From StarTalk.
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Do we need new math to explain dark matter? Neil deGrasse Tyson and comedian Paul Mecurio explore unsolved problems in math, simulation theory, base systems and more with mathematician Terence Tao.
We take a look at the boundary between pure and applied mathematics. You’ll learn intentional simplifications of a messy world that allow researchers to isolate complex truths. Terence explains how curiosity-driven research into patterns often leads to accidental breakthroughs, such as how abstract group theory eventually paved the way for faster, more efficient MRI scans.
We then tackle some famous unsolved problems in the field, including the Collatz Conjecture (the "hailstone sequence"). What does it mean to prove something in math? We explore chaos, where iterating simple operations creates vast complexity.
We work though fan-submitted Cosmic Queries talking about the history of base systems from Babylonian base-60 to computer binary. We discuss the emotional hurdles of math education. Do we need a new math to explain dark matter and dark energy? Finally, we look at the Simulation Theory through the lens of Bayesian probabilities. Could a cutoff in the cosmic microwave background be the glitch in the matrix that proves we’re living in a program? From the idiosyncratic life of Paul Erdős to the "malice" of an unsolved proof, we’re revisiting the universe of math.
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Timestamps:
00:00 – Introduction: Terence Tao
7:38 – Pure vs. Applied Math
10:58 – Toy Models & Intentional Simplified Reality
14:13 – Unsolved Problems in Math
18:26 – Collatz Conjecture & Hailstones
23:57 – Are We Getting Closer to Solving Unsolved Problems?
26:29 – Erdos problem 1026
32:36 – Useful Pure Math Discoveries
37:11 – If We Didn’t Use Base Ten
40:13 – How Would You Change Teaching Math?
40:37 – How to Work on a Proof
46:18 – Will We Need New Math to Explore Space?
49:30 – Can Math Prove We Are Not in a Simulation?
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Science meets pop culture on StarTalk! Astrophysicist & Hayden Planetarium director Neil deGrasse Tyson, his comic co-hosts, guest celebrities & scientists discuss astronomy, physics, and everything else about life in the universe. Keep Looking Up!
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