I theorize this is a good way to build mathematical maturity, at least the “parse advanced math” part. I remember when I became mathematically mature enough to read Math Wikipedia, I want to go further in this direction till I can read math-y papers like Wikipedia.
This seems like an interesting idea. I have this vague sense that if I want to go into alignment I should know a lot of maths, but when I ask myself why, the only answers I can come up with are:
Because people I respect (Eliezer, Nate, John) seem to think so (BAD REASON)
Because I might run into a problem and need more maths to solve it (Not great reason since I could learn the maths I need then)
Because I might run into a problem and not have the mathematical concepts needed to even recognise it as solvable or to reduce it to a Reason 2 level problem (Good reason)
I wonder if reading a book or two like that would provide a good amount of benefit towards Reason 3 without requiring years of study.
#3 is good. another good reason is so you have enough mathematical maturity to understand fancy theoretical results.
I’m probably overestimating the importance of #4, really I just like having the ability to pick up a random undergrad/early-grad math book and understand what’s going on, and I’d like to extend that further up the tree :)
Quantum computing since Democritus is great, I understand Godel’s results now! And a bunch of complexity stuff I’m still wrapping my head around.
The Road to Reality is great, I can pretend to know complex analysis after reading chapters 5,7,8 and most people can’t tell the difference! Here’s a solution to a problem in chapter 7 I wrote up.
I’ve only skimmed parts of the Princeton guides, and different articles are written by different authors—but Tao’s explanation of compactness (also in the book) is fantastic, I don’t remember specific other things I read.
Started reading “All the math you missed” but stopped before I got to the new parts, did review linear algebra usefully though. Will definitely read more at some point.
I read some of The Napkin’s guide to Group Theory, but not much else. Got a great joke from it:
There are a series of math books that give a wide overview of a lot of math. In the spirit of comprehensive information gathering, I’m going to try to spend my “fun math time” reading these.
I theorize this is a good way to build mathematical maturity, at least the “parse advanced math” part. I remember when I became mathematically mature enough to read Math Wikipedia, I want to go further in this direction till I can read math-y papers like Wikipedia.
This seems like an interesting idea. I have this vague sense that if I want to go into alignment I should know a lot of maths, but when I ask myself why, the only answers I can come up with are:
Because people I respect (Eliezer, Nate, John) seem to think so (BAD REASON)
Because I might run into a problem and need more maths to solve it (Not great reason since I could learn the maths I need then)
Because I might run into a problem and not have the mathematical concepts needed to even recognise it as solvable or to reduce it to a Reason 2 level problem (Good reason)
I wonder if reading a book or two like that would provide a good amount of benefit towards Reason 3 without requiring years of study.
#3 is good. another good reason is so you have enough mathematical maturity to understand fancy theoretical results.
I’m probably overestimating the importance of #4, really I just like having the ability to pick up a random undergrad/early-grad math book and understand what’s going on, and I’d like to extend that further up the tree :)
3 is my main reason for wanting to learn more pure math, but I use 1 and 2 to help motivate me
which of these books are you most excited about and why? I also want to do more fun math reading
(Note; I haven’t finished any of them)
Quantum computing since Democritus is great, I understand Godel’s results now! And a bunch of complexity stuff I’m still wrapping my head around.
The Road to Reality is great, I can pretend to know complex analysis after reading chapters 5,7,8 and most people can’t tell the difference! Here’s a solution to a problem in chapter 7 I wrote up.
I’ve only skimmed parts of the Princeton guides, and different articles are written by different authors—but Tao’s explanation of compactness (also in the book) is fantastic, I don’t remember specific other things I read.
Started reading “All the math you missed” but stopped before I got to the new parts, did review linear algebra usefully though. Will definitely read more at some point.
I read some of The Napkin’s guide to Group Theory, but not much else. Got a great joke from it: