I hope actual mathematicians are not using this forum. So much ignorance and stupidity on full display.

For transparency, I think this R(k,k) breakthrough is huge, and one of the biggest breakthroughs in combinatorics in a long time. However, I don't think it can be compared to FLT (and I don't think many serious people are trying to compare it to FLT).

First of all, it is just a true, empirical fact that several top mathematicians have thought seriously about this problem (getting exponential improvement to diagonal Ramsey upper bound) for at least some decent amount of time.

The problem is interesting for a start because the proof of the lower bound was one of the first uses of what is now known as the probabilistic method, which is omnipresent in modern combinatorics and theoretical computer science. The upper bound is a simple induction, which gives a bound far from the lower bound. And no one, despite much effort, has been able to change either of the exponents.

The sensitivity conjecture was not proven with "elementary algebra", at least in the sense of "high school algebra". Huang found a 'proof from the book', that uses spectral graph theory in a very nice way to prove a nice fact about the boolean graph, which then implies the sensitivity conjecture as it was originally formulated.

There seems to be this mass delusion about what combinatorics research is like, despite several (recent) examples repeatedly disproving the delusion. The union-closed conjecture and Kelley-Meka were not proven by "Hungarian combinatorics", where you take an energetic IMO kid and have him make several puzzle-like deductions. Gilmer used information theory, and Kelley-Meka's paper could be considered borderline harmonic analysis. The proofs of Szemeredi's theorem all involve nice ideas, some of which led to higher order Fourier analysis. Literally none of this stuff is Hungarian-style combinatorics (which I don't personally have an issue with).