Grok 4.5 vs GPT-5: AI Competition Solving Mathematical Conjectures

The Grok 4.5 vs. GPT-5 competition goes beyond chatbots and coding. Both model families are associated with solving open-ended mathematical problems, but some reports conflate conjectures, models, and discovery processes, requiring careful consideration.

Key Takeaways

• Grok 4.5 claims to have found a counterexample to Graffiti Conjecture 284, while the much-discussed GPT-5.6 case concerns a different indivisible flow conjecture.
• Elon Musk has indeed praised Grok 4.5's capabilities, but social media posts are no substitute for mathematical scrutiny and formal publication.
• Achievements in mathematical AI should be judged by reproducibility, precision of definition, completeness of proof, and independent validation, not just time to completion.

What Happened in the Grok 4.5 vs GPT-5 Competition?

In July 2026, Grok 4.5 came into the spotlight after a Grok 4.5-based agent Medium reportedly found a counterexample to a graph theory conjecture that had been open for about 30 years.

According to a post from the team involved, the issue was shared via a Slack conversation. An agent named Capy then attempted to find a counterexample and reportedly obtained the following results:in about eight minutes. The conjecture mentioned in the post isGraffiti Conjecture 284.

Elon Musk then heightened public concern by stating that Grok 4.5 had just solved a graph theory conjecture that had been open for about three decades.

Around the same time, another report emerged about using GPT-5.6 Pro to find counterexamples toDinitz–Garg–Goemans conjecture. 

Sumber: AI Generated Image

One researcher stated that a long conversation with the model resulted in a graph with a fractional flow cost of 58, while each indivisible flow meeting the capacity violation limit costs at least 60. If true, this difference is enough to disprove the conjecture.

These two events are often presented as a head-to-head match between Grok 4.5 and GPT-5. However, publicly available evidence suggests that they involve different problems and different experimental processes.

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What is a Conjecture in Mathematics?

A conjecture is a mathematical statement that is thought to be true based on patterns, experiments, or previous results, but for which no complete proof has been provided.

A conjecture can be solved in two ways:

• Proven, namely showing that the statement is true for all objects included in its definition.
• Denied, that is, finding a counterexample that satisfies all the conditions, but does not follow from the conclusion of the conjecture.

Finding a counterexample often seems simpler because it only requires a single case. However, the object must be examined very carefully.

A graph that appears to be a counterexample may fail because:

• Misunderstanding the definition.
• Does not meet any of the assumptions.
• Error calculating graph invariant.
• Using graph types that are not within the scope of the conjecture.
• Program error while performing enumeration.
• Ignore alternative configurations.

Therefore, the claim that "AI solves a conjecture" isn't complete just because the model generates a single graph. Mathematicians must still ensure that all the conditions, calculations, and logical implications are correct.

Read also:Grok Computer Coming Soon: Elon Musk's Big Vision for AI

What Does Grok 4.5 Claim?

Grok 4.5 launched on July 16, 2026, as a model focused on coding, agentic work, science, engineering, mathematics, and knowledge-based tasks. It is also positioned as a system that prioritizes token efficiency and execution speed.

A few days after launch, an agency running Grok 4.5 Medium reportedly tried out Graffiti Conjecture 284 via internal chat.

The team stated that the agent:

• Understanding conjectural statements.
• Tracing the set of candidate graphs.
• Finding counterexample candidates.
• Calculate the required parameters.
• Conduct additional checks to ensure consistent results.

The counterexample in circulation is associated with the Hoffman–Singleton graph, a graph long known in graph theory. Thus, the model's primary value is not in creating a new graph, but in recognizing that a known graph can disprove the mathematical relationship proposed in the conjecture.

However, this achievement still requires context.

Graffiti is a program that generates numerous conjectures based on numerical patterns in graph invariants. Some of these conjectures have survived for so long not because they are a major focus of the mathematical community, but because no researcher has systematically examined all relevant candidate graphs.

This doesn't make Grok's results unimportant. Rather, the case demonstrates that AI models combined with computation can be an effective tool for matching formal statements against large libraries of examples.

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Why Is Elon Musk Praising Grok 4.5?

Musk hailed the results as proof that Grok 4.5 can contribute to research-level mathematical problems. His post helped make the story go viral and reinforced the perception that AI models had moved from problem-solving to generating new knowledge.

The praise is understandable because Grok 4.5 was just launched and developed for technical tasks with long reasoning.

However, there is a difference between the following three statements:

1. The model produces answers that appear to be correct.
2. The internal team checked the answers and found no issues.
3. The results are published and independently verified by experts in the relevant field.

Grok's current claims are closer to the first and second stages. Before formal records, reproduction codes, and more extensive external audits are available, the most appropriate term is reported counterexample, not a final conclusion that cannot be debated.

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What Problems Does GPT-5 Solve?

The GPT case compared to Grok is related toDinitz–Garg–Goemans conjecture, a problem in single-source unsplittable flow.

This problem can be imagined as a delivery network.

A single source must send goods to multiple destinations. In a fractional solution, a single request can be split across multiple paths. In an unsplittable solution, each request must be sent in its entirety through a single path.

Classical results show that fractional solutions can be converted to indivisible flows with certain additional capacity constraints. A subsequent conjecture asked whether such a conversion could also be achieved without increasing the total cost. The academic literature as of 2024 still refers to this costly version as an open problem.

In the published conversation, GPT-5.6 Pro is used iteratively to explore the graph, test paths, fix failing candidates, and ultimately generate a structure with:

• Fractional flow cost is 58.
• The minimum cost of an undivided flow is 60.
• Capacity violation limit of 15.

If all these calculations are correct and agree with the original formulation, the graph disproves the conjecture because the indivisible solution cannot sustain the cost of the fractional solution.

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Do Grok 4.5 and GPT-5 Solve the Same Conjecture?

There is not enough public evidence to suggest that the viral achievement is a match on the same issue.

Sumber: AI Generated Image

The case is strengthened by Elon Musk referring toGraffiti Conjecture 284. Meanwhile, the widely shared GPT-5.6 conversation refers toDinitz–Garg–Goemans conjecture.

Both are within the broad area of ​​graph theory and combinatorial optimization, but their mathematical content is different.

Direct comparisons are also difficult because:

• The prompts used are different.
• Models acquire different contexts.
• Computation time is different.
• Programming tools are not the same.
• The level of human involvement varies.
• Verification methods are different.
• The difficulty of the two conjectures cannot be equated based solely on their age.

Thus, the title “Grok 4.5 vs GPT-5” is more accurately understood as a competition of AI capabilities in mathematical research, rather than a controlled race to solve the same problem.

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How is GPT-5 Used in Mathematical Research?

GPT-5 has previously been used by mathematicians to explore open optimization problems for about 40 years.

In such cases, the model doesn't immediately produce a final proof. Instead, it suggests many directions, some of which are incorrect, and then human researchers select promising ideas and verify each step. The process takes about 12 hours over three days.

The case shows a different working pattern from the narrative “AI answers questions in one prompt”.

The model acts as:

• Hypothesis generator.
• Brainstorming machine.
• Finder of relationships between branches of mathematics.
• Experimental code generator.
• Examiner of minor cases.
• Assistant to eliminate dead-end approaches.

More recent GPT models have also been associated with autonomous mathematical results, including disapproval of conjectures in discrete geometry that were then checked by external mathematicians.

This demonstrates that AI's mathematical abilities are no longer solely measured by exam or Olympiad questions. Models are beginning to be tested on problems for which answers are not readily available in the literature.

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Grok 4.5 vs GPT-5: Which One Is Better at Math?

There is no solid basis yet to determine a winner from just these two conjectural stories.

Grok 4.5 shows potential in:

• Quick search for candidates.
• Integration with agents and work conversations.
• Using code to check multiple graphs.
• Technical response with relatively efficient computational costs.
• Discovery of counterexamples from a collection of known structures.

GPT-5 and its next generations show potential in:

• Exploration of arguments in long conversations.
• Combination of techniques from different fields.
• Structured proof or counterexample construction.
• Iterative collaboration with mathematicians.
• Problem solving that has received external validation.

GPT-5.6 also reportedly scored high on advanced math assessments, including FrontierMath. However, benchmark scores don't automatically predict the ability to discover new research results, as open-ended problems require different search, creativity, tool use, and verification.

A fairer comparison requires experimentation with:

• Same set of problems.
• The prompt and context are identical.
• Token budget is equivalent.
• Access the same tools.
• Same number of trials.
• Independent verifier.
• Reporting all failures, not just the best results.

Without such conditions, claims that one model “beats” another remain marketing or community interpretation.

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Why Are AI's Math Skills Improving Rapidly?

Longer Reasoning

Modern models can use more computing time to explore multiple paths before producing an answer.

Integration with Code

Many graph theory problems involve combinatorial search. Models can write programs to construct graphs, compute invariants, or test thousands of candidates.

Use of Agents

An agency can divide the work into literature search, candidate generation, verification, and writing up the results.

Verification is Easier than Discovery

In some problems, finding a counterexample is very difficult, but checking a single candidate is quite easy. This situation is ideal for AI, which can generate and test many possibilities.

Wide Range of Knowledge

Models can connect mathematical structures with examples from other fields that might not immediately occur to the researcher.

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What are the requirements for an AI claim to be considered a conjecture solver?

A result should satisfy several layers of scrutiny.

Problem Statement Must Be Accurate

The model must use the correct version of the conjecture, including all its assumptions and constraints.

Evidence or Counterexample Must Be Open

Objects, calculations, code, and arguments must be available for others to inspect.

Results Must Be Reproducible

Independent researchers should be able to repeat calculations using different tools.

Cannot Rely on Numerical Errors

For exact claims, numerical approaches alone are often insufficient. Values ​​must be proven symbolically or strictly constrained.

Experts Must Check Its Relevance

A computationally correct counterexample does not necessarily disprove the conjecture if its object lies outside the domain in question.

Formal Publication Remains Important

Peer review is not perfect, but it provides a more systematic examination of definition, originality, and logic.

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What Are the Risks of Relying on AI for Math Problems?

False Arguments That Look Convincing

Models can produce proofs that use precise terms, but hide logical leaps.

Edge Case Error

An argument can be true for many small examples, but fail on a particular graph.

Misquoting the Theorem

Models can mention results that do not exist or use theorems outside of their validity conditions.

Data Leak

On problems that already have informal proofs on the internet, it is difficult to be sure whether the model actually finds a solution or reconstructs the training material.

Best Result Selection

Teams can run hundreds of experiments and only publish a single success story. Without reporting failures, the public doesn't know the true probability of success.

Dependence on Tools

Answers can come from brute-force searches or external software, not just model reasoning. While these are still useful, they should be reported transparently.

Read also:Fed Up With Google's AI? DuckDuckGo Offers an AI-Free Search Extension

What Impact Does This Have on the Future of Research?

This development does not mean that mathematicians will soon be replaced.

Instead, the role of humans can shift towards:

• Choose an important issue.
• Writing a formal definition.
• Determine meaningful experiments.
• Checking originality.
• Assess whether the results provide new insights.
• Transforming machine output into learnable evidence.
• Connecting results to broader theory.

AI can speed up tedious work, such as examining graphs, trying variations, and testing conjectures. Mathematicians are still needed to ensure that the results are correct, relevant, and scientifically sound.

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Conclusion

The Grok 4.5 vs GPT-5 competition shows that AI models are increasingly capable of tackling mathematical problems that were previously only explored by specialist researchers.

Grok 4.5 is claimed to generate counterexamples for Graffiti Conjecture 284 through agents running on Slack. GPT-5.6 Pro is credited with discovering counterexamples for the Dinitz–Garg–Goemans conjecture through an iterative exploration process.

These two achievements shouldn't be directly compared as a race on a single problem. The conjectures are different, the workflows are different, and the validation status isn't identical.

Elon Musk may have praised Grok 4.5, but corporate acclaim is no substitute for mathematical verification. Thorough proofs, code, independent reproduction, and expert review remain the gold standard.

The most balanced conclusion is that Grok 4.5 and GPT-5 have demonstrated their capabilities as mathematical search partners. The winner is yet to be determined, but the direction of development is clear: AI is shifting from answering old knowledge to helping discover new results.

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FAQ

Does Grok 4.5 really solve a mathematical conjecture?

Grok 4.5 reportedly found a counterexample for Graffiti Conjecture 284. The result appears to be checkable, but still requires formal documentation and more extensive independent validation.

Does Grok 4.5 beat GPT-5?

It's not yet possible to draw a conclusion. Both are related to different problems, using different processes and tools, so they don't constitute a direct comparison.

What conjectures are associated with GPT-5?

GPT-5.6 Pro is associated with a counterexample to the Dinitz–Garg–Goemans conjecture regarding the cost of fractional and unsplittable flows. The claim still needs formal academic scrutiny.

What does counterexample mean?

A counterexample is a single example that satisfies the assumptions of a conjecture but violates its conclusion. One valid counterexample is sufficient to prove the universal conjecture false.

Can AI replace mathematicians?

Not yet. AI can speed up idea generation, experimentation, and candidate vetting, but humans are still needed to formulate problems, verify results, and assess their significance.