Story perspectives

ChatGPT Cracks 80-Year Erdos Problem, Humans Refine Solution

6/25/2026

Summary

Story summary

OpenAI’s ChatGPT solved the 80-year-old Erdos distance problem with a single prompt.
Mathematicians say limited expert time and high opportunity costs prevented the solution before AI could use massive token budgets.
A Princeton researcher later refined ChatGPT’s construction to achieve a better arrangement, confirming human contribution.
Experts warn that the Riemann Hypothesis, which underlies cryptographic security, remains beyond AI’s capabilities.

History

Historical Context

In June 1976, Kenneth Appel and Wolfgang Haken announced the first major computer-assisted proof, using an IBM mainframe at the University of Illinois to check 1,936 reducible configurations over about 1,200 hours, sparking debate over verification. By 2024 OpenAI’s ChatGPT solved the 80-year-old Erdos distance problem, showing how massive computational and AI resources now extend the same controversy into human-machine collaboration.

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Story summary

OpenAI’s ChatGPT solved the 80-year-old Erdos distance problem with a single prompt.
Mathematicians say limited expert time and high opportunity costs prevented the solution before AI could use massive token budgets.
A Princeton researcher later refined ChatGPT’s construction to achieve a better arrangement, confirming human contribution.
Experts warn that the Riemann Hypothesis, which underlies cryptographic security, remains beyond AI’s capabilities.

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