Of course, the whole platonist/realist/phenomenologist (sometimes characterized as the 'discovered' vs 'invented' argument) is hardly new, nor likely to be resolved (if that were even possible). I certainly recall an enormous amount of cheap on-campus beer being spent exploring the issue when I was an undergrad 4 decades ago.
I did find a couple of things quite refreshing in the article, though: (1) Wigner's essay is delightful and I'm glad it's seeing a wider audience. We should be reminded of it every time this conversation comes up, if only for its last paragraph. (2) The reference to the fact that Galileo proved that falling objects accelerate at the same rate, not by some experimental demonstration, but wholly within his mind---and it's a proof that any middle-schooler has no difficulty completely understanding. As a reminder that mathematics isn't symbols and rules, but a way of looking at problems (Eugenia Cheng's book, How to Bake Pi, is an excellent look at this way of thinking and approaching the world.). (3) It managed not to get bogged down in the whole pointless and hypocritical "what is math good for" instrumentality debate, that these sorts of questions tend to devolve into.
I did find a couple of things quite refreshing in the article, though: (1) Wigner's essay is delightful and I'm glad it's seeing a wider audience. We should be reminded of it every time this conversation comes up, if only for its last paragraph. (2) The reference to the fact that Galileo proved that falling objects accelerate at the same rate, not by some experimental demonstration, but wholly within his mind---and it's a proof that any middle-schooler has no difficulty completely understanding. As a reminder that mathematics isn't symbols and rules, but a way of looking at problems (Eugenia Cheng's book, How to Bake Pi, is an excellent look at this way of thinking and approaching the world.). (3) It managed not to get bogged down in the whole pointless and hypocritical "what is math good for" instrumentality debate, that these sorts of questions tend to devolve into.