The guy who said it meant it as a joke, because they turned up in so many areas of mathematics.
Things don't really turn up, though. We use to say, say, that "addition is a group over the integers", but really what we mean is "we are allowed to see addition as a group over the integers, because it obeys the rules we've made for that abstraction".
There are many other fruitful abstractions, and even more not-so fruitful abstractions, that we can use as a lens to view things through.
And conversely, you don't have to view addition as a group over the integers if all you're doing is counting apples. Talk about overkill.
Modular forms are a fruitful lens to view many things through, apparently. Though, from the number of very educated people in the thread who have never really learned about or used them, they're apparently not so commonly useful as to get trivial. It's a niche abstraction, which has been used to get a grip on some problems where nothing else has worked - famously, Fermat's last theorem. Not what mathematicians reach for in everyday matters, but with a big wow factor when someone successfully does so.
Things don't really turn up, though. We use to say, say, that "addition is a group over the integers", but really what we mean is "we are allowed to see addition as a group over the integers, because it obeys the rules we've made for that abstraction".
There are many other fruitful abstractions, and even more not-so fruitful abstractions, that we can use as a lens to view things through.
And conversely, you don't have to view addition as a group over the integers if all you're doing is counting apples. Talk about overkill.
Modular forms are a fruitful lens to view many things through, apparently. Though, from the number of very educated people in the thread who have never really learned about or used them, they're apparently not so commonly useful as to get trivial. It's a niche abstraction, which has been used to get a grip on some problems where nothing else has worked - famously, Fermat's last theorem. Not what mathematicians reach for in everyday matters, but with a big wow factor when someone successfully does so.