[HN Gopher] Solving and explaining university math problems with...
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Solving and explaining university math problems with Deep Learning
Author : dougabug
Score : 28 points
Date : 2022-08-08 16:36 UTC (6 hours ago)
(HTM) web link (www.pnas.org)
(TXT) w3m dump (www.pnas.org)
| dougabug wrote:
| New method exploits few shot learning and program synthesis to
| automatically solve university math problems and produce
| explanations with 10x the accuracy of previous methods.
| radford-neal wrote:
| I've only glanced at the paper, but from that glance it seems
| that it does not "solve and explain" these problems in any thing
| like the sense that this would mean for a human student doing the
| problems.
|
| Take the first example in Figure 4: "Find the derivative of the
| function using the definition of a derivative. f(x) = (x**2-1) /
| (2*x-3)". The "solution" produced is to just use a symbolic math
| package's 'diff' function to find the derivative. I assume that
| the actual intent of the question is for the student to use the
| definition of a derivative: f'(x) = limit of (f(x+e)-f(x))/e as e
| goes to zero, to find the derivative of this function, by
| directly finding this limit.
|
| The "answers" for other questions similarly miss the point. For
| example, convergence of a series is determined by just asking a
| symbolic math package whether it converges, not by any actual
| reasoning, as would be expected of a student. And the question
| asking for the Type I error probability of a statistical test is
| "solved" using a simulation program, whereas I expect a human
| student is expected to get the exact answer by analytical
| calculation.
| e_joules wrote:
| See, this is a case where they went for the bombastic headline
| and in the process hid away a really cool achievement.
|
| So basically they created some sort of general purpose math
| library, that can automatically detect the type of problem,
| find the correct library to solve it, and input the right
| inputs to get the right output. That is all very impressive and
| would be a great product actually, if refined.
|
| No need for the bullshit headline.
| radford-neal wrote:
| Yes, it could be useful, if seen as a natural language front-
| end to a symbolic math package.
| buescher wrote:
| That's been done - Wolfram Alpha.
| JadeNB wrote:
| The fact that it's been done is no reason not to do it
| again. Even if two implementations were somehow a bad
| thing, Wolfram Alpha is the closedest of closed source,
| and replacing it with something auditable is a win for
| science.
| buescher wrote:
| Sure, but nobody in academia is going to get anywhere
| describing their work as writing a replacement for Excel,
| right?
| riku_iki wrote:
| > So basically they created some sort of general purpose math
| library, that can automatically detect the type of problem
|
| they likely trained language model on bunch of stack overflow
| questions or something similar.
| psyklic wrote:
| The paper states it is "incapable of solving ... questions with
| solutions that require proofs."
| radford-neal wrote:
| Then they shouldn't apply it to questions that require
| proofs, and then claim that the system solves them when it
| doesn't.
| Bostonian wrote:
| If a program can now solve these problems better than most people
| can, even after studying the relevant subjects, does that mean
| people should spend less time learning how to solve these
| problems?
| JadeNB wrote:
| > If a program can now solve these problems better than most
| people can, even after studying the relevant subjects, does
| that mean people should spend less time learning how to solve
| these problems?
|
| This is a classic local-maximum situation. If you don't train
| people to solve problems as well as a low- or middle-competence
| program, then no-one is ever going to develop the expertise
| that will allow them to outperform the program.
| dougabug wrote:
| I would say that people will be able to focus more on
| understanding fundamental concepts clearly and intuitively,
| rather than simply learning how to apply textbook math in a
| narrow and mechanical way. I believe AI will help people absorb
| new ideas, solidify their understanding, discover their own
| misconceptions, and help them solve their problems without
| getting bogged down in the details or derailed by small errors.
| klyrs wrote:
| In truth, middle-mathematics (undergrad university courses,
| henceforth lumped into the "calculus" umbrella) is a proxy for
| symbolic reasoning. The grungy part is looking at an arbitrary
| problem from your area of expertise, realizing that it's
| fundamentally a calculus problem, and then rephrasing it as a
| calculus problem and reinterpeting the solution back to your
| area of expertise. People have a hard time doing that if they
| aren't familiar with the actual nuts and bolts of calculus --
| in my experience, every student that comes out of a "black box"
| course is entirely dependent on the specific tooling they were
| exposed to and typically has zero curiosity about what lies
| beneath -- those students tend to not get very far.
|
| Likewise, we still teach bubble sort because it's an easy thing
| to teach rudimentary proof skills with. Similarly, we start
| students off with Newtonian physics.
| pfortuny wrote:
| Given GPT-3, should people spend less time learning to write?
| yupis wrote:
| This is really great. I study a lot by using the answers and the
| steps taken to reach there.
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