Penelope Maddy, who is a Distinguished Professor emeritus of logic and philosophy of science and mathematics at UC Irvine, is a prominent American philosopher of logic, science and mathematics known for her work on mathematical realism. Simply put, it’s the idea that mathematics exists independently of human cognition and that we discovered math rather than inventing it.

“Realism in Mathematics” was the title of Maddy’s first book, published in 1990, followed by “Naturalism in Mathematics” published in 1997, which explores mathematical naturalism. These days, she sees herself as having landed somewhere between the two extremes.

“In the days of Galileo and Newton, it wasn't unreasonable to regard mathematics as the language of the Great Book of Nature,” Maddy explained in an email interview with Salon. “But over the course of the 19th Century, developments in both mathematics and science undermined this view.” 

Geometry as developed by Euclid, she said, was once thought to be “a unique collection of undeniable truths about physical space.” But then non-Euclidean geometries were developed and so Euclidean geometry was reduced to one competing theory among many. When Einstein was able to hang his physical ideas about gravity (known as  general relativity) on the mathematical structure provided by a different kind of geometry, Riemannian geometry, that could have been curtains for what was once considered Euclid’s undeniable truth about the real world.

Continue reading:  https://www.salon.com/2024/07/27/numbers-game-is-math-the-language-of-nature-or-just-a-human-construct/