A remarkable paper appeared on arXiv tonight by Thomas Bloom, Will Sawin, Carl Schildkraut and Dmitrii Zhelezov. In this paper, they prove that there exists c>0 and arbitrarily large finite sets A of real numbers such that max(|A+A|,|AA|)≤|A|^{2-c}. This disproves the well-known sum-product conjecture over the real numbers. The sum-product conjecture considers the two most basic operations: addition and multiplication. A+A is the set of all pairwise sums of two elements in A while AA is the set of all pairwise products of two elements in A. (1/5) Taking A to be an arithmetic progression, one can have |A+A| approximately the size of A, while taking a geometric progression makes |AA| roughly the size of A. The sum-product conjecture is essentially the statement that both of these cannot occur simultaneously in a very strong sense. Building on a long line of work, before this result, the best known lower bound for max(|A+A|,|AA|) was |A| raised to the power (4/3)+c where c is a small constant. These results demonstrate a weak version of the phenomenon that both |A+A| and |AA| cannot simultaneously be small, but it remained an enduring mystery until now whether the stronger |A|^{2-o(1)} statement held. (2/5)