Caltech Mathathon

How can we use AI to augment human understanding of mathematics?

[Caltech Mathathon @math_hackathon]

3 days until the Mathathon! Teams are getting ready to spend 40 hours uncovering new secrets in old theories.

Here’s a sneak peak at the NP-Completeness of the HP Protein Folding Model:

Berger and Leighton (RECOMB 1998) and Papadimitriou et al. proved that the protein folding problem, using the hydrophobic-hydrophilic (HP) model, is NP-complete on the 2D and 3D lattice. Teams will revisit the constructions in this proof to look for simplifications and develop more accessible explanations of the methodology.

Want to learn more? Check out Berger and Leighton’s paper (https://t.co/nGMt5RJgAN)

[Caltech Mathathon @math_hackathon]

12 days until the Mathathon! Teams are getting ready to spend 40 hours uncovering new secrets in old theories.

Here’s a sneak peak at Unrepresentable Finite Lattices:

Recently, OpenAI provided a negative solution to the finite lattice representation problem, which asks whether every finite lattice is isomorphic to the congruence lattice of some finite algebra. They provided a finite lattice which does not exhibit this isomorphism; however, the minimum size of such a lattice is unknown. Teams will work to clarify these new results and improve the known bounds on the minimum size for unrepresentable finite lattices.

Want to learn more? Check out OpenAI’s preprint (https://t.co/tk2xl4a5oR). Application for judges is open at https://t.co/TWX0ss1yFO!

[Caltech Mathathon @math_hackathon]

13 days until the Mathathon! Teams are getting ready to spend 40 hours uncovering new secrets in old theories.

Here’s a sneak peak at the Definability of the Turing Jump:

In a 1999 paper, Slaman and Shore proved that the Turing jump, an operation that maps between decision problems of increasing difficulty, is definable in the first order theory of the Turing degrees. However, their work does not provide a simple definition of this jump. Teams will search for conditions in which an explicit definition is (or is not) attainable.

Want to learn more? Check out Slaman and Shore’s paper (https://t.co/nNLJNTTVw8). Application for judges is open at https://t.co/TWX0ss1yFO!

[Caltech Mathathon @math_hackathon]

15 days until the Mathathon! Teams are getting ready to spend 40 hours uncovering new secrets in old theories.

Here’s a sneak peak at the Robertson-Seymour Graph Minor Theorem:

This foundational result in modern graph theory proves that any family of graphs which is closed under taking minors can be characterized by a finite set of forbidden minors. Aspiring teams will work to simplify and shorten the elaborate proof of this result to make the theory more accessible and illuminate useful new arguments.

Want to learn more? Check out any of Robsertson and Seymour’s papers in the “Graph Minors’’ series (https://t.co/0I978qmxoO). Applications for judges are still open at https://t.co/TWX0ss1yFO!

[Caltech Mathathon @math_hackathon]

16 days until the Mathathon! Teams are getting ready to spend 40 hours uncovering new secrets in old theories.

Here’s a sneak peak at Iskovskikh’s classification of 3-folds:

Iskovskikh provides a classification of special Fano varieties, building off of a series of papers written by Gino Fano in the first half of the 20th century. Iskovskikh’s work has had significant impacts in the field of algebraic geometry, such as contributing to the success of Japanese mathematician Shigefumi Mori’s minimal model program. Teams will study Iskovskikh’s original classification and its broader implications, using current techniques in algebraic geometry to modernize, generalize, simplify, and contextualize this work.

Want to learn more? Check out Iskovskikh’s original paper (https://t.co/TgPCX91uT0) and find more problems at https://t.co/TWX0ss1yFO!

[Caltech Mathathon @math_hackathon]

What math will you discover?

[Sathvik Redrouthu @_sathvikr]

We redesigned the Mathathon Challenge.

Introducing Mathathon 2.0.

Old problems, new proofs.

[Tony Tanuki @tonyyueyu]

One main component will be the communication of new ideas and results 🚀

[Sathvik Redrouthu @_sathvikr]

We partnered with @AnthropicAI @OpenAI
to host the world's first math hackathon.

40 hours, $2M compute - solve, understand, and present an open problem.

Applications are live: https://t.co/3oSEmPPohL