If you mean “make it easier for new people to get up to speed”, I’m all for that goal. That goal encompasses a significant chunk of the value of the Alignment Newsletter.
If you mean “create courses that allow new people to get the required mathematical maturity”, I’m less excited. Such courses already exist, and while mathematical thinking is extremely useful, mathematical knowledge mostly isn’t. (Mathematical knowledge is more useful for MIRI-style work, but I’d guess it’s still not that useful.)
I’m not sure I understand the difference between mathematical thinking and mathematical knowledge. Could you briefly explain or give a reference? (e.g. I am wondering what it would look like if someone had a lot of one and very little of the other)
Mathematical knowledge would be knowing that the Pythagoras theorem states that a2+b2=c2, mathematical thinking would be the ability to prove that theorem from first principles.
The way I use the phrase, mathematical thinking doesn’t only encompass proofs. It would also count as “mathematical reasoning” if you figure out that means are affected by outliers more than medians are, even if you don’t write down any formulas, equations, or proofs.
Depends what you call the “goal”.
If you mean “make it easier for new people to get up to speed”, I’m all for that goal. That goal encompasses a significant chunk of the value of the Alignment Newsletter.
If you mean “create courses that allow new people to get the required mathematical maturity”, I’m less excited. Such courses already exist, and while mathematical thinking is extremely useful, mathematical knowledge mostly isn’t. (Mathematical knowledge is more useful for MIRI-style work, but I’d guess it’s still not that useful.)
I’m not sure I understand the difference between mathematical thinking and mathematical knowledge. Could you briefly explain or give a reference? (e.g. I am wondering what it would look like if someone had a lot of one and very little of the other)
Mathematical knowledge would be knowing that the Pythagoras theorem states that a2+b2=c2, mathematical thinking would be the ability to prove that theorem from first principles.
The way I use the phrase, mathematical thinking doesn’t only encompass proofs. It would also count as “mathematical reasoning” if you figure out that means are affected by outliers more than medians are, even if you don’t write down any formulas, equations, or proofs.