The asymmetry in storytelling between math and the other sciences

Real talk: pure maths was way more fun, interesting, and applicable to my life as a software engineer than all the applied math and modelling that I wrote/learned/etc. Pure mathematics expanded my mind unlike any other subject matter.

I suck at those, but I do well with abstractions and proofs. Makes me wonder how many pure mathematicians the field misses out on.

Putting that aside, of the professors who had pure focuses, I'd say more often than not they tried to do their responsibilities as educators and put forth examples to try and make the material more accessible—but that kind of thing seemed to be how they thought on the matter. Actually, the applied mathematicians were very similar. I felt that most of their thoughts were constructive and there wasn't really any sense of comparison with the traitorous physicists or anything.

In the first place, before any popularization of mathematics can occur, it needs to be introduced in a way that doesn't leave all our secondary school students traumatized for their entire education, which goes back to the education system.

I'd say it's betraying mathematics.

At the end of the day his theory remained to incomplete. Chirality problems were hand-waved away unconvincingly. It's more a mathematical curiosity than a proper proposal for unification.

A problem is called "NP" if I can give you a solution to it and you can easily verify that the solution is correct. For example, "find 3 different odd numbers that together add up to ten" (here's a possible solution: 3, 5, 7). What's awesome about this is that there are a lot of problems of that form where we don't know whether or not it's possible to find a solution to the problems before dying of old age -- or before the sun runs out of fuel, even though you could check the answer in a few minutes using pencil and paper. Nobody has ever figured out how to solve them fast, but it's a huge open question of whether they can be solved fast. The P = NP question is whether there exists a fast solution to any problem that you can verify easily if I give you a solution.

And it's not just of theoretical interest: some those problems underlie everything from cryptography (communicating and storing information securely using encryption) to things like optimizing airline routes or the way UPS chooses where to route packages. Amazingly, there's a set of problems that if you find way to solve any one of them fast, you can solve all problems in NP fast. Which means the NSA and everyone else will try to kidnap you to find out the secret. Fortunately, most people who study it don't think that there's a solution. But it's one of the most famous and important problems in computing, and nobody -- of some of the smartest people in the field -- has ever managed to prove it either way.

(Truth in advertising: We actually use subset sum as the example, and walk through it a little, but that's because we're trying to teach it in more detail than just telling the story. And have also taught a handwavy version of asymptotic analysis. If you want to show someone how hard it gets quickly, subset sum is a nice way to do it. The "talking" example above is, of course, an instance of subset sum, but it doesn't explain the general form of the problem.)

Unless I'm mistaken, if proved the Riemann Conjecture could provide insights on the distribution of prime numbers or a polynomial-time algorithm for prime factorization, which would enable attacks on ciphers that rely on the difficulty of this problem (e.g. RSA).

This is not assured by the yes/no answer of the conjecture, but the underlying work to reach that.

Here's something uncontroversial: if its in physics, then its in math.

Here's a weird proposal: if its in math, then its in physics at a greater than trivial level or it can easily be proven not to be in physics. Or if its in math, either its obviously not in physics or it is in physics even if we don't know yet.

Discussion: Aside from souls and such your brain used physics to come up with some math thats not in physics so at a very trivial level that non-physics math was simulated in your physics brain, so it is now in physics because a physics simulation of the particles of your brain, however impractical to actually simulation ... naw thats trivial cheat that would include everything. And speaking of easily be proven, a classic example is we know two dimensional geometry fairly well and it doesn't apply to the greater world although it makes an entertaining plot for a book named "Flatland".

So as your buddies gulp down some beers, challenge them to think up a math that is not in physics as kind of a parlor game. It can be fun, especially if you allow extremely extended analogies and have a very relaxed beer fueled attitude toward handwaving arguments.

Some topics like string theory or the multiverse will have to be banned to prevent pointless fighting.

Anyway the relevance to OP and the comment is that in a drunken handwaving sense math that hasn't been found in physics is possibly a failure of the imagination of the physicist, so Riemann seems useless today is an attack on physicists not an attack on mathematicians.

You can just picture some seance between Newton and Maxwell, Yo Mr Physicist I invented all the math you needed centuries before you got around to noticing electromagnetism, like whats your excuse for the delay?

If anything, I wish we had something akin to a mathematics monastery. I'm not talking about academia - that avenue clearly leads to financial enslavement at this point. I'm talking about a place with lots of chalk boards and pretty basic room/board.

What would it contribute to society? How about...people with increased thinking skills and a place to belong? It could also taken on consulting work from everywhere.

It may end up looking like a liberal arts college or the math wing of the NSA - sans secrecy. I'd also want the barriers to entry to be low.

It is the closest we have to pure maths with direct, real-life consequences.

I do agree with the notion that profs are more effective when the homework is harder than the exam, however. I had the exact opposite for a fourth-year crypto class. For homework, we'd work through some basic cryptanalysis with lots of hints. Then the test would come around, and two or three of the ten questions would involve breaking a cypher, from scratch. I got about 25% on the first test, which ended up being 65% after he scaled it. Brutal class.