It's not mathematics that you need to contribute to (2010)

> William Paul Thurston (October 30, 1946 – August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds.

Source: https://en.wikipedia.org/wiki/William_Thurston

The most frustrating part of academia, and one of the main reasons I left, was the sense that everyone had completely lost their service mindset. The result is a set of sclerotic institutions -- protected from competition by rules and norms motivated by an ostensibly noble purpose -- wrecking havoc on society.

In research, in particular, it's now rare to find researchers who really give a damn about anyone except themselves. Their PhD students are tools for increasing faculty influence. The motivation section of their grants are polite lies and everyone knows it. The whole thing is a big inside joke that people laugh about in elevator bays, backed by billions of taxpayer dollars. The selfishness and complete disinterest in stewardship of public funds is nauseating.

But things are worst in undergraduate education. You occasionally meet someone worried about the educational mission, but no one was ever interested in the overall well-being of students. Financial well-being, in particular, is a verboten topic. The question of whether a particular degree program might be doing irreversible and crippling financial damage to nearly every student is considered rude. The question of whether requiring a certain course might be a waste of a customer's money is derided ("they aren't customers!", despite paying mid 5 figures per year for shockingly little face-to-face time.)

Academia has completely lost its historically service-oriented pursuit. The faculty are motivated by a combination of laziness, entitlement, and ego. The administration is motivated by the same incentives as any other industry. But huge quantities of tax dollars are locked up in this broken and corrupt industry.

> This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.

> Thematically this is similar to a (much longer) essay Dr. Thurston wrote several years ago, which I highly recommend:

https://arxiv.org/abs/math/9404236

I had the honor of meeting him several times here in Berkeley; he encouraged me to make Klein bottles and other topological shapes.

One of the great things about software is that you don't need a living community that holds every bit of every code base in their head. You can rely on abstraction boundaries, and then jump down rabbit holes only if and when necessary.

I really wonder how the work of Mathematics will change once computer-encoded proofs become mainstream. I have to imagine that will happen within the next generation or two -- as soon as the automation becomes more helpful than the hindrance of formality.

Then people go into a library and start opening books.

The arcane symbols of Math would be indistinguishable from books of magic. Without the understanding, fresh minds would be hard pressed to distinguish math formula from magic runes.

The understanding of the math comes from some community of people passing it along from generation to generation more than from the symbols.

It’s a great read for young people interested in mathematics and influenced me while in undergrad deciding to persue a PhD in math. Thurston, the author, was one of the best mathematicians of his time.

this is a problematic way to frame the issue which I agree is very difficult.

by framing it like this, I think, it sets up this task to be impossible. I'm also considering a subtle distinction between 'teaching' and 'education'

he's using a teaching framework. to put the idea in the head of the student. but education is more about guiding the student to find the answer on their own; if teaching is difficult, education may seem freaking impossible.

with a 'teaching framework' simple ideas are more difficult (and complex ones turn impossible)

but with the 'education framework' (which in my direct experience is not available publicly) simple ideas may be trickier, but the hope is that sophisticated ideas will become easier to communicate.... dunno

in my opinion the 1st/biggest contribution to math (and any science, discipline, art, and work) is to study/pratice it, is the best contribution to a living body of knowledge and wisdom, new ideas and discovery are side effect, welcomed, but not mandatory.. but is the discipline involved that change the single and later the world. The sea is made of drops..

the true goal is the/any-single way in praticing, not the end/highest point (if exist).

Ends, of course, need a terminus. While a practical or productive act terminates in something other than itself, you must now ask what the end itself is for. Is it for itself, or something else further still? When we follow practical and productive ends, they must ultimately terminate at something that is not for the sake of anything else, but is valuable in itself. Indeed, when I said the truth has practical consequences, it was an understatement; the entire regime of practical and productive activity presupposes an ultimate end for the sake of which it exists, that justifies it, that it is in service of.

I will omit discussion of the ultimate here intentionally, because my purpose here is to frame the problem first and predispose the mind toward the answer; giving the answer straight away, or an answer, is more likely to trigger reflexive prejudices here, I think. Once framed this way, people are liberated to ask "whom or what do I ultimately serve? why do I live? why do I act?". The vista of ends and order is thrown open for examination. This clarity enables one to leave Plato's "cave" and makes it difficult to obfuscate and settle for cheap answers as it can corner the conscience into pestering us to reject dishonest rationalizations. Of course, people will often try to do so, but doing so is more likely to gnaw at the soul, something that can prompt people to keep searching instead of holing up in an intellectual ghetto and persist in mediocrity.

Now you can approach the original question.