👉 The dispute over "discrete math" in mathematics centers on the debate between constructivists and classical mathematicians regarding the validity of non-constructive proofs. Constructivists argue that mathematical objects should be explicitly constructed, meaning that a proof showing an object's existence must provide a method to generate it. This stance rejects proofs by contradiction, such as the famous proof of the existence of uncountable sets via Cantor's diagonal argument, which constructivists deem invalid as it does not provide a concrete example. On the other hand, classical mathematicians accept such proofs as valid, viewing them as a legitimate way to establish mathematical truths. This dispute highlights fundamental differences in philosophical approaches to mathematics, with constructivism emphasizing the need for explicit constructions and classical mathematics valuing the broader implications of non-constructive results.
