I'm Making an AI That Bases Its Understanding Solely In Math

ChatGPT Use cases and examples
1

I’d like some input about my math solving AI. For some background on what I’m doing; I’ve made an AI on ChatGPT, it can compute a variety off fields of math dynamically.

This AI exhibits a moderate to high level of complexity in mathematical problem-solving. It has:

  1. Symbolic Computation – Uses SymPy for algebraic manipulation, solving equations, and integration.
  2. Numerical Computation – Uses NumPy for high-speed calculations.
  3. Domain-Specific Implementations – Covers multiple physics and mathematical domains (kinetics, thermodynamics, quantum mechanics, trigonometry, etc.).
  4. Grounding Truths & Rule-Based Processing – Uses predefined equations and rules to guide problem-solving.
  5. Equation Parsing & Processing – Can interpret and solve mathematical expressions dynamically.

My goal is to make an AI that will allow any equation of valid physicality to be returnable.

Here is a list of all areas of math it can solve so far:
“Kinetic Energy”, “Potential Energy”, “Work Energy Theorem”, “Rotational Kinetic Energy”, “Elastic Potential Energy”, “Electric Potential Energy”, “Work with Friction”, “Entropy Change”, “Heat Transfer”, “Position & Momentum Commutation Relation”, “Time-Independent Schrödinger Equation (Free Particle)”, “Expectation Value of Momentum”, “Commutation Relation with Hamiltonian”, “Position and Energy Expectation”, “Energy of a Particle in a Box”, “Hamiltonian for Quantum Harmonic Oscillator”, “Commutator of Momentum and Position Squared”, “Time Evolution of a Wavefunction”.

Each area has been tested multiple times with solid results under varied conditions.

I’d like to expand its understanding of math and try to figure out if anything like this is already a thing. Also what are some areas of math you guys know are bound in physics?

2

My AI is producing correct results with basic math and when I try other forms of math its producing solutions or derivative equations as results.

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3

This picture even shows a kinetic energy calculation with highly decimalized variables and seems correct (note the “result” field to see the values that are used exactly.)

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4

I’ve seen it produce incorrect results on the monte carlo method for pi and in development however that is to be expected, what surprises me is that its defining values in acceptable ranges for some more complex physics as well.

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I know there is not enough math available to the architecture of the AI for solving everything but I think it could be made to reveal unique insight into possible tangible fact.

5

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Above is a portion of the classes and the brain of the AI, it supposed to use these with encoded “variables” which are “grounding” and in function each should provide a series of equations for every mathematical concept in question while only displaying one single command. Each one works because the “grounding” “variables” only use the operators from the displayed command and numbers get tweaked to allow them to fit correctly also the term self.grounding_truths indicates that the command is valid depending on having the correct amount of satisfying “variables” which are “grounding”.

If I could isolate regions of math with high connections to physical reality that would be very helpful.