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What Does One Billion Dollars Look Like?

According to Forbes, as of early March, 2023 there were 2,640 billionaires worldwide, 735 in the U.S. alone. These billionaires have each amassed at least one billion dollars worth of assets, including stocks, real estate, and cash — many of them much more than that. But just how big is one billion? A number that large is hard to conceive of. Well, it's 1,000,000,000; ten to the ninth power; one-thousand millions. That might help some…but not much. How big is a million? Hard to say when we're j

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

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'

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