1. The four color theorem is a useful case study, for which the original proof was validated and 400 pages long. My prediction is that the first couple waves of proofs will be hard enough that a layman couldn't produce them, but simple enough that experts can verify them. Over time the most advanced proofs will get more and more complicated until humans can no longer verify them, this process could happen over the course of a few month or could take literally hundreds of years.
2. Especially early on the overwhelming majority of the proofs are likely to be uninteresting and more novel just because actually producing them would take expert time that's better spent elsewhere. That being said, as above over time I expect the interestingness of proofs to go up until they eventually regularly produce interesting proofs. The vast majority of proofs are likely to maintain their position as of no interest to humans for the simple reason that the vast majority of proofs are of no interest to humans.
In neither case will I make any particular guesses about a timeline beyond it seems like the way things will go.
Mathematics seems like the ideal candidate for AIs to achieve absurd results. It's a purely abstract grammar with true auto-verifiability. Even SWE has the requirement of interacting with real physical things. In math there's no external feedback required, you're solely bounded by the rate and quality of token generation.
The evidence says that during disasters ppl come together and help each other during disaster while state and business institution act in an at best obstructionist and at worst predatory way. So why do ppl in power believe the exact opposite? The simple explanations are that it's a delusion they actually hold, or a lie they project and either way it serves as a justification for the systems they benefit from.
Time to do that most desperate of things, actually read past the abstract.
First, this study was only in academia, and not industry so the results aren't necessarily generalizable. They probably do have some correlation, but they're very different environments.
Second, the very first paragraph after the abstract goes into why actually getting hired is just a tiny part of why women don't go in to stem, "...including inadequate mentoring and networking (1); a chilly social climate (2); downgrading of work products such as manuscripts (3), grant proposals (4), and lectures (5); and gender bias in interviewing and hiring (6–9)."
Third, this was rating an applicant for a third party, not actually hiring an applicant for them self, ppl act different when they have no skin in the game. While experiment 5 did try to account for this by removing the direct competition aspect so they only rated a single candidate rather than selecting a better choice from 2 options, however again there's no consequence for the choice except having your response presented in a paper.
What this study does show is that academics think that other academics view hiring equally women over men as socially desirable. This is not the same as actually doing it when given the opportunity, for an example of this see https://www.jstor.org/stable/3711747?seq=1 and the general trend of Americans saying they go to church even when they don't.
There's a lot going on but the basic reasons are:
Evangelical white Christians think the existence of Israel is necessary to bring about the Apocalypse, a thing they want because they go to heaven.
The Israeli right wing wants criticism of Israel to be inseparable from criticism of Jewish people. This means you can't criticize Israel without being painted as anti-Semitic, and to be fair there are a lot ppl who criticize Israel for deeply anti-Semitic reasons.
Quick rule of thumb, the reason we associate it with cancer is because the only ppl we systemically tested for it had cancer. If you tested everybody you'd probably find it in everybody since it was in a mandatory vaccine
Parts of India might get uninhabitable in the summer in some of the worse case scenarios. Given the population there and the fact they're a nuclear armed state that's a geopolitical powder keg.
If my choice is between definitely dying of boring old hypoxia and maybe dying in a cool explosion I know which one I'm picking.
But to be serious it's risk management and if the patient is definitely going to die of low oxygen then the patient having a risk of dying another way is still a lower risk.
This is a nightmare. Getting spammed by ads on my devices is bad enough. Now when I go out in public I get shamed for all to see. Targeted automated advertising has got to be banned outright.
2. Especially early on the overwhelming majority of the proofs are likely to be uninteresting and more novel just because actually producing them would take expert time that's better spent elsewhere. That being said, as above over time I expect the interestingness of proofs to go up until they eventually regularly produce interesting proofs. The vast majority of proofs are likely to maintain their position as of no interest to humans for the simple reason that the vast majority of proofs are of no interest to humans.
In neither case will I make any particular guesses about a timeline beyond it seems like the way things will go.