. But it raises questions about relations between mathematics and society that may well be of interest to the mathematical community. This issue is commonly discussed in terms of outreach—the challenge of communicating research-level mathematics to the public. In Olsson’s case it also becomes a question of reach: how can we help someone who feels a powerful attraction to mathematical ideas but cannot negotiate the rugged terrain of prerequisite knowledge?
The heart of Olsson’s book is a personal essay, in which she describes her own intense and turbulent encounters with the world of mathematics. That narrative is braided into the stories of the Weil siblings—whose lives were also marked by intensity and turbulence. . . .”
Notices of the American Mathematical Society, vol. 68, no. 2 (Feb. 2021) (book review)
Mathematics and the Mystical in the Thought of Simone Weil
On Simone Weil’s “Pythagorean” view, mathematics has a mystical significance. In this paper, the nature of this significance and the coherence of Weil’s view are explored. To sharpen the discussion, consideration is given to both Rush Rhees’ criticism of Weil and Vance Morgan’s rebuttal of Rhees. It is argued here that while Morgan underestimates the force of Rhees’ criticism, Rhees’ take on Weil is, nevertheless, flawed for two reasons. First, Rhees fails to engage adequately with either the assumptions underlying Weil’s religious conception of philosophy or its dialectical method. Second, Rhees’ reading of Weil reflects an anti-Platonist conception of mathematics his justification of which is unsound and whose influence impedes recognition of the coherence of Weil’s position.
Philosophical Investigations, vol. 43, nos. 1-2 (January-April 2020), pp. 76-100.
The Weil Conjectures: On Math and the Pursuit of the Unknown
New York: Farrar, Straus & Giroux
Mathematics and Religion: on a Remark by Simone Weil
Logic in Theology, pp. 219-236
Simone Weil’s Spiritual Critique of Modern Science: An Historical-Critical Assessment
Simone Weil is widely recognized today as one of the profound religious thinkers of the twentieth century. Yet while her interpretation of natural science is critical to Weil’s overall understanding of religious faith, her writings on science have received little attention compared with her more overtly theological writings. The present essay, which builds on Vance Morgan’s Weaving the World: Simone Weil on Science, Necessity, and Love (2005), critically examines Weil’s interpretation of the history of science. Weil believed that mathematical science, for the ancient Pythagoreans a mystical expression of the love of God, had in the modern period degenerated into a kind of reification of method that confuses the means of representing nature with nature itself. Beginning with classical (Newtonian) science’s representation of nature as a machine, and even more so with the subsequent assimilation of symbolic algebra as the principal language of mathematical physics, modern science according to Weil trades genuine insight into the order of the world for symbolic manipulation yielding mere predictive success and technological domination of nature. I show that Weil’s expressed desire to revive a Pythagorean scientific approach, inspired by the “mysterious complicity” in nature between brute necessity and love, must be recast in view of the intrinsically symbolic character of modern mathematical science. I argue further that a genuinely mystical attitude toward nature is nascent within symbolic mathematical science itself.
Providence College, Philosophy Department Faculty Publications
A 1940 Letter of André Weil [to Simone Weil] on Analogy in Mathematics
Notices of the American Mathematical Society, vol. 52, no. 3, 334-341
