Terence Tao on why we need math — and maybe a spherical cow — to understand the universe

UCLA mathematician Terence Tao, often called "the Mozart of math," picked up another label during a recent appearance on StarTalk: "badass mathematician."

The description, offered by astrophysicist Neil deGrasse Tyson, set the tone for a wide-ranging, hour-long conversation that blended deep theory with humor and pop culture. Joined by comedian Paul Mecurio, Tao explored everything from unsolved mathematical problems to simulation theory and the logic behind different numerical systems.

"In most professions, you don't get to play with toy models," Tao said. "You're not allowed to fail. But in math, failure is very cheap. You try a problem, you don't solve it - fine. You just toss the paper away and try again. No one gets hurt. No one dies."

That mindset surfaced in one of the episode's recurring metaphors: the "spherical cow," a deliberately unrealistic model used by mathematicians and physicists to make complex systems easier to study.

"Spherical cow-type assumptions … make it easier if the cow is a complete sphere and frictionless," Tao explained. "That's not realistic, but it's a good starting point."

Throughout the conversation, Tao and Tyson examined the interplay between pure and applied mathematics, from abstract, curiosity-driven questions to real-world modeling used in fields like climate science and engineering.

The result is an accessible entry point to how mathematicians can help general audiences understand how math helps people comprehend the universe around them.

Watch above or on YouTube.