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I hope it went well! I am in my fifties and enrolled in a master degree program for pure mathematics about 2 years ago (I don't need the degree, so I"m just tak

I hope it went well! I am in my fifties and enrolled in a master degree program for pure mathematics about 2 years ago (I don't need the degree, so I"m just taking all the classes they offer, so not about to graduate). It definitely took some time to get my brain sharper, but I am better each semester. I hope people don't take away the negative side of the article, brain slows down, but the positive side: brain gets better with usage. Its uncomfortable, I can churn out programs as complex as programs I've already written and go to review meetings and planning meetings without much effort. But being able to solve PDEs reasonably quickly and accurately, I cannot, or have not without a great deal of practise. It's unconfortable in some weird mental but physical sense. But I'm sharper in everything else I do. One interesting thing about software as career followed by math classes is that there's no compiler - you can type any janky thought into LaTeX and if you don't detect that it's bogus, nothing will, until you show it to a professor. Also, the information density of maths notation is way higher than (good) code. We want code to be readable by some that doesn't know it; a lot of math seems to be readable when you sort of 80% already are familiar with all the prereqs. So no just skimming and then hitting compile/test/run (whatever validation you do). It's typing letter by letter and taking the mental effort to actually see and decipher the letter (at least, for me in my current stage; I'm trying to do novel research, but my demonstrated understanding of the details of the previous research is embarrassing low). Also, weirdly, I still have the same fear of professors that I did as a young person. I manage it better with my decades of maturity (really) but it is still a part of my social interactions.

BeetleB 2y ago
> But being able to solve PDEs reasonably quickly and accurately, I cannot, or have not without a great deal of practise. No one - young or old - does well in math without a great deal of practice :-)
- JadeNB 2y ago
  A related ancient XKCD with a slightly different take: https://xkcd.com/447/ https://xkcd.com/447/
semireg 2y ago
The information density is incredible. A 2x2 matrix (Jordan constants) containing enough information to produce a slice of a hyperbolic paraboloid. Leaves me mesmerized... It's funny, at the end of each lecture I just want to yell... "NO! Don't stop! I must see how this ends!" Very similar to when I stop our children's movie and tell them to go take a bath.
- mycall 2y ago
  I guess nobody knows all of math and it is constantly a learning process, but things like "Jordan constants" which defines proper nouns to thousands upon thousands of math concepts, symbols, theorems and approaches just makes it a even harder to memorize the whole shebang. Fascinating but sometimes overly complex.
JadeNB 2y ago
> One interesting thing about software as career followed by math classes is that there's no compiler - you can type any janky thought into LaTeX and if you don't detect that it's bogus, nothing will, until you show it to a professor. The formal proof community is very interested in exactly this problem! It's not my specialty, but I believe that Lean (https://en.wikipedia.org/wiki/Lean_(proof_assistant) https://en.wikipedia.org/wiki/Lean_(proof_assistant)) is one of the very active communities.
- lanstin 2y ago
  I've done some intro to lean things, but no one in the maths program is into lean, so I'm just focusing on the math side. Terry Tao is big into the idea of lean tho, and combining LLMs with Lean.
  - JadeNB 2y ago
    > I've done some intro to lean things, but no one in the maths program is into lean, so I'm just focusing on the math side. Terry Tao is big into the idea of lean tho, and combining LLMs with Lean. One of the best things about entering an underpopulated space is that you can become one of the leading experts very quickly. If it's something that appeals to you and fits your skill set, it might be worth investing the time to learn! (Again, I say this as someone who's always been interested in formal proof, but haven't investigated it much myself, much less explored the merits and demerits of particular systems—so this is not an endorsement of Lean specifically, though it does seem to be one of the most active communities, which is important when you're trying to get into a topic.)
codesuki 2y ago
I like your point about feedback. That's how I describe my difficulties with proofs, too. There is no way of knowing a proof is right without knowing it's right. (Or maybe I am just missing the point) I will look into Lean that is mentioned here.

BeetleB 2y ago

> But being able to solve PDEs reasonably quickly and accurately, I cannot, or have not without a great deal of practise. No one - young or old - does well in math without a great deal of practice :-)

JadeNB 2y ago
A related ancient XKCD with a slightly different take: https://xkcd.com/447/ https://xkcd.com/447/

semireg 2y ago

The information density is incredible. A 2x2 matrix (Jordan constants) containing enough information to produce a slice of a hyperbolic paraboloid. Leaves me mesmerized... It's funny, at the end of each lecture I just want to yell... "NO! Don't stop! I must see how this ends!" Very similar to when I stop our children's movie and tell them to go take a bath.

mycall 2y ago
I guess nobody knows all of math and it is constantly a learning process, but things like "Jordan constants" which defines proper nouns to thousands upon thousands of math concepts, symbols, theorems and approaches just makes it a even harder to memorize the whole shebang. Fascinating but sometimes overly complex.

JadeNB 2y ago

> One interesting thing about software as career followed by math classes is that there's no compiler - you can type any janky thought into LaTeX and if you don't detect that it's bogus, nothing will, until you show it to a professor. The formal proof community is very interested in exactly this problem! It's not my specialty, but I believe that Lean (https://en.wikipedia.org/wiki/Lean_(proof_assistant) https://en.wikipedia.org/wiki/Lean_(proof_assistant)) is one of the very active communities.

lanstin 2y ago
I've done some intro to lean things, but no one in the maths program is into lean, so I'm just focusing on the math side. Terry Tao is big into the idea of lean tho, and combining LLMs with Lean.
- JadeNB 2y ago
  > I've done some intro to lean things, but no one in the maths program is into lean, so I'm just focusing on the math side. Terry Tao is big into the idea of lean tho, and combining LLMs with Lean. One of the best things about entering an underpopulated space is that you can become one of the leading experts very quickly. If it's something that appeals to you and fits your skill set, it might be worth investing the time to learn! (Again, I say this as someone who's always been interested in formal proof, but haven't investigated it much myself, much less explored the merits and demerits of particular systems—so this is not an endorsement of Lean specifically, though it does seem to be one of the most active communities, which is important when you're trying to get into a topic.)

codesuki 2y ago

I like your point about feedback. That's how I describe my difficulties with proofs, too. There is no way of knowing a proof is right without knowing it's right. (Or maybe I am just missing the point) I will look into Lean that is mentioned here.