What if math isn't about grinding through equations, but about training your intuition and changing how your brain works? Mathematician and author David Bessis tells EconTalk's Russ Roberts that the secret of mathematics isn't logic--it's the way we learn to see. He explains why math books aren't meant to be read like novels, how great mathematicians toggle between images and formal proofs, and why we need a third mode of thought--"System 3"--that patiently retrains our intuition and the power of imagination. Bessis and Russ Roberts swap stories about the humility of great mathematicians, how Andrew Wiles "saw" the fix to his proof of Fermat's last theorem, and Ramanujan's dream-revelations that proved true.

Quantitative, contrarian, and nuanced: these are the hallmarks of the Freakonomics approach. Hear journalist and podcaster Stephen Dubner speak with EconTalk's Russ Roberts about the 20th anniversary of the popular-economics book Dubner co-authored with Steven Levitt. They discuss how the book came to be, how the journey changed Dubner's life, and how it changed his thinking about various economics issues. The conversation includes a lengthy discussion on the role of private equity in the American economy, and Roberts's claim that Dubner and co-author Steven Levitt's treatment of incentives overlooks the role of competition and markets.

What drives the seeming relentless dynamism of Tokyo? Is there something special about Japanese culture? Joe McReynolds, co-author of Emergent Tokyo, argues that the secret to Tokyo's energy and attractiveness as a place to live and visit comes from policies that allow Tokyo to emerge from the bottom up. Post-war black markets evolved into today's yokocho--dense clusters of micro-venues that turn over, specialize, and innovate nightly--while vertical zakkyo buildings stack dozens of tiny bars, eateries, and shops floor by floor, pulling street life upward. The engine? Friction-light rules: permissive mixed-use zoning, minimal licensing, and no minimum unit sizes let entrepreneurs launch fast and pivot faster. And surrounding this emergent urban landscape there's plenty of new housing with excellent transportation infrastructure to let ever-more people enjoy Tokyo's magic.