[FredZarguna]

Hard to take a list seriously that doesn't include some version of

1) C = 2πr

2) a₀ + a₁x + a₂x²+ ... + a_nxⁿ = 0 has at least one complex root for every n > 0. [The Fundamental Theorem of Algebra]

3) f(x) = d/dx ∫_a^x f(t) dt [with suitable restrictions on f. The Fundamental Theorem of Calculus.]

4)

The binomial Theorem.

5) Euler's formula: e^iθ = cosθ + i sinθ

All of these are far more important than the Navier-Stokes equation, The Shannon Entropy Information Equation, May's Map, or The Black-Scholes Equation.

[So Cal Rocket]

As a corollary to Euler’s theorem, it fascinates me that:

e^(pi x i) = -1

The fact that three somewhat unrelated concepts such as e, pi and i can be put together to make such an elegant formula blows me away.

[KC_for_Freedom]

Agreed,

Your equations represent fundamental basic equations that must be mastered on the way to the author’s final list.

As basic elements, they are part of the foundation, and far more important, but not as extreme.