Without touching on the mathematics at all, I feel I can saw with incontestable authority and conviction that Monsterous Moonshine is the coolest mathematical term in a field awash with cool terminology.
The discovery of clever links to mathematics doesn't lend credence to string theory. It only suggests that it's mathematically sound. Countless non-Euclidian geometries are mathematically sound; but the universe isn't non-Euclidian.
Certainly interesting, though, and invaluable if we ever do verify string theory via experimentation. You know, if string theory ever provides a testable prediction.
Admittedly my comprehension is shallow.
What I'd like to have explained to me, is whether or not this finding isn't possibly inevitable. It seems to me that string theory is a complex model of the physical world, whereas the algebra derived from symmetries of space might be fundamentally the same, and thus, their paths might be destined to cross.
Yeah, this is like being thrown a new bone that I've never chewed on before. Thanks.
- What I'd like to have explained to me, is whether or not this finding isn't possibly inevitable.
It was absolutely inevitable. This is a fundamental mathematical relationship. You can formulate it in hex, octal, base-whatever, and you'd still have mathematicians eventually stumbling across these theorems. This process is probably akin to a universal indication of technological proficiency, and we will continue our progression with time.
Disclaimer: I do not sufficiently understand the "how" of this matter, but the preceding paragraph was what I took away from the article.
Already, there are mathematical similarities in concept to both General Relativity and Quantum Mechanical theories. GR - four dimensional shapes (K3 surfaces) vs. spacetime (4D), and algebraic topology (major keyword left out by article's author) structures vs. spacetime manifolds. QM - The 90 degree rotational analogies vs. the Pauli exclusion principle of orthogonality (one example - the three orthogonal P-shells for electrons filling orbitals), and the mathematics of number theory and QM both playing out on the complex plane.
I'm just scratching the surface here. I actually think that the importance of developing this direction of maths is under-emphasized in the article. It could always just be another beautiful dead end though.