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Updated: Jun 11, 2025

A Practical Guide to Phylogenetics for Nonexperts

A Practical Guide to Phylogenetics for Nonexperts

Published on: February 5, 2014

CHATGPT FOR COMPUTATIONAL TOPOLOGY.

Jian Liu¹, Li Shen², Guo-Wei Wei^2,3,4

¹Mathematical Science Research Center, Chongqing University of Technology, Chongqing 400054, China.

Foundations of Data Science (Springfield, Mo.)

|October 10, 2024

Summary

This summary is machine-generated.

This study demonstrates how artificial intelligence (AI) tools like ChatGPT can help mathematicians translate complex topological data analysis (TDA) theories into functional computational codes. This bridges the gap between theoretical concepts and practical applications in computational topology.

Keywords:

ChatGPT Dirac Laplacians computational topology homology persistence

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Last Updated: Jun 11, 2025

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Area of Science:

Computational Topology
Artificial Intelligence
Topological Data Analysis

Background:

Artificial intelligence (AI) shows promise but struggles with mathematical concepts.
Topological Data Analysis (TDA) is advancing but limited by computational skill gaps among theorists.

Purpose of the Study:

To bridge the gap between theoretical topology and computational implementation using ChatGPT.
To enable mathematicians without coding experience to generate computational topology codes.

Main Methods:

Mathematicians train ChatGPT on pure mathematical concepts.
ChatGPT is guided to generate computational topology codes.
Generated codes are validated using established examples and novel theories.

Main Results:

Demonstrated ChatGPT's ability to translate mathematical formulations into functional code for computational topology.
Successfully computed Betti numbers, Laplacian and Dirac matrices, and homology/Laplacian persistence.
Applied ChatGPT to novel theories for hypergraphs, digraphs, and persistent harmonic space.

Conclusions:

ChatGPT can effectively transform pure mathematical theories into practical computational tools.
This approach facilitates the application of advanced topology in diverse fields.
Initial step towards AI-assisted development in computational mathematics.