One day late… but wouldn’t spoil the title of this segment 😛 Today’s bit is on the never-ending debate on the nature of Mathematics:
Is Math invented or discovered?
Anti-realists: Math is invented
Anti-realists argue that Mathematics is a pure invention of the human mind. They believe Math to be a mere logical construct, comprising a set of manmade rules and an intricate web of abstract relationships formulated on top of fundamental axioms, similar to rules and strategies in a chess game. Henri Poincare, one of the founders of non-euclidean geometry, claimed that non-euclidean geometry disqualified the traditional Euclidean geometry as a universal truth, and implied that it is only “an outcome of a particular set of game rules”. Mathematical knowledge, hence, is analytic a priori and has no external bearings on the reality.
Realists: Math is discovered
Realists argue that Mathematics is discovered from an external reality. They believe that there exists an objective Mathematical universe, in which numbers and theorems are “both living entities and universal principles”. This thought originated from the ancient Pythagoreans. Euclid, the founder of Euclidean geometry, considered nature as a manifestation of Mathematical laws. Indeed, we cannot ignore the foundational and pivotal roles Mathematical knowledge has played in modelling regularities in the physical world. Eugene Wigner suggested that such an effectiveness would seem “unreasonable” if math an invention of the internal mind. He argued that Math is discovered, as theories and laws created by Mathematicians without practical intentions were later proven useful in explaining and modelling natural phenomena. This must imply the origin of Mathematical knowledge in the natural world. For example, Number theory, a purely theoretical domain by Hardy, were later applied in laws of genetic inheritance in biology.
What are the implications for Math as an area of knowledge?
Tune in for the next Philo-byte Friday (any day of the week TBH)!