4 ms·

On that note, I've been using ChatGPT to (re-)teach myself mathematical induction and working with proofs. It's like having my own tutor. There is huge potentia

by Sakos 3y ago

On that note, I've been using ChatGPT to (re-)teach myself mathematical induction and working with proofs. It's like having my own tutor. There is huge potential here just for helping people learn new topics and skills.

SOLAR_FIELDS 3y ago
I really wish I had ChatGPT when I was teaching myself programming. I wouldn’t have failed university programming courses and would have been in the workforce years faster.
- Sakos 3y ago
  Absolutely. I've been teaching myself Haskell and C++ too. For the first time in my life, learning is fun and not a dire struggle every step of the way (particularly as somebody with ADHD). Need to know how to handle building a C++ project or dependencies? No longer have to go through dozens of posts on Reddit or DO or pages upon pages of documentation. I can just ask, then focus on what I actually want to learn. Confused about some bizarre syntax in Haskell that gives me nothing on Google? Just ask. Don't understand how a function is constructed? Don't need to figure out what the correct terms are in what combination to find out what I'm looking at. Want a step by step explanation? Easy. Even though it's far from perfect and I have plenty to complain about, it's already a valuable part of my everyday life with its impact on how I learn new things and experiment.
  - empath-nirvana 3y ago
    It's been _incredibly_ useful for bringing new Rust devs up to speed here.
- bongodongobob 3y ago
  With all due respect, if you couldn't get a passing grade in intro programming courses I'm not sure how much GPT would have helped. Additionally, if college was the first time getting your feet wet in programming, you were likely already years behind the curve. I'm not trying to be nasty, but for loops, variables, the concept of program flow etc are very elementary concepts that many children and teens are fully capable of teaching themselves, even pre-internet. I think ChatGPT could pass any intro programming course so I have a hunch that it's just going to lead to lots of cheating and poor programming skills. Did you end up sticking it out? Grats if so and you're probably better off for not having had ChatGPT hold your hand. For me, the temptation to just have it pass my classes for me would have been way too tempting. It's too good at boilerplate programming which is every programming 101 project. "Write me an employee tracking system in java." Change up the comments and boom done with the assignment.
  - maroonblazer 3y ago
    When I was learning programming I was grateful for Stackoverflow and other internet resources. I couldn't imagine learning as quickly as I did without those resources. It's the same with LLMs. Now I don't have to wait hours or days for someone on SO or Reddit to read and respond to my question. Or spend who knows how long Googling for a similar - but not the SAME - question and trying to bend their solution to my problem.
  - deleted 3y ago
    [deleted]
radiator 3y ago
How is this better than a mathematics book with exercises (and solutions to them at the end or in a second book)?
- eru 3y ago
  GPT very naturally encourages you to write out questions. That by itself can be useful for learning. You can even get answers for your questions. And for a well trodden basic technique like mathematical induction, GPT is probably 'smart' enough to be able to explain everything. Basically, most questions a beginner might have are already covered in something like Stack Overflow, so GPT 'just' has to give you the right cached answer, instead of coming up with new thoughts of its own. (This is very hand-wave-y.)
- Sakos 3y ago
  Isn't it obvious? I can't have a conversation with an exercise and the solution. ChatGPT has helped me uncover gaps in my mathematical knowledge because I can ask it questions about what something means, how something was arrived at, or how it works. Sometimes proofs involve logical "jumps" that aren't immediately or intuitively obvious, or require some mathematical maturity that I otherwise wouldn't be aware of. Something I would've otherwise needed a tutor for to determine.
- pests 3y ago
  How do you ask a textbook a question? Exercises are great until the student is stuck at some "core concept" they could simply ask or explain their confusion and get a direct answer.
thaumasiotes 3y ago
> to (re-)teach myself mathematical induction Induction is just set membership. Every inductive proof looks like this: 1. There's a set, S. 2. There's a scalar value, e, in S. 3. e has property p. 4. There is a function, f, from S to S. 5. f preserves property p. 6. Every element of S can be reached from e by repeated application of f. (Often because S is defined to consist of e plus f(x) for any x in S.) --------- 7. Therefore, every element of S has property p.
- Sakos 3y ago
  Abstractly, sure. That doesn't help me at all when doing any of the exercises.
  - thaumasiotes 3y ago
    [dead]
rvz 3y ago
I wouldn't be so reliant on AI black-boxes like ChatGPT to learn anything from medicine, law or even mathematics and you don't even trust if its outputs are even correct. Terrance Tao doesn't even trust its outputs either and can verify if it is outputting nonsense that may look 'correct' in your eyes.
- Sakos 3y ago
  I don't blindly believe everything it says. I've caught it making mistakes plenty of times. But there's simply no going back anymore. There's no replacing what it can do and the kind of workflow it offers.
- pfdietz 3y ago
  Ah, but the nice thing about constructing formal proofs is you can immediately tell if the output is correct.
  - practal 3y ago
    Yes, but you also need to make sure the input is correct! For example, your idea of automatically formalising a paper needs to somehow make sure that the result means the same as the paper.

by Sakos 3y ago

SOLAR_FIELDS 3y ago

I really wish I had ChatGPT when I was teaching myself programming. I wouldn’t have failed university programming courses and would have been in the workforce years faster.

Sakos 3y ago
Absolutely. I've been teaching myself Haskell and C++ too. For the first time in my life, learning is fun and not a dire struggle every step of the way (particularly as somebody with ADHD). Need to know how to handle building a C++ project or dependencies? No longer have to go through dozens of posts on Reddit or DO or pages upon pages of documentation. I can just ask, then focus on what I actually want to learn. Confused about some bizarre syntax in Haskell that gives me nothing on Google? Just ask. Don't understand how a function is constructed? Don't need to figure out what the correct terms are in what combination to find out what I'm looking at. Want a step by step explanation? Easy. Even though it's far from perfect and I have plenty to complain about, it's already a valuable part of my everyday life with its impact on how I learn new things and experiment.
- empath-nirvana 3y ago
  It's been _incredibly_ useful for bringing new Rust devs up to speed here.
bongodongobob 3y ago
With all due respect, if you couldn't get a passing grade in intro programming courses I'm not sure how much GPT would have helped. Additionally, if college was the first time getting your feet wet in programming, you were likely already years behind the curve. I'm not trying to be nasty, but for loops, variables, the concept of program flow etc are very elementary concepts that many children and teens are fully capable of teaching themselves, even pre-internet. I think ChatGPT could pass any intro programming course so I have a hunch that it's just going to lead to lots of cheating and poor programming skills. Did you end up sticking it out? Grats if so and you're probably better off for not having had ChatGPT hold your hand. For me, the temptation to just have it pass my classes for me would have been way too tempting. It's too good at boilerplate programming which is every programming 101 project. "Write me an employee tracking system in java." Change up the comments and boom done with the assignment.
- maroonblazer 3y ago
  When I was learning programming I was grateful for Stackoverflow and other internet resources. I couldn't imagine learning as quickly as I did without those resources. It's the same with LLMs. Now I don't have to wait hours or days for someone on SO or Reddit to read and respond to my question. Or spend who knows how long Googling for a similar - but not the SAME - question and trying to bend their solution to my problem.
- deleted 3y ago
  [deleted]

radiator 3y ago

How is this better than a mathematics book with exercises (and solutions to them at the end or in a second book)?

eru 3y ago
GPT very naturally encourages you to write out questions. That by itself can be useful for learning. You can even get answers for your questions. And for a well trodden basic technique like mathematical induction, GPT is probably 'smart' enough to be able to explain everything. Basically, most questions a beginner might have are already covered in something like Stack Overflow, so GPT 'just' has to give you the right cached answer, instead of coming up with new thoughts of its own. (This is very hand-wave-y.)
Sakos 3y ago
Isn't it obvious? I can't have a conversation with an exercise and the solution. ChatGPT has helped me uncover gaps in my mathematical knowledge because I can ask it questions about what something means, how something was arrived at, or how it works. Sometimes proofs involve logical "jumps" that aren't immediately or intuitively obvious, or require some mathematical maturity that I otherwise wouldn't be aware of. Something I would've otherwise needed a tutor for to determine.
pests 3y ago
How do you ask a textbook a question? Exercises are great until the student is stuck at some "core concept" they could simply ask or explain their confusion and get a direct answer.

thaumasiotes 3y ago

> to (re-)teach myself mathematical induction Induction is just set membership. Every inductive proof looks like this: 1. There's a set, S. 2. There's a scalar value, e, in S. 3. e has property p. 4. There is a function, f, from S to S. 5. f preserves property p. 6. Every element of S can be reached from e by repeated application of f. (Often because S is defined to consist of e plus f(x) for any x in S.) --------- 7. Therefore, every element of S has property p.

Sakos 3y ago
Abstractly, sure. That doesn't help me at all when doing any of the exercises.
- thaumasiotes 3y ago
  [dead]

rvz 3y ago

I wouldn't be so reliant on AI black-boxes like ChatGPT to learn anything from medicine, law or even mathematics and you don't even trust if its outputs are even correct. Terrance Tao doesn't even trust its outputs either and can verify if it is outputting nonsense that may look 'correct' in your eyes.

Sakos 3y ago
I don't blindly believe everything it says. I've caught it making mistakes plenty of times. But there's simply no going back anymore. There's no replacing what it can do and the kind of workflow it offers.
pfdietz 3y ago
Ah, but the nice thing about constructing formal proofs is you can immediately tell if the output is correct.
- practal 3y ago
  Yes, but you also need to make sure the input is correct! For example, your idea of automatically formalising a paper needs to somehow make sure that the result means the same as the paper.