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I just want to add, this is coming from someone who has completed a mathematics PhD, and so has a very very high bar for psychosis (seriously, math departments are fun, but also FUN).
...uh oh. How so?
While it's not true that intelligence is correlated with mental problems, advanced mathematics tends to attract or create odd ducks.
There are multiple mathematicians in the modern era who are well regarded, technically homeless and just showed up at people's houses to collaborate on some math. One, who coined the phrase "another roof, another proof", was a staunch proponent of mixing amphetamines, coffee, and 70's antidepressants.
People didn't notice John Nash devolved into a deep schizophrenic break for a long time because it's not weird for advanced mathematicians to be talking about very complex unintelligible ideas. Scary Wheels and Super Shrubs is an example of a good title and not-transparent description.
Another was the uni-bomber.
There's plenty of perfectly well balanced mathematicians. You just can't help but get some weird ideas when your life's work is to think outside the box about very complicated things all the time.
If you go deep into math work, you'll meet people who think the universe is a simulation. You'll meet others who think that's silly, because the universe is clearly actually an abstract embodiment of the platonic ideal of mathematics. 7, blue, and cat are all equally real or not real, and we don't need a simulation as the equation defining structure is sufficient to give rise to what we experience, and requiring it to be written or executed is just an odd affectation.
You'll just nod and concede the appeal because it's not the first time someone has shared that idea with you.
So when the mathematicians start saying the ideas are getting odd, you know it's not just "I don't understand therefore it's weird".
Maybe this implies I'm one of the weirdos, but my experience has been wildly different. My experience has been mathematicians are just people, what they have in common is a passion for math. Sometimes they're weird, but that's because they're people and not because they do math. I never got the impression I was talking with a schizophrenic or a Kaczynski type. They exist, but non-mathatician schizophrenics do too.
I don't think heard of this and I'm skeptical. Give me a couple names to jostle my memory?
I don't know this quote but I'd give it a 90% chance it's Erdös.
Come on man, this isn't weird. It's representation theory, there literally isn't a transparent description. It's weird to think having fun with a title isn't a normal impulse from time-to-time.
This reads as partially random to me, what is "the equation defining structure"?
I had hoped I was making it very clear that it's not a case that all mathematicians are weirdos or even difficult to talk to, because they're not.
Thinking about complicated things all the time results in complicated conclusions, so you'll end up talking to people with very detailed thoughts if you're talking about work. Probably perfectly normal thoughts on cooking beyond a bias towards using their analytical ability where others might not.
My point was not that they're all weird, but that the bar is higher because you deal with more people who have thought about something much more than you have.
My point with the paper wasn't that it's weird to have fun, or that the title was bad. It's that it was complicated and an example of the field requiring you to deal with profoundly unfamiliar ideas and terminology, potentially quite regularly. To some people "that sounded like gibberish" is a sign you dismiss it. In this case, it means you need to do more research to catch up to the terminology.
The two that I was thinking of were erdos and diffie. I'll concede to featuring some of the more notable characters because their stories are more fun.
The idea being described was a paraphrase of platonic realism and structuralism taken to an extreme to match simulation theory. If the universe is a simulation it means there is, "somewhere", an equation or algorithm describing our physical reality. Needing that equation to be evaluated to give rise to our universe is an odd perspective since the existence of the equation would be sufficient. An equation describing the motion of a point in a circle doesn't need to be evaluated to describe that, nor does it need to be written down.
It's a notion that I thought fit well with my point of "agree or disagree, it's not delusional, and it's not obvious"
You clearly weren't saying they all are, but what I'm saying is that my impression is that the bar for weirdness isn't higher at all. There will always be examples of mathematicians behaving weirdly, because there will always be examples of people behaving weirdly. Spending a lot of time thinking about abstract nonsense definitely improves your proficiency at thinking about abstract nonsense, but I can't see how it could affect the way you process other things any more than frequent practice with sudoku or chess would.
The mental process in math is no more special than any other intellectual hobby. If you invest decades into chess I'm sure you'll think about chess in a very different way than a beginner, but in my opinion seeing chess differently should have minimal impact on how someone thinks about things unrelated to chess.
I feel like that's very similar to what I said, including the bit about being routine in most other regards.
People who spend a lot of time thinking are prone to having thoughts, and sometimes those thoughts are less common.
The more abstract the topic you're working with, the more accustomed you'll be to hearing things that don't make sense at first.
Might just be me, but in general the more educated people I've met have been more likely to qualify as odd ducks, and the mathy folks tend towards the upper edge.
Mostly, we all see the world in unique ways - picture a building of possessed dwarves and you have the average mathematics department.