But that is trivial

Every field has its own share of its-obviously-true-but-insanely-hard-to-prove problems. In complexity theory, it is $$\mathrm{P}$$ vs. $$\mathrm{NP}$$1. In number theory, it is the Riemann hypothesis….

But these problems are relatively non-trivial to state. You need an undergrad in CS and respectively math to properly understand these problems (Unless you’re at Waterloo, in which case you need a BMath in CS for the former2. ;p). For instance, $$\mathrm{P}$$ vs. $$\mathrm{NP}$$ isn’t exactly about verification vs. provability but rather about polynomial deterministic verification vs. deterministic provability. (Yes, the probabilistic version–$$\mathrm{BPP}$$ vs. $$\mathrm{MA}$$ is also open and so is $$\mathrm{P}$$ vs. $$\mathrm{PSPACE}$$ but I think you get my point!)

But try this: It is not yet proven that $$e+\pi$$ is irrational! To refresh your memory, a rational number is one that can be expressed as $$\frac{p}{q}$$ for $$p,q$$ being integers and $$\gcd(p,q) = 1$$. But we know due to the wonderful work of Hermite (1973) and Lindemann (1882) that $$e$$ and $$\pi$$ respectively are transcendental. Again, transcendental means that it is not algebraic over the rationals. For those of you with social lives, it means that it cannot be expressed as a root of a polynomial with rational coefficients. And from this it follows that any real transcendental number is irrational.

For a friendly introduction to the Riemann hypothesis see “A Friendly Introduction to The Riemann Hypothesis” by Thomas Wright. And for $$\mathrm{P}$$ vs. $$\mathrm{NP}$$, see “The Golden Ticket P, NP, and the Search for the Impossible” by Lance Fortnow3.

1. A friend of mine recently pointed out to me that I was being insanely cocky by saying “$$\mathrm{P} \neq \mathrm{NP}$$ is open” when some giants like Donald Knuth believe otherwise. So, yeah, I will stick to saying $$\mathrm{P}$$ vs. $$\mathrm{NP}$$ till Ketan Mulmuley finishes sharpening his Algebraic Geometry and Representation Theory tools and kills the hope of all equalists.
2. For non-Waterloo readers, this is a reference to the fact that you can get a Bachelor of Computer Science from Waterloo without taking any “real CS theory” courses.
3. Although, I would never consider a world where $$\mathrm{P} = \mathrm{NP}$$ to be “Beautiful”.