Royen proof of gaussian correlation inequality

hi all theres been a recent shock of awareness of the Royen proof of gaussian correlation inequality, pop-sci publicized by Wolchover for Quanta, a big milestone… this is a nearly ½-century-open problem![a] Quanta funded by Simons institute is one of the top outlets for scientific/ mathematical writing around today. a real community resource/ treasure!

the Royen proof is not exactly my area so cant write a lot on it but do note that its a key case study in dynamics of scientific peer review, and seems like it has some parallels to the ongoing mochizuki proof analysis.[b] it took over ~1½ year for “community” to begin to grasp the correctness of this proof and Wolchover has a nice historical timeline for how others began to notice/ accept it, a mapping of the spread of awareness. it did not help that Royen was somewhat isolated and did not seem to personally contact any cohorts for peer review. he published openly but it got lost in the noise. it shows how community acceptance is sometimes far from a black/ white binary decision, esp for “big problems”.

is there any way to improve peer review? its definitely a bit of an achilles heel of the scientific process. my feeling is that there is no way to improve it very much except maybe to try to increase transparency somehow. its very similar to the problem of “fake news”. how do you measure quality in content? we live in the vast Information Age but as has long been noted, theres a big difference between Information and Wisdom, and in a way peer review is the major mechanism that is designed to separate/ discriminate the two.

but Review is a sort of vague concept at heart. its both singular and plural, individual/ collective. one cannot really get an idea of the significance of a paper from a single Review. its a collective process, its interconnected. its an at-times awkward comparison but legitimate: its similar to how viruses spread. top scientific papers have a “virality” aspect. its a trust network. how does trust/ reputation propagate? this is a deep question that relates also to cybercurrencies like bitcoin. it looks like trust networks will continue to be built up, but will continue to be somewhat plagued with distinctly human properties/ challenges/ problems.

elsewhere there is great positive news in math with leaders/ awards,[c] and continued effort on other Big Problems.[d]

a. royen
b. mochizuki
c. leaders/ awards
d. big problems/ (unclaimed) prizes
e. news
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