In October 2024 I attended a workshop at Harvard University where mathematicians talked through the uses of artificial intelligence in their field. Most were less worried about the future of math than ...

Abstract: This paper shows the analysis and design of feedforward neural networks using the coordinate-free system of Clifford or geometric algebra. It is shown that real-, complex-, and ...

The AoPA library allows one to encode Algebra of Programming (BdM97) style program derivation, both functional and relational, in Agda. Since the 90s, the program derivation community has been ...

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See more of our trusted coverage when you search. Prefer Newsweek on Google to see more of our trusted coverage when you search. A mathematician has uncovered a way of answering some of algebra's ...

To a nonmathematician, having the letter “i” represent a number that does not quite exist and is “imaginary” can be hard to wrap your head around. If you open your mind to this way of thinking, ...

You can probably think of a time when you’ve used math to solve an everyday problem, such as calculating a tip at a restaurant or determining the square footage of a room. But what role does math play ...

This paper concerns the more foundational tasks of distributed dense linear algebra. While a single TPU core can already store and operate on large matrices (e.g., of size 16,384, 32,768 in single ...

Hurwitz’s theorem says that there are only 4 normed division algebras over the real numbers, up to isomorphism: the real numbers, the complex numbers, the quaternions, and the octonions. The proof was ...