It's interesting to recall Turing's own position: "There would be great opposition [to AI] from the intellectuals who were afraid of being put out of a job. It is probable though that the intellectuals would be mistaken about this. There would be plenty to do, i.e. in trying to keep one’s intelligence up to the standard set by the machines, for it seems probable that once the machine thinking method had started, it would not take long to outstrip our feeble powers. There would be no question of the machines dying, and they would be able to converse with each other to sharpen their wits."
On the other hand, Thomas Bernhard's The Loser is a horrifying account of the opposite standpoint---of an essentially second best piano student who cannot stand existing in a world with Glenn Gould.
Mathematics represents the rational skeleton that upholds and stabilizes our vague, formless but far more common belief-based thinking.
Without it, losing it from neglect, we would collapse back into a pre-rational state of fantastical, wishful thinking.
Pretty much exemplified by large parts of US society already, but there is no bottom otherwise keeping society from collapse.
> What would such a world look like?
Major religions, minor religions, cults will have a field day. Or more like a field century or a millennium or twenty, who knows.
Up to a few years ago, I would see or read some science fiction that was medieval times with spaceships (ala Dune) and I would roll my eyes and think “ffs, can’t people move on and invent something more original?”. Now I seriously believe that’s one of the most benign futures waiting for our species[^1]. Not that there aren’t lots of lights in this tunnel, it’s just that its shadows are very black.
They have nothing to fear if that is their motivation. New players get into chess every year despite computer vastly outperform us.
Not just the pay, but motivation doesn't work on math insight alone. If you look from a distance it's clearly a mix of status, money etc. If what you say was true, many of them would be recluses up in the mountains, but none of them are.
LE. Think about it this way: if someone truly only cares about his ability to do "non-AI-contaminated" mathematics, nothing stops them from ignoring all the AI-related papers and just carrying on on his own. The thing that they are passionate about is not taken away by the field being more rapidly developed. What's being potentially taken away is the impact of their potential contribution.
Except, for instance, Wiles and Perelman? And I’m pretty sure that mathematicians are rather more introverted and solitary on average than most people.
In any case, that just doesn’t follow. Mathematicians realize that collaboration is important in math just as it is in most other fields. Humans are also social animals and many of us enjoy collaboration and social interaction for its own sake. And yes, that means social status is a thing that motivates many humans. But nobody decides to study math in order to gain status! Any status stuff is entirely contextual to and conditional on having already decided to study math.
Humans are built to focus on some objectives and not others at any given time.
Humans naturally prioritize objectives differently. Drives have exclusionary impacts on each other. In both real time and lifetime frames.
Reinforcing experiences further differentiate objective prioritization.
This leads people's behavior to be driven by entirely different net objective directions.
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This diversity would be inevitable due to genetic diversity. But it is also a survival advantage.
Lots of studies show that populations maintain stable diversity of genes for entirely different life strategies, because operating differently from the majority is an advantage.
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We don't actually have a "status drive".
We have drives that tend to generate status seeking behavior but can be subsumed by many different status-like pursuits, such as self-status of solving problems or completing single-person video games, being good at a hobby nobody else cares about, pleasing certain people even to the point of harming any recognizable definition of social status, acting to please (raise status with) internally generated or deceased personalities, a need to be contrarian or difficult to the point of low-social status but high internal status, etc.
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Your assumption that same basic nervous system -> same net drives/behaviors, fails in much simpler species.
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So no, mathematicians are no more motivation clones than they are genetic clones.
And mathematics is not a field that is attractive to people who give social status high priority, because it impedes social status.