To follow up on this, I had it solve a nasty ODE problem that I saw in the recent Mathematica 15 release post:

    Solve the following first-order ODE for f(x):

    ((-1 - 2*x)*f(x)*tan(1 + x - exp(-61 - 2*x)*f(x)/x)
    + exp(61 + 2*x)*x*(1 - x*tan(1 + x - exp(-61 - 2*x)*f(x)/x))
    + x*tan(1 + x - exp(-61 - 2*x)*f(x)/x)*f'(x)) = 0

    Find the general solution f(x).

    f(x) = x*exp(61 + 2*x)*(1 + x - arccos(C/x))

    C is an arbitrary constant.

How do you know it’s a valid solution? Are you able to verify it yourself?

How do we know the solution isn't in the weights though?

Interesting!

I just tried the quantized Q4_K_M from [1] in my RTX 2070 Super, it ran at 110 tok/s with 1800 tok/s prefill, and found the same solution to your prompt. It generated valid LaTeX for the answer but its reasoning trace uses mostly compact ASCII math notation. Took 3min 22s to answer, spending 22k tokens almost all on thinking.

[1] https://huggingface.co/prithivMLmods/VibeThinker-3B-GGUF