The Leiden Declaration on Artificial Intelligence and Mathematics calls for action to address the challenges posed by the use of artificial intelligence within mathematics research.
Do we live in a random universe? Does it help to think like a statistician? A confident “yes” on both counts, though of course I’m biased, having spent a career helping other scientists make sure their data is well understood. Here we’ll consider two especially random phenomena, survival and prediction.
What was special about the perceptron was that it didn’t just consist of circuits that were built out of neurons. It used experience to learn how those neurons should be connected to one another.
The property of “all-5s” that I noticed in gelbes feld immediately raises a suite of possibly new questions for magic squares. In particular, can every magic square be “pipified”?
There is an elegant style of mathematical argument by which one proves an existence claim not by exhibiting any particular instance, but rather by proving that a randomly chosen instance from a suitable class exhibits the property with nonzero probability.
This article will present a summary of Abel’s proof, in the style in which he presented it, in which it will be seen both as the culmination of a long story in the history of mathematics and the beginning of a new one.
We give a brief introduction to the history of the Markoff equation, describe number theoretic problems both old and new, and highlight connections that Markoff-like equations have to other branches of mathematics.
In this article we explain the ideas involved in the proof of the monotonicity of the Fisher information for the space-homogeneous Landau equation. In particular, this monotonicity allowed us to prove that a smooth solution exists for all time.
In this article, we describe the details of designing printable manifolds with enough detail so that—along with the provided code—a reader will be able to apply these techniques to design and print their own examples.
