I interviewed someone recently who worked at Meta a couple years ago. He was a software engineer, was paid a bunch of money to mostly up dashboards all day, and eventually quit because it was neither interesting nor challenging.
It is not determined by the derivative, it's the antiderivative, as someone else mentioned. The derivative is the rate of change of a function. The "area under a curve" of the graph of a function measures how much the function is "accumulating", which is intuitively a sum of rates of change (taken to an infinitesimal limit).
This is some high quality content. Love the visual animations to go along with the mathematical ideas. Did a great job helping to tie the algebra to geometric intuition, but I think the importance of commutators could have gotten a little bit more exposition.
The disk model of hyberolic geometry is made to map hyperbolic 2 space (which is infinite in area) into the finite interior of the disk. In order to capture this, the normal euclidean notion of distance is distorted by a function which allows "distances" to go to infinity as a curve approaches the boundary of the disk.
Binary search minimizes the number of expected moves until you find the target. If you are already ahead, this is a natural thing to want to do. The reason why this doesn't work when you're behind is that your opponent can also do that and probabilistically maintain their lead.
In my mind that is a problem with your lazy developer colleague, not AI as a whole. You can't expect it to be right on the first try (just like human code), you have to iterate with it and have the experience to know when it's off track and you have to take over.
I don't know about other use cases, but AI is definitively a game changer for software development. You still need to know what you're doing and test/think critically about what it's giving you, but the body of software problems that you can conceptually treat as "boilerplate" becomes massively larger with the help of a good AI coding tool.
Do you have any recommended references on this subject? Seems like this sort of system would be able to obfuscate a lot of metadata that can be used to deanonymize activity. Very interesting.
The guy might be smart and write popular textbooks, but he has not successfully managed real money over an extended period of time as far as I can tell. He "left" Guggenheim after his algos were basically found to be crossing trades with the firm, and he "left" AQR after it was determined that he essentially brought nothing new to the table.
...this...has to be a troll right? The guy helped bring space flight out of a stagnant era into commercial viability and put electric cars into the world's popular psyche.