Core Equations from Mathematics and Science [Something Interesting #67][Basic Knowledge Stuff #16]

My brain basically turns into pudding any time equations and formulas are brought up but they're still vital to know (or at least be aware of). In my scrounging around online, this post from Reddit listed 17 essential formulas and equations found throughout history by mathematician Ian Stewart in his book In Pursuit of the Unknown. I figure that it's a good jumping point to delve deeper into the topic.

Image by Jeswin Thomas (Unsplash)

The original list is posted below first. After that, I've gone ahead and found various Wikipedia pages and other links connected to all 17 of these equations so that you can read more on them at your own leisure.

Disclaimer: Like everything else I post in some depth, this is both no way definitive in scope nor any indication of my own knowledge. For this, I was a mediocre-to-poor student when it came to mathematics and physics, so this is as much me learning 20 years later what I should've known then (and still having some trouble actually understanding it).

The Original List by Stewart

The Context

1. Pythagorean theorem

2. Logarithms (logarithm product identity)

3. Calculus (definition of the derivative)

4. Newton's law of gravity

5. Square root of minus one

6. Euler's formula for polyhedra

7. Normal distribution

8. Wave equation (one dimensional)

9. Fourier transform

10. Navier–Stokes equations (for conservation of momentum)

11. Maxwell's equations (in vacuum, in Gaussian units)

12. Second law of thermodynamics

13. Relativity (Mass–energy equivalence)

14. Schrödinger equation

15. Information theory (Shannon entropy)

16. Chaos theory (logistic map)

17. Black–Scholes equation