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Nvidia beats Apple to a $4T valuation as it rides AI wave

Nvidia, the US company specializing in high-performance GPU cards, has become the first ever company with a market capitalization of four trillion dollars. It is now the most valuable company in the world, ahead of Apple and Microsoft. It’s a little over a year since the company overtook AAPL thanks to a spectacular rise in value that saw it go from being worth $2T to more than $3T in just four months … Nvidia is best known for its high-end GPU chips used in gaming computers, and until the las

The US dollar is on track for its worst year in modern history

The US dollar is on track for its worst year in modern history and may not be done falling yet. The greenback is down more than 7% this year and Morgan Stanley predicts it could fall another 10%. A weaker dollar could make US exports more competitive, boosting Trump’s plan to rebalance US trade, but makes imports more expensive, adding to the sting of tariffs. The question ahead is whether the dollar doesn’t just lose its value, but its role at the center of the global financial system. So far,

A Leading Indicator Has Emerged Suggesting That the AI Industry Is Cooked

In the world of cultural commentary, there are plenty of benchmarks used to determine when a trend is on its deathbed. From the classic shark-jumping episode of "Happy Days" to the adoption of Facebook by grandparents the world around, those with their ears to the ground can spot when a craze is on its way out. In that vein, the news that Meta founder and CEO Mark Zuckerberg is spending hundreds of millions of dollars to build supercharged AI sure strikes us as bad news for that industry. Let'

The $50 Billion Company That Does Almost Nothing

Something strange is happening on Wall Street. It isn’t Elon Musk, AI, or a late-night post from Donald Trump. It’s a crypto company called Circle Internet Group, and it’s making the market feel like the glory days of the dot-com bubble are back. Circle went public on June 5. In just eleven trading sessions, its stock exploded by an almost unprecedented 675%, adding over $42 billion to its market cap. The company now trades at a valuation that puts it in the same league as tech unicorns and AI

Bitcoin Who? Wall Street Has a New Crypto Obsession

For over a decade, Bitcoin has been the undisputed face of digital finance. When you think “crypto,” you think Bitcoin. Its surges and crashes have been treated as bellwethers for the entire industry. This year, it even set new records, solidifying its reign. But for the past month, the crypto world hasn’t been talking about Bitcoin. The spotlight has been stolen by a company that most people have never heard of. While Bitcoin’s price reached an all-time high this spring, its dominance is bein

Verified dynamic programming with Σ-types in Lean

1. Introduction If you’ve taken an algorithms class, you have likely seen dynamic programming, specifically a technique called memoization. Memoization works to optimize recursive algorithms by caching the solutions to subproblems in a table, and when a subproblem is encountered, it queries the table instead of recomputing the solution. This gives us an exponential performance boost. This blog post will show how to solve a dynamic programming problem using memoization in Lean, and verify its c

Verified Dynamic Programming with Σ-types in Lean

1. Introduction If you’ve taken an algorithms class, you have likely seen dynamic programming, specifically a technique called memoization. Memoization works to optimize recursive algorithms by caching the solutions to subproblems in a table, and when a subproblem is encountered, it queries the table instead of recomputing the solution. This gives us an exponential performance boost. This blog post will show how to solve a dynamic programming problem using memoization in Lean, and verify its c