The Mathematician vs. the Computer. On the Surprising Dislike for Computer-Assisted Proofs in Mathematics

(Philosophy of Mathematics, English)

omputer-assisted proofs have produced outstanding results in mathematics. Surprisingly, these proofs are not well received by the mathematical community. Often, this behaviour is grounded in claims about the complexity of the computer-assisted proof, whereas the goal of mathematics is taken to be the search for elegant and beautiful proofs.

In my talk, I will analyse the connection between the acceptance of a proof technique and mathematical ''beauty-talk'' to understand (1) why mathematicians dislike computer-assisted proofs, and (2) whether this dislike is well-founded.

I will first draw upon examples to argue that ''beauty-talk'' is widely used to apply to a standard of value. As such, mathematicians rely on it to evaluate research results, to explain why they are motivated to work on a project, and to justify choices made within ongoing research processes. Therefore, ''beauty-talk'' is not limited to computer-assisted proofs, but can be found everywhere in the mathematical practice.

Then, I will turn to the nature of ''beauty-talk''. Empirical evidence suggests that mathematicians count different features as relevant for constituting the beauty of a proof. Since all of these different features yield statements of ''beauty-talk'' which are accepted by the mathematical community, I will conclude that ''beauty-talk'' is a pluralistic phenomenon, which allows for multiple different, yet successful concepts of mathematical beauty, each grounded in different features of the proof.

On this view, it is perfectly clear that these concepts may change over time. Thus, with regards to computer-assisted proofs, I will conclude that these proofs simply tack the features mathematicians are currently valuing when talking about a proof's beauty. But since these concepts are not set in stone, this may (and perhaps will) change in the future.

Chair: Sara Ayhan

Time: 15:20-15:50, 12 September 2018 (Wednesday)

Location: SR 1.005

Paul Hasselkuß

(Heinrich Heine University, Germany)

I am a graduate student at the department of philosophy at the Heinrich Heine University Düsseldorf, Germany. I am interested in history and philosophy of science, philosophy of mathematics and aesthetics.

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