Claude did not solve the Riemann Hypothesis. But what it actually
did may be one of the clearest examples yet of how rapidly AI
systems are changing the way difficult mathematics can be attacked.
In Episode 53, Lester Nare and Krishna Choudhary go from first
principles on arguably the most famous unsolved problem in
mathematics. We begin with Euler and the Basel problem, build the
Riemann zeta function from the ground up, explain its deep
connection to prime numbers, move into the complex plane and
analytic continuation, unpack the famous 1 + 2 + 3 + 4 + … = -1/12
result, and finally arrive at the Riemann Hypothesis itself: the
claim that every non-trivial zero of the zeta function lies on the
critical line. Then we get into Claude. An unreleased Anthropic
model was prompted to take a serious run at the problem. It
orchestrated roughly 60 autonomous sub-agents, tested hundreds of
mathematical approaches, executed code, searched academic
literature, challenged its own strategies, created adversarial
referees to attack its work, and ultimately produced a result
pushing a related mathematical bound well beyond the previous state
of the art. The human behind the prompt was not a mathematician.
One of his instructions was essentially: believe in yourself. We
explain what Claude actually accomplished, what it absolutely did
not accomplish, why moving a bound toward two-thirds does not mean
the Riemann Hypothesis is “two-thirds solved,” and what the process
tells us about agentic AI, mathematical research, scientific
discovery, and AI safety. Then it’s transfer season. For the first
FFP Summer Transfer Window for Scientists, we look at prominent
researchers leaving American institutions for universities and
research centers abroad. Using the language of football transfers,
we examine major moves in chemistry, battery research,
gravitational-wave astrophysics, and neuroscience—and what they
reveal about research funding, immigration, scientific
infrastructure, and the global competition for talent. Explore the
FFP science funding tracker:ffppod.com/funding Help shape Year Two
and enter the anniversary merch giveaway:ffppod.com/survey Support
the show:ffppod.com/donate Follow:@FFPPod on X / Instagram / TikTok
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