News for hackers. Stuff that matters.
Re:Terence Tao, "Machine Assisted Proof" [video] by Sakos on Wednesday February 14, 2024 @07:34PM (#39377599)
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.
Re:Terence Tao, "Machine Assisted Proof" [video] by SOLAR_FIELDS on Wednesday February 14, 2024 @08:04PM (#39377850)
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.
Re:Terence Tao, "Machine Assisted Proof" [video] by Sakos on Wednesday February 14, 2024 @08:18PM (#39377973)
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.

Re:Terence Tao, "Machine Assisted Proof" [video] by empath-nirvana on Thursday February 15, 2024 @06:43AM (#39381557)
It's been _incredibly_ useful for bringing new Rust devs up to speed here.
Re:Terence Tao, "Machine Assisted Proof" [video] by bongodongobob on Wednesday February 14, 2024 @08:30PM (#39378058)
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.

Re:Terence Tao, "Machine Assisted Proof" [video] by maroonblazer on Wednesday February 14, 2024 @08:38PM (#39378104)
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.

Re:Terence Tao, "Machine Assisted Proof" [video] by radiator on Wednesday February 14, 2024 @08:58PM (#39378232)
How is this better than a mathematics book with exercises (and solutions to them at the end or in a second book)?
Re:Terence Tao, "Machine Assisted Proof" [video] by pests on Wednesday February 14, 2024 @09:27PM (#39378416)
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.
Re:Terence Tao, "Machine Assisted Proof" [video] by eru on Wednesday February 14, 2024 @09:10PM (#39378307)
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.)

Re:Terence Tao, "Machine Assisted Proof" [video] by Sakos on Wednesday February 14, 2024 @09:23PM (#39378393)
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.
Re:Terence Tao, "Machine Assisted Proof" [video] by thaumasiotes on Wednesday February 14, 2024 @09:23PM (#39378392)
> 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.

Re:Terence Tao, "Machine Assisted Proof" [video] by Sakos on Wednesday February 14, 2024 @09:25PM (#39378407)
Abstractly, sure. That doesn't help me at all when doing any of the exercises.
Re:Terence Tao, "Machine Assisted Proof" [video] by rvz on Wednesday February 14, 2024 @10:28PM (#39378766)
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.

Re:Terence Tao, "Machine Assisted Proof" [video] by pfdietz on Wednesday February 14, 2024 @11:23PM (#39379083)
Ah, but the nice thing about constructing formal proofs is you can immediately tell if the output is correct.
Re:Terence Tao, "Machine Assisted Proof" [video] by practal on Thursday February 15, 2024 @10:59AM (#39384288)
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.
Re:Terence Tao, "Machine Assisted Proof" [video] by Sakos on Wednesday February 14, 2024 @10:41PM (#39378842)
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.