Lakatos’s seminal work Proofs and Refutations introduced the methods of proofs and refutations by discussing the history and methodolog- ical development of Euler’s formula V − E + F = 2 for three dimensional polyhedra. Lakatos considered the history of polyhedra illustrating a good ex- ample for his philosophy and methodology of mathematics and geometry. In this study, we focus on the mathematical and topological properties which play a role in Lakatos’s methodological approach. For each example and counterexample given by Lakatos, we briefly outline its topological counter- part. We thus present the mathematical background and basis of Lakatos’s philosophy of mathematical methodology in the case of Euler’s formula, and thereby develop some intuitions about the function of his notions of positive and negative heuristics.
Hashemi,H. (2023). An Examination of Counterexamples in Proofs and Refutations. Mathematical Culture and Thought, 41(2), 151-172. doi: 10.30504/mct.2022.1179.1823
MLA
Hashemi,H. . "An Examination of Counterexamples in Proofs and Refutations", Mathematical Culture and Thought, 41, 2, 2023, 151-172. doi: 10.30504/mct.2022.1179.1823
HARVARD
Hashemi H. (2023). 'An Examination of Counterexamples in Proofs and Refutations', Mathematical Culture and Thought, 41(2), pp. 151-172. doi: 10.30504/mct.2022.1179.1823
CHICAGO
H. Hashemi, "An Examination of Counterexamples in Proofs and Refutations," Mathematical Culture and Thought, 41 2 (2023): 151-172, doi: 10.30504/mct.2022.1179.1823
VANCOUVER
Hashemi H. An Examination of Counterexamples in Proofs and Refutations. An Expository Journal of the Iranian Mathematical Society, 2023; 41(2): 151-172. doi: 10.30504/mct.2022.1179.1823
