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One free scan finds every outdated or missing driver and matches the right update for your exact hardware.Free scan · exact hardware matchThere is not enough verified evidence to say that OpenAI models hallucinate more in mathematics than Gemini—or that Gemini does. The sources available here report results on factual question answering and summary faithfulness, not a head-to-head math evaluation. A fair comparison needs matched math tasks, identified model versions, and separate counts for correct answers, errors, and abstentions.
Why the headline’s comparison is unverified
“Math hallucination” can refer to different failures: a wrong final answer, an invalid step presented as sound, or a fabricated claim about a calculation. A comparison is meaningful only when the evaluation defines what counts as a hallucination and applies the same rule to both providers.
The verified OpenAI results discussed below concern factual question answering. FaithBench evaluates whether generated summaries stay faithful to source passages. Neither establishes how OpenAI compares with Gemini on mathematics. The sources available here do not provide a direct OpenAI–Gemini math comparison.
What OpenAI’s factual-answering results show
SimpleQA: correctness, errors, and abstention
In a 2025 explanation of SimpleQA, OpenAI reported that gpt-5-thinking-mini abstained on 52% of questions, answered 22% correctly, and gave an incorrect answer on 26%. For o4-mini, the corresponding figures were 1% abstention, 24% accuracy, and 75% error. OpenAI said the higher error rate indicated a substantially higher hallucination rate, even though o4-mini’s accuracy was slightly higher. These are results on a factual question-answering benchmark, not a mathematics test. OpenAI’s explanation of language-model hallucinations states: “Strategically guessing when uncertain improves accuracy but increases errors and hallucinations.”
#1 Best Overall
System-card results vary by model and benchmark
OpenAI’s 2024 o1 system card reports hallucination rates on two fact-oriented evaluations:
| Benchmark | GPT-4o | o1 | o1-preview | GPT-4o-mini | o1-mini |
|---|---|---|---|---|---|
| SimpleQA | 0.61 | 0.44 | 0.44 | 0.90 | 0.60 |
| PersonQA | 0.30 | 0.20 | 0.23 | 0.52 | 0.27 |
On these evaluations, the card says o1 and o1-preview hallucinated less frequently than GPT-4o, while o1-mini did so less frequently than GPT-4o-mini. The card also cautions that broader understanding is needed, particularly for domains outside the evaluations. These figures compare OpenAI models on fact-focused tests; they do not establish math performance or compare OpenAI with Gemini. See the OpenAI o1 System Card.
Why other hallucination benchmarks do not answer the math question
FaithBench evaluates whether summaries are faithful to source passages, distinguishing unwanted, questionable, and benign hallucinations. Its authors caution that the results come from selected challenging samples and may not represent all samples. The annotation process retained 800 samples after noisy samples were removed. That work is useful for summarization evaluation, but its faithfulness results are not measures of mathematical reasoning accuracy. See the FaithBench paper from the Association for Computational Linguistics.
What a fair OpenAI–Gemini math test needs
A credible head-to-head result should make the comparison reproducible and specify:
- Model versions and dates: name each tested model and record when it was accessed, since results can differ across versions.
- Matched tasks and prompts: give both models the same questions, mathematical domains, difficulty levels, instructions, and tool access.
- Scoring rules: state whether graders assess only final-answer correctness, each reasoning step, or fabricated mathematical claims, and how they handle equivalent forms.
- Sample size and repeat runs: report how many problems were tested and whether questions were run more than once.
- Separate outcome rates: report correct answers, errors, and abstentions separately. Accuracy alone can conceal a model’s tendency to guess rather than decline to answer.
Without these details, a broad claim that one provider’s models hallucinate more in math than the other’s is not supported by the evidence described here.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How to interpret future comparison claims
Check what was tested before applying a headline to everyday math use. A result on factual questions, source-grounded summaries, or one narrow type of arithmetic does not automatically generalize to proofs, word problems, symbolic algebra, or other mathematical tasks. Also check whether the evaluation counts an incorrect answer as a hallucination, distinguishes errors from abstentions, and tests the same model versions under the same conditions.
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