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Zoom Talk: Gisele Secco (Universidade Federal de Santa Maria, Brasil)

Meeting ID: 925-6562-2309

22.10.2020 16:00  – 18:00 

Please contact office.leitgeb@lrz.uni-muenchen.de for the password.

Title:

Computer-assisted proofs as a new form of mathematical culture?
The case of the Four-Color Theorem

Abstract:

The Four-Color Theorem (4CT, delivered in [1] and [2]) is the first case of an original mathematical result obtained through the massive use of computing devices. The philosophical citizenship of this result was due to an argument presented in [3], in which the use of computational machinery is intended as a clear-cut case for the introduction of experimentation in mathematical practices. In my talk, I intend to show how despite having been exceptionally advertised and philosophically commented on, this mathematical result is still relevant as a case study in the philosophy of mathematical practice. Building on the methodological guidelines suggested in [4] I offer a partial description of [1] and [2], showing how computing devices interact with other vital resources of the proof: diagrams. With this description, I aim to propose the 4CT proof as the turning point in the relations between mathematics and computer science – the advent of new forms of cultures of proving [5] whose understanding is one of the many current tasks for philosophers and scientists.

Keywords: computer-assisted proofs, diagrams, mathematical culture.

[1] APPEL, K., & HAKEN, W. (1977). Every planar map is four colorable. Part I: Discharging. Illinois Journal of Mathematics, 21(3), 429–490.
[2] APPEL, K., HAKEN, W., & KOCH, J. (1977). Every planar map is four colorable. Part II: Reducibility. Illinois Journal of Mathematics, 21(3), 491–567.
[3] TYMOCZKO, T. (1979) The four-color problem and its philosophical significance. The Journal of Philosophy, 27(2), 57–83.
[4] CHEMLA, K. (2018) How has one, and How could have one approached the diversity of mathematical cultures? In: Mehrmann, V. & Skutella, M (eds.), Proceedings of the 7th European Congress of Mathematics 2016, Berlin, 18-22 July 2016: 1-61.
[5] MacKENZIE, D. (2005) Computing and the cultures of proving. Philosophical Transactions: Mathematical, Physical and Engineering Sciences – The Nature of Mathematical Proof, v. 363, nº 1835: 2335 – 2350.