Discrete mathematics is about precision in reasoning as much as it is about solving problems. Proof techniques like induction, contradiction, and direct reasoning are used to establish results in ...

Introduces students to ideas and techniques from discrete mathematics that are widely used in science and engineering. Mathematical definitions and proofs are emphasized. Topics include formal logic ...

VUB's Data Analytics Lab has published new results showing that it is possible to develop original mathematical proofs using commercial language models. In a paper posted to the arXiv preprint server, ...

Computers are extremely good with numbers, but they haven’t gotten many human mathematicians fired. Until recently, they could barely hold their own in high school-level math competitions. But now ...

Some scientific discoveries matter because they reveal something new — the double helical structure of DNA, for example, or the existence of black holes. However, some revelations are profound because ...

Marijn Heule turns mathematical statements into something like Sudoku puzzles, then has computers go to work on them. His proofs have been called “disgusting,” but they go beyond what any human can do ...

Kendra Pierre-Louis: For Scientific American’s Science Quickly, I’m Kendra Pierre-Louis, in for Rachel Feltman. In 1997, Deep Blue, a supercomputer built by IBM, did the unexpected: it defeated chess ...

GPT-5.4 Pro cracked a conjecture in number theory that had stumped generations of mathematicians, using a proof strategy that no human had ever considered.

A series of recent research papers have shown that ChatGPT and related large language models can produce original, verifiable mathematical proofs, including solutions to problems that had not been ...