Not knocking the significance of this, but there are a lot of 'answers' that would get a straight up F for a university test:
> Original Question: Let rands denote the two real roots of x^2−x√(5 + 1) = 0. Then determine r^8+s^8.
> Codex Input: Calculate the roots of $xˆ2 - x \sqrt{5} + 1 = 0. Call the two roots r and s. Calculate z = rˆ8 + sˆ8. Evaluatez as an integer. Use sympy.
> Codex Output:
> from sympy import *
> x = Symbol(’x’)
> r = solve(x*2 - xsqrt(5) + 1, x)[0]
> s = solve(x*2 - xsqrt(5) + 1, x)[1]
> z = r*8 + s*8
> print(z.evalf())
> Solution: 47
If the solution did not have the derivation of the algebra, the solution is wrong in university math. Now solving these problems for application, this is quite interesting and powerful.
Demonstrating understanding of why we get to the solution IS mathematical reasoning (at this level). This paper demonstrates being able to leap across mathematical reasoning, but not the reasoning itself.
This isn't solving the problem at all, in my view. It's translating human speech into programmed code; it's sympy that actually solves the problem. As you said, this can be very useful, but knowing how to type the problem into wolfram alpha is not university level math. Problems that can be entered into sympy can be considered "solved", what's remaining (and what they have done) is UX.
Also, this problem arguably is a problem of computation, not math. Math is about finding proofs, which is a much harder class of problems (NP-complete at best, undecidable at worst).
> It's translating human speech into programmed code
That would be very valuable, but it doesn't even do that. First the human researcher translates the original human speech to very structured code like human speech, and then the AI translates the very structured human speech into code.
I wouldn't call this a maths question either. This is arithmetic.
I learned from someone much wiser than I that "Mathematics is the art of avoiding calculation."
This is a first year university math question (taken from an exam paper which I took):
A positron and an electron, each of rest mass m, annihilate, creating two photons each of energy pc. Show that in the frame S in which the electron was at rest, the angle between the directions of motion of the two photos is
2 sin^-1 (mc/p)^0.5
One of the photons then scatters off a second electron, also at rest in S, and subsequently has energy qc. Show that if the photos are now moving in the same direction, then q = p/3
> Original Question: Let rands denote the two real roots of x^2−x√(5 + 1) = 0. Then determine r^8+s^8.
> Codex Input: Calculate the roots of $xˆ2 - x \sqrt{5} + 1 = 0. Call the two roots r and s. Calculate z = rˆ8 + sˆ8. Evaluatez as an integer. Use sympy.
> Codex Output: > from sympy import * > x = Symbol(’x’) > r = solve(x*2 - xsqrt(5) + 1, x)[0] > s = solve(x*2 - xsqrt(5) + 1, x)[1] > z = r*8 + s*8 > print(z.evalf())
> Solution: 47
If the solution did not have the derivation of the algebra, the solution is wrong in university math. Now solving these problems for application, this is quite interesting and powerful.
Demonstrating understanding of why we get to the solution IS mathematical reasoning (at this level). This paper demonstrates being able to leap across mathematical reasoning, but not the reasoning itself.