What links certain mathematical models of traffic flow, shallow-water waves, and quantum particle scattering? The surprising answer lies in a corner of the algebraic combinatorics world that goes by the name of positive Grassmannian. In simple terms, the positive Grassmannian is a shape that classifies other shapes. Remarkably, pieces of the positive Grassmannian can be reassembled in forms that reveal shared structures in these and many other seemingly unrelated mathematical systems.

That we know the positive Grassmannian crops up in many real-world settings is largely down to the theoretical work of Lauren Williams at Harvard University. In this latest episode of The Joy of Why, Williams talks to co-host Steven Strogatz about her work, how she realized the surprising pervasiveness of the positive Grassmannian, and how she has made a career of finding connections among fields that don’t at first sight seem connected. The conversation then switches to another project Williams is working on, called First Proof, which is trying to measure objectively how good AI systems are at coming up with proofs of research-level mathematical statements, and which leads to an exploration of whether AI may or may not take over mathematics.

Note: Since this conversation was recorded, results from the First Proof, Second Batch project were released on June 10 2026.

One of the most surprising and remarkable discoveries in recent scientific history has been CRISPR. Short for Clustered Regularly Interspaced Short Palindromic Repeats, CRISPR is a form of immune system that evolved in bacteria more than a billion years ago to defend against persistent viral threats. Under attack, bacteria can snip a small fragment of a virus’s DNA, store it in the CRISPR region of their genome, and then use it to recognize and destroy the same virus if it returns. The CRISPR-Cas9 system, to give it its longer name, consists of a short strand of guide RNA that identifies where to cut the DNA and a protein that acts as the molecular scissors.

What made this system truly revolutionary was the demonstration in 2012 that it could be reprogrammed with different pieces of guide RNA to edit virtually any genome in any species, and at a level of precision and ease that far surpassed existing gene-editing tools. Since then, the editing capability of CRISPR has been tested on everything from developing disease treatments to engineering drought-resistant crops to resurrecting genes of extinct species. The possibilities have expanded so rapidly that researchers, ethicists, and regulators have found themselves struggling to keep up.

One person acutely aware of the power of CRISPR is Jennifer Doudna, co-developer of the technology. Doudna, who received the Nobel Prize in Chemistry in 2020 with Emmanuelle Charpentier for this pioneering work, has been a prominent voice not only for its vast potential but also for its responsible and ethical use. In this episode of The Joy of Why, Doudna tells co-host Janna Levin how her early, “rebellious,” decision to study RNA led her on a serendipitous path to one of biology’s most transformative discoveries. They also discuss the breakthroughs, barriers, and frontiers that will define CRISPR’s true impact.

What is the future of gene editing with CRISPR? Has AI changed mathematics forever? Will we find other civilizations in the universe? What if we’ve been wrong about dark energy all along? These are just a few of the big, bold questions we’ll be exploring in the new season of The Joy of Why.

Mathematician Steven Strogatz and physicist Janna Levin are back as your hosts for these and other conversations that explore the frontiers of basic science and mathematics. Each episode features an in-depth conversation in which Steven or Janna sits down with a leading scientist or mathematician to unpack one big idea or area of research. The two hosts also chat together throughout each episode, sharing their own thoughts, reactions, and questions.