Well, a general statement about technology and invention is not exactly the same as a highly specific branch of knowledge becoming mature and not having anything innovative left to add to it.
If there's one thing that history has taught us, regardless of which field, it's that anything we manage to answer raises at least half a dozen other questions. Saying that math, of all fields, is running out of problems is one of the most absurd statements in this day and age. I was blown away by the capabilities of dumb SVMs in university and today SVMs look like a child's play - just over a decade later.
For as long as humanity has existed, whenever we feel like we've reached our peak, something happens and completely shatters our understanding. Say we have prime numbers and their occurrence is completely unpredictable - the same way Aristotle was convinced that objects come to a rest because they get tired. It's not a specific branch of knowledge, it's an outrageous claim like many have already pointed out. Could it be that math is running out of problems? Yes - in the same way that the universe might vanish tomorrow. Both of those claims are equally absurd.
I am sort of surprised that no one has countered with the quote often misattributed to Lord Kelvin. More interesting was the advice given to Max Planck:
One of Jolly's students at the University of Munich was Max Planck, whom he advised in 1878 not to go into theoretical physics.[5] Nevertheless, Planck's later work lead to the discovery of quantum mechanics.[5] Later in life Planck reported:[2][6]
As I began my university studies I asked my venerable teacher Philipp von Jolly for advice regarding the conditions and prospects of my chosen field of study. He described physics to me as a highly developed, nearly fully matured science, that through the crowning achievement of the discovery of the principle of conservation of energy it will arguably soon take its final stable form. It may yet keep going in one corner or another, scrutinizing or putting in order a jot here and a tittle there, but the system as a whole is secured, and theoretical physics is noticeably approaching its completion to the same degree as geometry did centuries ago. That was the view fifty years ago of a respected physicist at the time.
Math is not running out of problems just like physics didn't stop advancing (or merely become more precise measurement) in the 19th and 20th centuries. Something new an innovative might be around the corner — it might not. It might result in a new field entirely. It might not.
I’m struggling to think of a field that is more general. Information theory? Oh wait, that’s a sub-field of math. Communications? Eh it’s pretty general but math has it beat handily I think.
The idea that it is “done” or “out of interesting problems” is just absurd.
I’m open it the possibility that it’s harder than it was before to find and articulate interesting problems, but that is a very different claim.
