Dear Michael:

I attempt to ask ChatGPT this query. Run this code to solve Hilbert's thirteenth problem, the septic equation. Please see attached file for your reference.

Given. ax^7+bx^6+cx^5+dx^4+ex^3+fx^2+gx^1+h = 0 and x^2+px+r = 0

Find the values of "p" and "r" in terms of "a, b, c, d, e, f, g, and h."

Code:

ClearAll[a, b, c, d, e, f, g, h]; {a, b, c, d, e, f, g, h} = {a, b, c, d, e, 
  f, g, h}; Solve[
 h + 1/2 g (-p + Sqrt[p^2 - 4 r]) + 1/4 f (-p + Sqrt[p^2 - 4 r])^2 + 
    1/8 e (-p + Sqrt[p^2 - 4 r])^3 + 1/16 d (-p + Sqrt[p^2 - 4 r])^4 + 
    1/32 c (-p + Sqrt[p^2 - 4 r])^5 + 1/64 b (-p + Sqrt[p^2 - 4 r])^6 + 
    1/128 a (-p + Sqrt[p^2 - 4 r])^7 == 0 && 
  h + 1/2 g (-p - Sqrt[p^2 - 4 r]) + 1/4 f (-p - Sqrt[p^2 - 4 r])^2 + 
    1/8 e (-p - Sqrt[p^2 - 4 r])^3 + 1/16 d (-p - Sqrt[p^2 - 4 r])^4 + 
    1/32 c (-p - Sqrt[p^2 - 4 r])^5 + 1/64 b (-p - Sqrt[p^2 - 4 r])^6 + 
    1/128 a (-p - Sqrt[p^2 - 4 r])^7 == 0, {p, r}]

Attachments:

Hilbert's thirte...nb

I responded to your comment here: https://community.wolfram.com/groups/-/m/t/2934998

This question raises an important point: the answer is definitively yes.

One of the key strengths of ChatGPT lies in its ability to inspect the results of a call to the plugin and determine the subsequent actions to take. However, it is crucial to acknowledge that as a Large Language Model, ChatGPT's output is not deterministic, meaning that there may be instances where it makes mistakes. Nevertheless, ChatGPT possesses the capability to rectify these errors. To illustrate this, let's examine a concrete example.

Here is a concrete example:

I use this prompt:

"In the following every time I input a task/query/problem, I want you 1) write down the relevant mathematical formulas 2) develop and display well-documented Wolfram Language code that solves the problem and displays the code in a terminal-like way (with proper line length) 2) evaluate the code on the Wolfram Language API (make sure to remember the formatting rules for this API) 3) display the result returned from the Wolfram Language API"

and this task:

"Let's consider Faulhaber's formula (the one with the Bernoulli numbers). Please implement it as a Wolfram Language function and then test it by comparing its result with the straightforwardly computed sum of the first twenty integers cubed."

In most cases ChatGPT will get things right the first time. Here is such a session: https://chat.openai.com/share/6981e6e4-31cf-4052-83ff-c60ef32db61c

But sometimes ChatGPT makes a mistake (e.g. confusing signed with unsigned Bernoulli numbers). And Then it takes a guess what went wrong. Sometimes even this guess can be wrong. After trying the above prompt and task a dozen times, I got a session with a mistake. And the ChatGPT tried to fix the mistake. First it assumed a numerical precision issue. But it detected that this wasn't the issue. Then it went back and revisited the original formula and then got it right. Here is the session: https://chat.openai.com/share/c82b4d0c-eb1d-4ea7-a7b8-5dc87c224f53

In conclusion, the ability of ChatGPT to inspect results, make corrections, and enhance its performance is indeed a significant strength. While it is not infallible and can occasionally make errors, its error correction mechanisms and the capacity to refine code based on test cases contribute to its overall efficacy.

It is the openai plugin structure that 'redacted the output', not the Wolfram plugin and not me personally. I do not know why they do this and I have asked openai about it, but haven't heard back.