And how can you pick the correct toll, if you don't know the arithmetical and algebraic procedures themselves? By at least learning to do them yourself, you understand them. — ssu
The problem is that there's simply too much math to study at a slow pace. — ssu
Sounds as if you are arguing for an intellectually impoverished populace, and I wonder why? — wonderer1
Oh, goodie! The six people who still understand some aspect of 'manual' programming can teach it to their children, set up dynasties and rule the world — Vera Mont
Neither activity is meaningful in any shape or fashion. That is, however, what mathematics education is all about. — Tarskian
You could generalize to a lot of what is taught and studied in universities here. Not only math.What problem does the math graduate intend to solve except for teaching math? — Tarskian
Well, this is a philosophy site, so people here do understand why in the university math is studied, even if the applications to engineering etc. are different. — ssu
https://en.wikipedia.org/wiki/Weil_pairing
In mathematics, the Weil pairing is a pairing (bilinear form, though with multiplicative notation) on the points of order dividing n of an elliptic curve E, taking values in nth roots of unity. More generally there is a similar Weil pairing between points of order n of an abelian variety and its dual. It was introduced by André Weil (1940) for Jacobians of curves, who gave an abstract algebraic definition; the corresponding results for elliptic functions were known, and can be expressed simply by use of the Weierstrass sigma function.
https://medium.com/@VitalikButerin/exploring-elliptic-curve-pairings-c73c1864e627
Exploring Elliptic Curve Pairings
Trigger warning: math.
One of the key cryptographic primitives behind various constructions, including deterministic threshold signatures, zk-SNARKs and other simpler forms of zero-knowledge proofs is the elliptic curve pairing.
https://en.wikipedia.org/wiki/Vitalik_Buterin
He dropped out of university in 2014 when he was awarded with a grant of US$100,000 (equivalent to $128,704 in 2023)[19] from the Thiel Fellowship, a scholarship created by venture capitalist Peter Thiel and went to work on Ethereum full-time.
The concert pianist actually intends to solve a problem. So does the athlete. — Tarskian
What problem does the math graduate intend to solve except for teaching math? — Tarskian
Concerning my academic background in a branch of applied math, if it were still relevant after decades, it would mean that I wouldn't have done anything meaningful in the meanwhile. — Tarskian
If a degree matters after your first job, it simply means that your first job did not matter. — Tarskian
My stints in pure math came much later. Sometimes because I was looking under the hood of the software I was using. Sometimes just out of interest. — Tarskian
For example, I did my first foray in abstract algebra by looking under the hood of elliptic-curve cryptography. In fact, you understand abstract algebra much better if you have first been exposed to subjects like ECDSA and Shnorr signatures. The other way around is not true. — Tarskian
You have a credentialist view on knowledge. — Tarskian
That is typical for teaching associates at university. — Tarskian
They think that credentialism matters. — Tarskian
Well, they have to, because their hourly rate clearly does not matter. — Tarskian
The academia are full of postdocs and other idiots who think they know but who in reality have nothing to show for. — Tarskian
Furthermore, the relevant math is elsewhere. — Tarskian
They really do not understand, not even to save themselves from drowning, which areas in pure math power technology. — Tarskian
That is why they are stuck in areas that are irrelevant. — Tarskian
Vitalik Buterin — Tarskian
A bit like Bill Gates (Microsoft) or Steve Jobs (Apple), Vitalik had to stop wasting his time and drop out of his university undergraduate in order to do something more important: — Tarskian
Perhaps you have learned a lot but still don't know everything there is to know, and perhaps you have made some wrong assumptions. — fishfry
https://writings.stephenwolfram.com/2014/08/computational-knowledge-and-the-future-of-pure-mathematics
Curating the math corpus. So how big is the historical corpus of mathematics? There’ve probably been about 3 million mathematical papers published altogether—or about 100 million pages, growing at a rate of about 2 million pages per year. And in all of these papers, perhaps 5 million distinct theorems have been formally stated.
Sour Grapes — Vera Mont
Sour Grapes. — Vera Mont
What exactly would I envy? Dealings with the HR department of a university? I have never had to go through any HR department. I find the practice insulting. — Tarskian
It says everything about your station in life. — Tarskian
Stephen Wolfram writes on this subject:
... (Wolfram quote omitted)
So, in order to know everything there is to know about mathematics, you need to read 3 million papers. Did I read them? Did I ever said that I read them? Did I even read 0.1% of them? — Tarskian
Knowledge is a gigantic database of (claim,justification) two-tuples that is for 99.999% stale and irrelevant. The only meaningful way of finding out what is relevant, is to work your way back from solutions that solve problems all the way into the math that directly or indirectly facilitates the solution. — Tarskian
So, is knowledge a good thing? Possibly, but it is first and foremost, utterly useless. — Tarskian
The idea of feeding students with some arbitrary excerpt from such knowledge database, assuming that it will ever be useful to them, is misguided and nonsensical. — Tarskian
That is the reason why the education system fails. Its knowledge-acquisition strategy simply does not make sense. — Tarskian
The only way to pick the right things to learn, is by going in exactly the opposite direction. You start by trying to solve a practical problem, for which there exists someone willing to pay for the solution, and only then you learn knowledge as required for producing the solution. — Tarskian
I am semi-retired now. If I was ever going to work again, I'd rather swear fealty as a serf to the lord of the manor than to deal with an HR department. — Tarskian
Okay then, maybe just a very dull axe. — Vera Mont
You are unhappy with students being taught the state of the art in their field. — fishfry
The president of the United States draws a paycheck. — fishfry
All the 18 year olds are apprenticed out to people who will pay them even though they're completely ignorant? You can't be serious. What are you talking about? — fishfry
So maybe you're against large organizations. — fishfry
I would never have wanted to be staff, though. When we talk about "bottom line", the only one that mattered to me was my own "bottom line". I was not interested in selflessly "sacrifice" myself for someone else's bottom line. I cannot identify with the profit of the company. I can only identify with my own profit. I understand that C-level execs somewhat care, since they receive payments for when the stock goes up, but the other salaried office drones? Seriously, why would anybody else care? — Tarskian
But why hate on the math professors? — fishfry
I don't hate on individual math professors. They are just pawns in the game.
This is the part I don't get. The administrators and bean counters and HR reps of the world, I can understand your frustration with institutional stupidity on such a grand scale.
But math professors aren't any of that. They're dreamers who sit in their office and push around symbols to prove theorems about things that nobody but other mathematicians understand.
They are totally harmless.
They serve the other academic departments by teaching calculus classes to the engineers and such. Everything else, the math major undergrad and math grad school, is all about training professional mathematicians. All of this has got nothing at all to do with the administrative stupidity you decry.
Why have you got it in for the math professors?
— Tarskian
One (or rather two) of the things I don't like, is the combo of academic credentialism combined with the student debt scam. Like all usury, it is a tool to enslave people. The banks conjure fiat money out of thin air and them want it back along with interest from teenagers who were lied to and most of whom will never have the ability to pay back. The ruling mafia even guarantees to the bankstering mafia that they will pay if the student does not. First of all, though, they will exhaust all options afforded by the use of violent threats of lawfare. — Tarskian
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