The paper provides a practical overview of the application of artificial intelligence in mathematics, with an emphasis on how LLM models can assist in proving complex claims and theorems.
ABSTRACT
The authors demonstrate how LLM chatbots (ChatGPT, Gemini, Claude, DeepSeek) helped them prove a mathematical claim regarding the shortest path between two points located on the opposite bases of a regular n-gon. More specifically, the claim is as follows: “Every odd regular prism has at least one p-independent shorter path, i.e., a shorter path whose length does not depend on the distance of points A and B (‘the ant’ and ‘the honey’) from the edge, whereas even prisms do not have one. The length of the shortest path is: d = b √(k² + 2 cos(π/n) k + 1)”.
The initial version of this mathematical problem (and the related computer game) was presented at the CASE 2020 conference under the title “Ant and Honey on a Prism (and Cylinder) – Mathematical Background and Game Concept”.
In the new paper, the focus is on the extent to which a “pure” LLM chatbot can be useful in proving mathematical theorems without the use of specialized theorem provers.