2 thoughts on “Has Mathematics Misled Modern Science?”

Lee Smolin is right. Too often we shoehorn nature to fit our mathematical models. A good example of this is work in the second half of the 20th century on population dynamics, where continuous models were used, even though it was known that discrete models did not reach the same conclusions. But we are still left with Eugene Wigner’s “unreasonable effectiveness of mathematics in the natural sciences”. Positrons were predicted as a result of solutions to equations that many assumed were meaningless. So we shouldn’t assume that mathematical solutions are “true” but we should also be alert to the idea that they may be generative. As George E.P. Box pointed out, “All models are wrong, but some are useful.”

Lee Smolin is right. Too often we shoehorn nature to fit our mathematical models. A good example of this is work in the second half of the 20th century on population dynamics, where continuous models were used, even though it was known that discrete models did not reach the same conclusions. But we are still left with Eugene Wigner’s “unreasonable effectiveness of mathematics in the natural sciences”. Positrons were predicted as a result of solutions to equations that many assumed were meaningless. So we shouldn’t assume that mathematical solutions are “true” but we should also be alert to the idea that they may be generative. As George E.P. Box pointed out, “All models are wrong, but some are useful.”

That seems like a decent balance Dylan – it would certainly seem that we are a long way from Popper’s criterion of demarcation of science from non-science, ie. falisifiability, being the whole story. Here are some responses from George Ellis and Joe Silk:

http://www.nature.com/news/scientific-method-defend-the-integrity-of-physics-1.16535

and a response to the response from Peter Woit

http://www.math.columbia.edu/~woit/wordpress/?p=7413