Whatever the benchmarks might say, there's something about Claude that seems to deliver consistently (although not always perfect) quite reliable outputs across various coding tasks. I wonder what that 'secret sauce' might be and whether GPT-5 has figured it out too.
I've always wondered how spatial reasoning appears to be operating quite differently from other cognitive abilities, with significant individual variations. Some people effortlessly parallel park while others struggle with these tasks despite excelling at other forms of pattern recognition. What was particularly intriguing for me is that some people with aphantasia have no difficulty with spatial reasoning tasks, so spatial reasoning may be distinct from reasoning based on internal visualization.
She certainly fell into the rage bait trap, and I don't really like her these days, but this video seems fine - no ranting, just a nice piece of science communication.
"The History of Approximation Theory" by Karl-Georg Steffens is a great reference for historical contexts.
For Chebyshev, who devoted his life to the construction of various 'mechanisms' [1][2], his motivation was to determine the parameters of mechanisms (that minimizes the maximal error of the approximation on the whole interval).
Calling this 'alternative' construction seems like coming full circle since this line of combinatorial argument is how Boltzmann came up with his H-function in the first place, which inspired Shannon's entropy.
What kind of ODE solvers are used to simulate chaotic systems? They must be very accurate if even a small error can result in a completely different result.
Exactly this. The features (or limitations) of medical data is inherent in the process of clinical practice, but this seems to be oftentimes overlooked.
Experiments justify 'predictions' of certain mathematical models, not 'interpretations'. As for a belief in interpretations, it's more of a philsophy, and Feynman said just 'shut up and calculate'.