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But now, what you write is it’s only 5% of the people being affected. Damn. So you acknowledge 5% are affected but that’s ok. It’s only 5%. It is profoundly immoral to think nothing is amiss because it only affects 15 million or so people. It’s not righteous pearl clutching to be alarmed when my neighbors are being illegally targeted. Having a conscience and an ounce of empathy is not righteous pearl clutching. As Edmund Burke said, all that is necessary for evil to prevail is that good men do nothing.

Illegal wars, illegal deportations, illegal cancellation of appropriated funds, illegal bribes to give pardons, etc. and your response is that the people alarmed by this are engaging in righteous pearl clutching. You are the problem.

I’ll read any response you wrote but won’t respond further. Those who remain silent while others are terrorized are dispicable.

EDIT: Being in the position of not belonging to a group targeted for retribution by the government isn’t an indication of having rights. When black men who are legally carrying guns are murdered by police without consequence then we don’t truly have the right to own guns. It shows that if one ever becomes part of an out group then you too can be targeted.

Clearly you are not part of a targeted group so you feel safe and naively think nothing is amiss. This is ignorant foolishness.

This is an indication you don’t understand what is going on. Some illegals have been deported but amongst those illegals are U.S. citizens and people who are legally allowed to be here. They are being deported without judicial oversight and in some cases in direct violation of judicial orders.

… none of this stuff or policy really affects most people's day to day lives.

Man. What a profoundly immoral thing to say and believe. This illegal shit going on doesn’t affect more than 49.999% of the population so… no big deal.

It is people like you that Martin Luther King described in his letter:

I have almost reached the regrettable conclusion that the Negro's great stumbling block in the stride toward freedom is not the White Citizen's Council-er or the Ku Klux Klanner, but the white moderate who is more devoted to "order" than to justice; who prefers a negative peace which is the absence of tension to a positive peace which is the presence of justice; who constantly says "I agree with you in the goal you seek, but I can't agree with your methods of direct action;" who paternalistically feels he can set the timetable for another man's freedom; who lives by the myth of time and who constantly advises the Negro to wait until a "more convenient season."

This is precisely the time to “overreact”. The government is clearly targeting dissidents and if we don’t “overreact” shit will get much worse.

We have kids sent to concentration camps. We have illegally deported U.S. citizens. The President has canceled monies allocated by Congress and signed into law. He is waging war against Iran without Congressional approval. He is openly selling pardons. The list goes on.

This isn’t enough to get you to “overreact”?

It says more how you write things and where you are coming from.

https://www.bbc.com/news/articles/c6pprpd3x96o

https://amazonwatch.org/news/2024/0214-chevrons-environmenta...

At some point an AI will prove a result that is so long and complicated that no human will understand it. This should not preclude people from using that result. In general, whenever the body of knowledge is increased it is a good thing. Even if it isn’t increased by humans.

Tying the worthiness of theoretical knowledge to the whether or not it improves a product is asinine in my opinion.

A lot of people spent a lot of time and effort to prove or disprove the Jacobian Conjecture. AI solved it easily. It is increasingly becoming the case that humans are not as good at mathematics as computers. You are free to ignore computer generated proofs but I don’t think this position will win out in the long run.

For what? Which product becomes better if it is correct?

This sentiment is anti-thetical to the whole point of pure math and theoretical science. No product became better when Euler proved the fundamental theorem of algebra.

Suppose an oracle tells us the Riemann Hypothesis is correct. There are a vast number of results of the form:

If RH is correct then A.

It would be very useful to have an oracle tells us whether or not RH is correct.

But the point is that pre-AI it was already the case that famous results were published that very few could understand or digest. I think it is reasonable to expect that we will soon be at a point that Lean says a theorem is correct but no human can or will ever understand the proof.

What if Lean verifies Mochizuki’s proof of the ABC conjecture. Do we disregard it becuase no other mathematician understands the proof?

To your first point. There a large number of cases that maps can be reduced to. Very few people have checked these reductions themselves. In 50 years there will be no human alive that will have checked the reductions by hand. Do we then discard the theorem? More importantly, do we trust the people that claim to have checked all the reductions? There are hundreds of cases. I trust a computer verification much more than I’d trust human verification. Humans will likely make mistakes due to the tedium. And some will claim understanding of all cases but be wrong in their understanding in some of the cases.

Properly explain is an enormous grey area. Soon, I think, there will be proofs of results that are verified in Lean that are so long that no one will be able to “properly explain”. I don’t think they should be discarded.

Resolution of singularities is a famous theorem of Hironaka. Abhyankar claimed that no one truly understood the proof of the theorem. He said that he and Zariski couldn’t get through the paper with a full understanding. But everyone accepts this theorem as being correct.

What AI is showing is that mathematics is mostly just pattern searching and AI can do this far better, faster, and with a much wider base than humans can. When I was working on my thesis problem I realized that I worked much less than my fellow students. I was an average student in my program but even for the best students they had to spend a lot of time thinking about stuff. They put in a lot of effort.

Is the difference between me and Tao mostly effort and that he has a much better memory of mathematical facts than me?

Republicans fought hard to discredit their own plan. They just wanted to move to the right of whatever it was that the black man championed.

Medicaid expansion saved lives. That is true and not in dispute. Other lives were saved too. It wasn’t just poor people who obtained life saving care from ACA. In an alternate world where only Medicaid expansion occurred fewer lives would have been saved than were saved with ACA as it exists now.