SpaceX, Anthropic and OpenAI are all racing to the public markets. We discuss what their I.P.O.s mean for the industry, charitable giving and anyone invested in an index fund. Then, more than 1,000 mathematicians signed a declaration this week raising concerns about the use of A.I. in their field. Author Kevin Hartnett joins to explain what the fuss is all about. And finally, we run through the biggest headlines of the week — including the new executive order on A.I. — in a round of HatGPT.   Guest: * Kevin Hartnett [https://kevinstenhartnett.com/], author of The Proof In the Code: How a Truth Machine is Transforming Math and AI [https://www.quantabooks.org/books/the-proof-in-the-code/] Additional Reading: * Anthropic Files to Go Public, Setting Stage for Huge I.P.O. [https://www.nytimes.com/2026/06/01/technology/anthropic-ipo.html] * As A.I. Makes Strides in Mathematics, Mathematicians Urge Caution [https://www.nytimes.com/2026/06/02/science/ai-mathematics-leiden-declaration.html?smid=nytcore-ios-share] * An SF Startup Is Secretly Testing Robots in Airbnbs, and Trashing Them, Lawsuit Claims [https://sfstandard.com/2026/05/28/sf-startup-secretly-testing-robots-airbnbs-trashing-lawsuit-claims/] * Trump Signs Executive Order Seeking Oversight of A.I. Models  [https://www.nytimes.com/2026/06/02/technology/trump-executive-order-ai.html] * U.S. Is Said to Be Investigating George Santos Over Kalshi Betting [https://www.nytimes.com/2026/06/02/us/politics/george-santos-investigation-prediction-markets.html] * Hackers Simply Asked Meta AI to Give Them Access to High-Profile Instagram Accounts. It Worked [https://www.404media.co/hackers-simply-asked-meta-ai-to-give-them-access-to-high-profile-instagram-accounts-it-worked/] * United Flight Forced to Turn Around Because of a Bluetooth Speaker Name [https://www.theverge.com/transportation/940486/united-flight-236-bluetooth-speaker-name-bomb] * ‘Survivor’ Boss Jeff Probst Says Kalshi and Polymarket Are ‘Incentivizing People to Lie, Cheat and Steal’; Kalshi Is Now Considering Measures to Prevent Spoilers [https://variety.com/2026/tv/news/survivor-jeff-probst-kalshi-polymarket-spoilers-1236757354/]   We want to hear from you. Email us at hardfork@nytimes.com. Find “Hard Fork” on YouTube [https://www.youtube.com/hardfork] and TikTok [https://www.tiktok.com/@hardfork]. Subscribe today at nytimes.com/podcasts [http://nytimes.com/podcasts] or on Apple Podcasts and Spotify. You can also subscribe via your favorite podcast app here https://www.nytimes.com/activate-access/audio?source=podcatcher [https://www.nytimes.com/activate-access/audio?source=podcatcher]. For more podcasts and narrated articles, download The New York Times app at nytimes.com/app. Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com [https://pcm.adswizz.com] for information about our collection and use of personal data for advertising.