We changed the URL from https://www.quantamagazine.org/how-failure-has-made-mathemat... to the article it's based on, but both are worth reading!

"If you want to go into mathematics, doing the mathematics itself has to be the thing that’s the reward" True. In other words mathematics is the biggest 'Nerd Sniping' source ever existed on Earth. Math was my hobby when I was younger, and every minute of learning and thinking about theoretical math had a huge opportunity cost of not learning something more useful. Fortunately math is no longer a hobby of mine, so my knowledge is becoming more rounded/practical nowadays. I have became an expert of detecting any nerd-sniping, which at a younger age I was prone to. Surely I still teach math to my children when they need help, but otherwise I use math only when needed, not l'art pour l'art. Coincidentally I comment much less on public forums too. (Another non-useful activity.)

The original content at https://www.quantamagazine.org/how-failure-has-made-mathemat... was replaced with a link to the essay. Writing a separate comment as it is not possible to reply.

IMO the magazine article was a much more accessible read, and a different story about the author himself and the essay.

Replacing the story feels disrespectful to both the journalist, for his work that certainly only amplified the reach of the essay, as well as the author for denying him the spotlight.

> Math is so competitive. Most people are struggling to get access to very limited resource

Does he mean academic positions and funding or community attention? Hard to be sure based on the rest of the interview.

>It wasn’t common for people to write multiple-author papers when I was a grad student; now it’s rare for a paper to have fewer than three authors.

I thought that's because people are trading. I'll put your name on my paper if you put mine on yours.

Danny Calegari's essay "Disappointment" in the Notices (https://www.ams.org/journals/notices/202309/noti2782/noti278...) is a nice reflection on how to think - and try to feel - about failures.

Again, epistemology and the recommended book "NEW DIRECTIONS IN THE PHILOSOPHY OF MATHEMATICS"[1].

It is always interesting how the people who were in the epistwemology of math could easily predict this. I personally participated in Gregory Chaitin [2] conferences.

[1] https://gwern.net/doc/math/1986-tymoczko-newdirectionsphilos...

[2] https://en.wikipedia.org/wiki/Gregory_Chaitin

I haven't read the article yet but the moment I saw the writer is "Jordana Cepelewicz" I knew it is going to be great! I have read few of her past articles and they were excellent think pieces.

And yet being able to practice that failure while in the classroom is all but outright disincentivized. I completely agree with the interview... but educational currents do not have the space for the type of failure that helps one become a good mathematician. In fact, failing can remove a lot of prospects.

the biggest disappointment is the absolute contempt with which the society treats high end knowledge work. Math, theoretical physics, theoretical computer science, these are the highest form of art and sophistication created with human brain, but people who love these subjects have to forgive financial independence, endure poverty, have less than 1% job prospect in academia, social snubbing & ridicule, for what, inner joy? Screw that.

These days, my main advice is the same as what Scott Galloway gives to avoid long term disappointment. Follow the bucks, once you have enough of it, you can then think of satisfying your inner curiosity.

Danny Calegari seems like that rare combination of humility, insight, and empathy. Some really good quotes in this interview:

> If you want to go into mathematics, doing the mathematics itself has to be the thing that’s the reward, because no one cares, and what’s considered important doesn’t always make sense. ... I think 100% of mathematicians think that no one cares, that no one even knows anything about their best work.

> G.H. Hardy was once asked what distinguished Ramanujan as a mathematician. One of the things he said was that Ramanujan had a remarkable capacity for coming up with hypotheses very quickly, but that he was also very quick to revise his hypotheses. He was nimble: If something didn’t work, he was able to pivot and revise his way of thinking.

> the same kind of psychological pressures that make it difficult for people to deal with failure are at work in making it hard for people to carefully and critically evaluate arguments that they have a huge personal investment in being correct.

> One of the great, tremendously useful and valuable functions of good writing is that it gives you a way of seeing what it’s like to be other people. You can see inside people’s heads. This is one of the great gifts of literature: You get to see that everyone else is weird, too, not just you.