Using AI to solve a Math Joke

I recently noticed this math joke in my Facebook feed. It was shared by my cousin Pat McCarthy, in Montana.

The joke/graphic I uploaded, followed by the prompt, and the response:

You are an expert at higher level math, can you please solve for the pin code?

I was pretty impressed. But after sleeping on it, I couldn't help but wonder what would happen if I ran the python myself locally.

So when I ran it nothing happened. I looked closer, and while the code was calculating something, it was not capturing the result, and printing it so I could see it.

I updated the script:

from sympy import symbols, integrate, sqrt
x = symbols('x')
numerator = 3*x**3 - x**2 + 2*x - 4
denominator = sqrt(x**2 - 3*x + 2)
integral = integrate(numerator / denominator, (x, 0, 1))
result = integral.evalf()
print(result)        

Now when I run it:

time python my_pin_calc.py
-2.98126694400554
python my_pin_calc.py 0.57s user 0.04s system 88% cpu 0.693 total        

Suggesting the pin is indeed: 2981 if 4 digits and maybe 298126 if 6 digits.

It's been a long time since I had to work with this type of math, so I asked chatgpt to describe the math involved, wondering if this had anything to do with differential equations.

Prompt: Can you tell me what this type of math is called?? Differential Equations??

Response: The integral given in the problem is not directly related to differential equations. The problem involves:

1. Integral Calculus: This is the primary field of mathematics used here, specifically evaluating definite integrals. Integral calculus focuses on finding the area under a curve and solving integrals.

2. Complex Fractions and Square Roots: The integral involves a complex fraction with a polynomial in the numerator and a square root of a polynomial in the denominator.

3. Definite Integrals: The specific type of integral being solved is a definite integral, which has set bounds (from 0 to 1 in this case).

In summary, this problem is firmly within the realm of integral calculus. It does not directly involve differential equations, which typically involve solving equations that include derivatives of functions.

So then I had to ask:

Prompt: Great thanks!? Can you give me a little description of differential equations.?

Response:

Expert: Mathematician

Objective: Provide a concise description of differential equations and their significance.

Assumptions: The user is looking for a general understanding of differential equations and their applications.

Description:

Differential equations are mathematical equations that involve functions and their derivatives. They describe how a particular quantity changes over time or space. These equations are fundamental in understanding and modeling the behavior of dynamic systems in various fields, such as physics, engineering, biology, and economics.

Types of Differential Equations:

1. Ordinary Differential Equations (ODEs): These involve functions of a single variable and their derivatives. For example, \(\frac{dy}{dx} = y\) is an ODE describing exponential growth or decay.

2. Partial Differential Equations (PDEs): These involve functions of multiple variables and their partial derivatives. An example is the heat equation \(\frac{\partial u}{\partial t} = \alpha \frac{\partial^2 u}{\partial x^2}\), which models the distribution of heat in a given region over time.

Applications:

1. Physics: Newton's laws of motion, Maxwell's equations for electromagnetism, and the Schr?dinger equation in quantum mechanics are all formulated using differential equations.

2. Engineering: Differential equations are used to model and analyze systems such as electrical circuits, mechanical vibrations, and control systems.

3. Biology: They describe population dynamics, the spread of diseases, and the behavior of biological systems.

4. Economics: Differential equations model economic growth, the behavior of markets, and financial systems.

Solving Differential Equations:

Solving differential equations can be complex and often requires specialized methods. Techniques include:

- Analytical Methods: Finding an exact solution using algebraic manipulations and integration. Examples include separation of variables and integrating factors for ODEs.

- Numerical Methods: Approximating solutions using computational algorithms. Methods like Euler's method, Runge-Kutta methods, and finite element analysis are commonly used for both ODEs and PDEs.

Importance:

Differential equations are crucial for modeling real-world phenomena where rates of change are involved. They provide a powerful tool for predicting future behavior based on current conditions, making them indispensable in scientific research and practical applications.

For more detailed exploration, consider resources such as textbooks on differential equations, online courses, or articles on specific applications in physics, engineering, or other fields.

I continue to be impressed with the rapid pace of Open AI and LLM's in general.

We are using them more and more in our day to day data engineering tasks at Cloud Data Consuting. More about that soon in a dedicated post.

#chatgpt #OpenAI #IsThisFunny #Math #Integration #DiffEQ #ProblemSolvingWithAI #CloudDataConsulting