The search in the US for the man who shot dead a Democratic politician in a targeted killing. Also: Israel and Iran threaten to step up their attacks, and getting away from the electro-magnetic radiation of modern life.
Lex Fridman Podcast - #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
Terence Tao is widely considered to be one of the greatest mathematicians in history. He won the Fields Medal and the Breakthrough Prize in Mathematics, and has contributed to a wide range of fields from fluid dynamics with Navier-Stokes equations to mathematical physics & quantum mechanics, prime numbers & analytics number theory, harmonic analysis, compressed sensing, random matrix theory, combinatorics, and progress on many of the hardest problems in the history of mathematics.
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Transcript:
https://lexfridman.com/terence-tao-transcript
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EPISODE LINKS:
Terence’s Blog: https://terrytao.wordpress.com/
Terence’s YouTube: https://www.youtube.com/@TerenceTao27
Terence’s Books: https://amzn.to/43H9Aiq
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OUTLINE:
(00:00) – Introduction
(00:36) – Sponsors, Comments, and Reflections
(09:49) – First hard problem
(15:16) – Navier–Stokes singularity
(35:25) – Game of life
(42:00) – Infinity
(47:07) – Math vs Physics
(53:26) – Nature of reality
(1:16:08) – Theory of everything
(1:22:09) – General relativity
(1:25:37) – Solving difficult problems
(1:29:00) – AI-assisted theorem proving
(1:41:50) – Lean programming language
(1:51:50) – DeepMind’s AlphaProof
(1:56:45) – Human mathematicians vs AI
(2:06:37) – AI winning the Fields Medal
(2:13:47) – Grigori Perelman
(2:26:29) – Twin Prime Conjecture
(2:43:04) – Collatz conjecture
(2:49:50) – P = NP
(2:52:43) – Fields Medal
(3:00:18) – Andrew Wiles and Fermat’s Last Theorem
(3:04:15) – Productivity
(3:06:54) – Advice for young people
(3:15:17) – The greatest mathematician of all time
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PBS News Hour - World - Former U.S. ambassador to Israel analyzes rising Israel-Iran conflict
Israel and Iran traded more missile strikes on Saturday. Iran’s state television reported that an Israeli airstrike on a housing complex in Tehran killed about 60 people, including 20 children. In Israel, Iranian missiles and drones have killed three and wounded dozens. Daniel Shapiro, former U.S. ambassador to Israel, joins John Yang to discuss the two countries’ most intense fighting in decades. PBS News is supported by - https://www.pbs.org/newshour/about/funders
PBS News Hour - World - News Wrap: Crews work to reunite remains of Air India crash victims with families
In our news wrap Saturday, recovery teams are working to identify remains of victims of the Air India crash that killed 270 so that they can be reunited with their families, Israeli airstrikes and gunfire are blamed for the deaths of more than two dozen people in Gaza, and parts of Alaska will be under a heat advisory for the first time ever. PBS News is supported by - https://www.pbs.org/newshour/about/funders
Newshour - Israel and Iran threaten escalation of military conflict
Israel and Iran threaten to step up their military confrontation, nearly 48 hours after the Israeli strikes began. Newshour analyses Israel's strategy and assesses how close Iran was to making a nuclear weapon.
Also in the programme: two US politicians are shot in Minnesota; and Bangladesh's interim Prime Minister Muhammad Yunus on the ending of aid to his country.
(Picture: Missiles launched from Iran are intercepted, as seen from the city of Ashkelon, Israel, June 13, 2025. Credit: Reuters)
Consider This from NPR - The spending cuts one state could face if Trump’s massive bill becomes law
Kentucky is one of the poorest states and is likely to see billions of dollars cut from Medicaid and other government benefits if Trump's spending bill becomes law.
For our weekly Reporter's Notebook series we hear from Kentucky Public Radio's Sylvia Goodman and Joe Sonka. The two reporters traveled through rural eastern Kentucky to gauge how cuts could impact people who rely on federal assistance and what that means for the health clinics that serve them.
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For our weekly Reporter's Notebook series we hear from Kentucky Public Radio's Sylvia Goodman and Joe Sonka. The two reporters traveled through rural eastern Kentucky to gauge how cuts could impact people who rely on federal assistance and what that means for the health clinics that serve them.
For sponsor-free episodes of Consider This, sign up for Consider This+ via Apple Podcasts or at plus.npr.org.
Email us at considerthis@npr.org.
Learn more about sponsor message choices: podcastchoices.com/adchoices
NPR Privacy Policy
Motley Fool Money - Airbnb Goes Beyond Stays
Travel can slow down temporary but the demand to get away from your home is everlasting.
Airbnb CFO, Ellie Mertz, joined Motley Fool CEO and Co-founder, Tom Gardner, and Chief Investment Officer, Andy Cross, for a conversation about:
- Why Airbnb is focusing on experiences and services.
- The stock’s long-term performance.
- How ideas develop at Airbnb.
Company discussed: ABNB
Hosts: Tom Gardner, Andy Cross
Guest: Ellie Mertz
Producer: Ricky Mulvey
Engineer: Dan Boyd
Advertisements are sponsored content and provided for informational purposes only. The Motley Fool and its affiliates (collectively, "TMF") do not endorse, recommend, or verify the accuracy or completeness of the statements made within advertisements. TMF is not involved in the offer, sale, or solicitation of any securities advertised herein and makes no representations regarding the suitability, or risks associated with any investment opportunity presented. Investors should conduct their own due diligence and consult with legal, tax, and financial advisors before making any investment decisions. TMF assumes no responsibility for any losses or damages arising from this advertisement.
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The Gist - The Gist List Live with Kat Rosenfield
Replay of the interview Mike Pesca did with Kat Rosenfield on The Gist List. Click the link below to subscribe for free to The Gist List.
Produced by Corey Wara
Production Coordinator Ashley Khan
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Audio Poem of the Day - Old Pro
By Emanuel Xavier
Bad Faith - Episode 480 – Towards a New U.N. (w/ Craig Mokhiber)
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Craig Mokhiber, international human rights law specialist who stepped down from his post as director of the New York office of the U.N. High Commissioner for Human Rights after October 7th, returns to Bad Faith to discuss the Rafah massacre in which dozens of Palestinians were killed by the IDF while waiting for aid, the Gaza Tribunal's Sarajevo Conference in which legal scholars, human rights experts, journalists, and survivors pushed a civil society-led initiative for accountability for Israel; and the potential for U.N. reform now that the U.S. is withdrawing funding, and perhaps influence, from the United Nations.
Subscribe to Bad Faith on YouTube for video of this episode. Find Bad Faith on Twitter (@badfaithpod) and Instagram (@badfaithpod).