It is absolutely mind-blowing how much time and passion humans have invested in understanding the consequences of nine simple statements...and how hard they resist against unveiling their secrets.
0∈ℕ
∀x∈ℕ:S(x)∈ℕ
∀x∈ℕ:S(x)≠0
∀x,y∈ℕ:S(x)=S(y) ⇒ x=y
0∈X∧∀x∈ℕ:(x∈X ⇒ S(x)∈X) ⇒ ℕ⊆X
x + 0 := x
x + S(y) := S(x + y)
x · 0 := 0
x · S(y) := x · y + x
These are the Peano axioms [1] defining the natural numbers with addition and multiplication. And for at least 3000 years humans are tying to figure out properties of these natural numbers, all consequences of these definition, and the end is not in sight.
[1] https://en.wikipedia.org/wiki/Peano_axioms