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Today’s Menu

• AI's Real Opportunity Is Replacing Your Most Expensive Bills

• Vanguard Finally Caves on Crypto After Missing $125B Wave

Markets

TODAY IN AI

AI's Real Opportunity Is Replacing Your Most Expensive Bills

Aristotle, an AI system built by Harmonic, just independently solved a 30-year-old Erdős problem, marking what researchers are calling the first real step into the "vibe proving" era of mathematics.

Aristotle solved a version of Erdős Problem #124, which has been open since the 1990s, in six hours, then formally verified the proof in Lean in a minute. The result came from Aristotle's beta version, updated with stronger reasoning and a natural language interface to explore and write step-by-step proofs.

Vlad Tenev, the founder of Harmonic, called this the arrival of "vibe proving" - AI-driven proof discovery followed by machine-verifiable rigor. The development follows Harmonic's $120M funding and Aristotle's IMO gold performance, putting it alongside Google and OpenAI in mathematical reasoning.

Harmonic's breakthrough is another push toward mathematical superintelligence, where proofs will be generated, verified, and scaled at superhuman speeds. Tools like these can open participation in advanced mathematics, turning it from something only experts do into something anyone can contribute to.

When AI solves problems that stumped mathematicians for decades in six hours, that's not incremental progress - that's a paradigm shift in human knowledge discovery.

TODAY IN CRYPTO

Vanguard Finally Caves on Crypto After Missing $125B Wave

Remember when Bitcoin ETFs launched last year and Vanguard had no interest? After years sitting on the sidelines, the world's second largest asset manager is opening crypto to its 50 million clients.

Starting this week, Vanguard will let customers trade ETFs and mutual funds that primarily hold cryptocurrencies on its brokerage platform. That includes funds tied to Bitcoin, Ethereum, XRP, and Solana, treated the same way as gold and other "non-core" assets.

For a firm that spent years saying "no crypto," this is a major pivot. Andrew Kadjeski, head of brokerage and investments, stated: "Cryptocurrency ETFs and mutual funds have been tested through market volatility, performing as designed while maintaining liquidity... The administrative processes have matured, and investor preferences continue to evolve."

This shift comes after Vanguard completely missed the first wave: spot Bitcoin ETFs grew from roughly $25B to around $125B in under two years, Ether ETFs expanded toward $20B, and new products rolled out for XRP, Solana, Dogecoin, and Litecoin.

Key points: Vanguard will support most crypto ETFs meeting regulatory standards, products tied to obvious memecoins or non-SEC-supported assets remain barred, and the firm has no plans to launch its own crypto ETFs.

This isn't about Vanguard becoming a "crypto company" - it's about giving its $11 trillion client base access to regulated wrappers. While prices slump mid-cycle and sentiment remains fragile, the largest traditional finance players keep doing the same thing: building more ways for clients to own crypto.

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Thanks for reading!

Until next time,

Damon James