Abstract / Synopsis
This article provides an overview of the limitations of checking out a few cases to prove conjectures in mathematics. To that end, I present a purposeful collection of number-theoretic conjectures where extensive checking of cases has found counterexamples, with emphasis on the historical backgrounds. Historical examples of long-term attempts to prove or disprove such conjectures could help individuals to realize more deeply that a limited number of observations does not guarantee the correctness of a conjecture, even though there may be many examples in its favor.
Ali Barahmand, "On Mathematical Conjectures and Counterexamples," Journal of Humanistic Mathematics, Volume 9 Issue 1 (January 2019), pages 295-303. DOI: 10.5642/jhummath.201901.17. Available at: https://scholarship.claremont.edu/jhm/vol9/iss1/17