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.
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.
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
“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.”
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 !!
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 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.
Extrapolating to other fields, we can say this development is the worst what one can do to mankind and society: pushing for AI but at the same time decimating the human capital that helped produce and understand it. What is the point of producing countless mathematical proofs or code that one cannot verify nor understand? It’s like having a machine to produce endless things that no one needs or will use. Just because the machine can bring profits for the (initial) investors?! That is the rottenest form of capitalism imaginable.
I strongly suspect most people already live in a world, that is not reasonable to them.
If you observe most policies to come from authority, you might not feel the loss of your own capabilities as much. Most people who are subjected to rules of law, bureaucracy, politics, or religion, might see these rules as arbitrary.
If you think of the way math gets taught in a this-is-right-everything-else-is-wrong way, it will evoke the same feeling of arbitrary authority.
Playing around and exploring math is usually only sometimes taught to children from academic/STEM families. So why would someone mourn the loss of capability for mathematical reasoning in people, if they only experienced it as following something incomprehensible anyway.
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[ 1.5 ms ] story [ 34.0 ms ] threadThen, 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.
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
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.”
Let's enjoy the ride. It might be last one!
In other words, the mathematicians want more funding.
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.
If you observe most policies to come from authority, you might not feel the loss of your own capabilities as much. Most people who are subjected to rules of law, bureaucracy, politics, or religion, might see these rules as arbitrary.
If you think of the way math gets taught in a this-is-right-everything-else-is-wrong way, it will evoke the same feeling of arbitrary authority. Playing around and exploring math is usually only sometimes taught to children from academic/STEM families. So why would someone mourn the loss of capability for mathematical reasoning in people, if they only experienced it as following something incomprehensible anyway.