AIs should be forced to show their work. Every tool they use, every program they generate and run in the background, and every logical inference. They should be forced to produce Lean or Rocq proofs or execution traces for all the computation they use. For facts, they should be able to produce sources. For any abstract reasoning, they should be able to break it down into explainable steps.

Then, on top of that, they should be able to explain any of that, at any level of detail, whether talking to an expert or a layperson.

What worries me isn’t AI replacing experts, it’s that we may stop producing people who know enough to notice when AI is confidently wrong.

It sounds ‘the singularity is near’ not so much because AI is reaching escape velocity forward, but because we’re systematically pushing humans back beyond the threshold where computers are legible?

I'm not exactly sure how you would go about grading mathematical proficiency. I went through calculus two and discrete mathematics, but I'm sure that there are things I have forgotten now even though I would be considered familiar with most leading edge AI technology. If I'm being honest, I'm not sure I could pass the final exams I took to get my CS degree right now.

See also Bill Thurston’s classic Math Overflow answer to a student wondering where they fit compared to a Gauss or Euler:

https://mathoverflow.net/questions/43690/whats-a-mathematici...

“The product of mathematics is clarity and understanding. Not theorems, by themselves. [Their importance is not just in their specific statements], but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding.

The world does not suffer from an oversupply of clarity and understanding (to put it mildly)… In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. The question of who is the first person to ever set foot on some square meter of land is really secondary. Revolutionary change does matter, but revolutions are few, and they are not self-sustaining --- they depend very heavily on the community of mathematicians.”

> "the essay makes the case for treating mathematical capacity as a strategic asset on a par with semiconductor capability."

In other words, the mathematicians want more funding.

I see many people reacting with fear towards IA and many of them do not feel the same level of danger in other places which are clear to me (and I think that what they fear most is the unknown, as it has to be bad, for sure). I like the quote of the other message from Whitehead !!

Let's enjoy the ride. It might be last one!

I think the differentiation going forward is going to be if you're a person that understands things or if you're a person that delegates your understanding. I don't think there's going to be a lot of economic or social value to prompting an AI to do things you don't understand. First, anyone can do it, so why should someone give you money or credibility for that? Second, as fewer and fewer people bother to learn hard things, the scarcity of that knowledge will increase its value.

I guess even if I end up being wrong about that, I'd rather enrich my life and grow as a person by continuing to learn and do hard things rather than become an annoying cheerleader dependent on unreliable tools.

"Civilization advances by extending the number of important operations which we can perform without thinking about them." - A. N. Whitehead

Yeah how many of us know how to build an ICE engine or shoes of any meaningful quality

We set upon end of human craftsmanship decades ago

Math is probably the easiest to reclaim given its right in front our faces going about daily life. The syntax of math is not that important; real world quantification the syntax is meant to represent will still exist. Our biochemistry implicitly operates on senses of enough food and water, etc.

Such measures are so embedded in the daily routines we live an intuition will always exist

No one is born knowing how to make a computer as we know them today. A cup half filled is obvious