I might be willing to agree that the Grothendieck-Riemman-Roch formula is an example of Jenga math. (Yes, I am leaving out Atiyah, Singer, Bott, Hirzebruch and possibly others.) However, if so, then it is an example of why Jenga math is sometimes worth doing. There are three major improvements from the original RR to the current version, and all of them are important for problems which mathematicians actually care about every day.

The original RR considered a holomorphic vector bundle L on a complex curve X. We have a “derivative” (the proper term is a dbar-connection) on L, whose kernel are the holomorphic sections. The original RR expressed the holomorphic Euler characteristic — roughly, the dimension of the kernel of this operator minus the dimension of its cokernel — in terms of purely toplogical facts about L and X.

This is useful, but mathematicians want to study complex varieties other than curves. Hirzebuch figured out how to permit X to be a smooth compact complex variety of any dimension, and L to be a vector bundle rather than a line bundle.

Atiyah, Singer and Bott figured out how to replace dbar by more general differential operators. I am not clear on why this is useful, but my friends in differential geometry tell me they use the more general form all the time.

Finally, Grothendieck figured out how to handle the case where L and X vary in a continuous family, and you want to understand how the holomorphic Euler characteristic varies. He realized that holmorphic Euler characteristic describes, in a formal sense, the “variation when mapping to a point” and forced himself to write the whole proof to work for any (proper) map. This shows up all the time in my own work, and the work of tons of other algebraic geometers. Moreover, by forcing himsself to consider the problem in such a high level of generality, he actually came up with one of the shortest and most elegant proofs.

I agree with Thomas Nyberg that Stone’s generalization is useful. Stone not only weakened the hypotheses, he simplified the proof. But the S-W theorem is starting to become inverted: some of the proof details are exposed in the hypothesis. Further generalizations are less original and more inverted.

Many theorems from number theory were turned into abstract algebra theorems simply by applying vocabulary that didn’t exist when the theorem was originally stated. That’s valuable, but the theorem shouldn’t be named after the person who updated the language.

I’ve tried to think of egregious examples of inverted proofs, but such theorems are inherently unmemorable.