A 30-year-old graph theory "mystery" collapsed overnight.
Today, GPT-5.6 Pro disproved a thirty-year conjecture in graph theory—the Dinitz-Garg-Goemans conjecture.
The evidence he provided was extremely straightforward: a chart showing the cost of the score flow at 58.
And any indivisible flow with a capacity violation of no more than 15 has a cost of at least 60.
58 < 60, a 30-year-old graph theory conjecture has fallen.
On the same day, Columbia University PhD student Shouqiao Wang solved six open Erdős problems in five days using the GPT-5.6 Sol paired with the Codex workflow.
Last night, the new Fields Medalists were announced.
But now, within the community, a claim is spreading rapidly: this might be the "last ever" Fields Medal.
A 30-year conjecture
GPT-5.6 Pro is falsified
This time, the complete chat log with GPT-5.6 Pro has been fully disclosed.
Dmitry Rybin said that "AI overturning old theories" is quickly becoming an internet meme.
But he truly cared about this issue, spending several weeks thinking about it from both the proof and disproof perspectives.
He added that this human-machine conversation itself is an absolute masterpiece of a meme.
First, let’s clarify what this problem is. Back then, Dinitz, Garg, and Goemans proved a beautiful result:
If there exists a fractional flow that satisfies the capacity constraints, then there must also exist an integral flow whose capacity usage exceeds the original limits by at most the maximum demand.
Goemans later added a natural conjecture: Can we avoid significantly increasing the cost while not exceeding the capacity?
No one has ever managed to create this cost version.
In the 2023 arXiv paper, it was open; in the 2026 January literature, it remains open.
Almost everyone involved in meme coins has thought about it.
The model's current counterexample is as follows: three terminals with demands of 15, 10, and 15, respectively. Each terminal has one "cheap path" (zero cost) and one "expensive path" (cost of 30).
The key point is that the three cheap paths conflict with each other pairwise; selecting any two will always result in one edge being overloaded.
Therefore, any legal move can use at most one cheap path, and the remaining two terminals must take the expensive path, resulting in a minimum cost of 60.
Meanwhile, the score stream can simultaneously utilize all three low-cost routes in the proportions of 1/3, 2/5, and 1/3, at a cost of only 58.
Anyone familiar with combinatorial optimization will immediately recognize this as a triangle stable set inequality.
The integer solution satisfies z₁ + z₂ + z₃ ≤ 1, while the fractional solution is 1/3 + 2/5 + 1/3 = 16/15, which is greater than 1.
Throughout the entire conversation, Rybin spoke only three sentences.
- First sentence: To construct a counterexample, you must make a breakthrough by finding a structured counterexample.
- Second sentence: Keep searching, and develop a clear strategy based on a deep understanding of the problem's structure.
- Third sentence: We have enough partial results; let us directly present a complete, unconditional counterexample.
Someone who won a gold medal at the Olympiad has gone into algorithms.
Dmitry Rybin, who overturned 30 years of graph theory, is currently a co-founder of a $100 million AI startup.
In his bio, Rybin earned his Ph.D. in Machine Learning from The Chinese University of Hong Kong, Shenzhen.
Notably, he also won gold medals at the International Mathematical Competition for University Students and the National Mathematical Olympiad.
What truly made him famous in the industry was the paper published in May 2025—
Rybin found a faster algorithm for computing a matrix multiplied by its transpose.
This operation may sound abstract, but it is the covariance matrix in statistics, the foundation of chip design and wireless communications, and something repeatedly computed during the training of large models today.
Immediately following October, he published another post: reducing the computation for precise causal attention by 10%.
He has a repository on GitHub named "Experiments in Algorithm Discovery and Optimization Using OpenEvolve."
An Olympic gold medalist who, during their PhD, didn’t pursue large models but instead dove into “how to get machines to help humans discover new algorithms.”
Chinese alumni of the School of Mathematical Sciences at Peking University
Solve 6 Major Challenges in Five Days
On the same timeline, another event occurred.
Columbia PhD student Shouqiao Wang said he solved six previously open Erdős problems in five days using GPT-5.6 Sol with Codex.
Approximately 13 attempts were made, with a success rate of 46%, and one individual task ran continuously for 32 hours.
He broke the method down into three steps.
In the topic selection process, only choose topics that mathematicians are already discussing, and then use AI to eliminate those tightly linked to major conjectures.
Define for yourself what counts as a solution: precisely restate the problem, specify exactly what a complete proof must establish, list which weaker conclusions do not count, and identify the specific pitfalls unique to this problem.
Finally, require an independent adversarial agent to challenge each candidate conclusion.
The entire process is a vicious cycle: attempt → fail → diagnose → switch routes → draft proof → combat audit → patch.
The model repeatedly overturns and attacks its own arguments until no substantive issues remain.
Notably, one of the questions was once studied by Terence Tao and remains unsolved to this day.
In response, Shouqiao Wang briefly mentioned: "I have a math background, but this workflow doesn't require deep mathematical knowledge."
But what he referred to as "some background" is slightly overblown.
At age 13, while his peers were following the standard curriculum in middle school, he skipped grades to register for the Waterloo Euclid Mathematics Competition and ranked first in the world.
In the following years, 2016 and 2017, he won two consecutive silver medals at the China Mathematical Olympiad (CMO) and naturally secured first place in the 2017 National High School Mathematics League.
In 2018, with maxed-out talent, he walked through the doors of Peking University’s Department of Mathematics, a realm where the best compete.
But the most interesting part of the story is that he didn’t stay in the world of pure mathematics as the script suggested.
Today, he enrolled in Columbia Business School to pursue a Ph.D. in Decision, Risk, and Operations.
He turned the sharpness of mathematical equations toward more practically impactful frontiers: studying mechanism design and game theory.
The "final edition" of the Fields Medal for humanity?
In four and a half hours, solved a 30-year-old mystery; in five days, cracked six tough problems.
The Fields Medal to be announced tonight may truly become the final masterpiece of pure human intelligence.
But this is not the end—it is the beginning of a new era of coexistence and exploration between AI and humanity.
From solo operations to multi-agent autonomous competition, AI is gradually becoming a true "research partner" that expands the boundaries of knowledge.
How far is AI from winning its own Fields Medal?
Reference materials:
https://x.com/DmitryRybin1/status/2079904005652893709?s=20
https://x.com/Qiaoqiao2001/status/2080003441821163958
This article is from the WeChat public account "New Intelligence Yuan," authored by ASI Revelation, edited by Peach.