The personal expression can get very far too, further than perhaps an advanced alien race may know. Supposing an alien race never discovered category theory, their mathematics could still be more advanced than ours, but perhaps more verbose, longer to write down or otherwise bulky and inelegant. The question of whether elegant mathematics is more advanced I guess becomes tricky to answer. But pedagogically and for practical application, elegance is paramount.
I think the most celebrated mathematicians are such because of their personal expression. And that "style element" also inspires people to go further than before. Grothendieck, who featured here a few weeks ago, is a case in point.
I think the most celebrated mathematicians are such because of their personal expression. And that "style element" also inspires people to go further than before. Grothendieck, who featured here a few weeks ago, is a case in point.