The knot and representation theories were used to find connections and patterns using DeepMind’s artificial intelligence. This artificial intelligence can produce data, look for patterns and connections, and train itself, according to a description in the journal Nature. While mathematicians still need to make theorem proofs, conjectures, and hypotheses. Mathematicians from the University of Oxford found a stunning discovery of connections between algebraic and geometric invariants of knots. And Mathematicians from the University of Sydney used the results to take another crack at a conjecture unproven for 40 years, getting close to proving it. Artificial intelligence is the future of math.

The process of creating a theorem is broken down in the article Nature, stating the process is to hypothesize, generate data, train a supervised model, and find patterns to create a conjecture candidate and repeat until you can prove the theorem. The current AI can only complete 3: generate data, train the supervised model (to train itself), and find patterns. The rest still has to be done by mathematicians, but as AI rapidly develops, that won’t be out of our reach.

The knot theory in mathematics is the study of 3-dimensional closed curves experimenting with their possible deformations without two parts cutting each other. In simpler terms, it is taking a piece of string and making a form, then connecting the two ends of it. The representation theory can’t be explained. In simple terms, it displays abstract mathematical structures in linear formations of vector spaces.

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Representation theory: https://en.wikipedia.org/wiki/Representation_theory

Knot theory: https://www.britannica.com/science/knot-theory

Science Daily: https://www.sciencedaily.com/releases/2021/12/211201111925.htm

Nature journal: https://www.nature.com/articles/s41586-021-04086-x