Mathematics

The Weil Conjectures

Brian Hayes read

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

John Kinsey read

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

Karen Olsson

New York: Farrar, Straus & Giroux

Simone Weil’s Spiritual Critique of Modern Science: An Historical-Critical Assessment

Joseph K. Cosgrove read

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

Andre Weil read

Notices of the American Mathematical Society, vol. 52, no. 3, 334-341

Weaving the World: Simone Weil on Science, Mathematics, and Love

Vance Morgan read

Weaving the World uses Simone Weil’s philosophy of science and mathematics as an introduction to the thought of one of the most powerful philosophical and theological minds of the twentieth century. Weil held that, for the ancient Greeks, the ultimate purpose of science and mathematics was the knowledge and love of the divine. Her creative assimilation of this vision led her to a conception of science and mathematics that connects the human person with not only the physical world but also the spiritual and aesthetic aspects of human existence. Vance G. Morgan investigates Weil’s earliest texts on science, in which she lays the foundation for a conception of science rooted in basic human concerns and activities. He then tracks Weil’s analysis of the development of science, particularly of the mathematics and science of the ancient Greeks.

Notre Dame, IN: University of Notre Dame Press, 2005

Simone Weil and the Divine Poetry of Mathematics

Vance Morgan

in Doering, E. Jane & Springsted, Eric, eds, The Christian Platonism of Simone Weil, Notre Dame: IN: University of Notre Dame Press, pp. 61-76