Natalie Wolchover

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)

New blog post: The third wave of American philanthropy Hundreds of billions of dollars in new philanthropic capital will soon become liquid. The OpenAI Foundation holds 26% of OpenAI, worth about $220B at today’s valuation. Anthropic’s seven co-founders have pledged to give away 80% of their wealth and have instituted the most aggressive donor matching program for employees in tech history. How much does this all add up to? And how meaningful is that in the context of philanthropy today? I was doing some simple napkin math to wrap my head around the scale of what’s coming, and radicalized myself in the process. I had dramatically underappreciated the scale of the philanthropic capital that’s about to become available and the corresponding gap in talent and organizations that will be needed to make the most of it. This piece aims to directionally sketch the scale of what’s coming, the gap in operational capacity needed to absorb it, and what we can do to fill it. (Link to full post in reply)

there's some really interesting commentary from one of the mathematicians in the companion paper not to pour cold water on the results necessarily - but it suggests this is a specific "kind" of proof these models might be particularly good at