Last updated 07-27-2026
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Minerva
Minerva is a large language model from Google Research built to solve math and science questions through step-by-step written reasoning. It reads problems that mix plain English with LaTeX notation, then writes out solutions involving arithmetic, algebra, and symbolic steps. The model was trained on scientific papers and web pages where mathematical formatting was kept intact, rather than stripped during preprocessing.
Most math-capable models lean on external tools like Python interpreters or calculators at inference time. Minerva takes the opposite bet: it generates full worked solutions from the model weights alone, using chain-of-thought prompting and majority voting across multiple sampled answers. That informal approach covers a wider range of problem types than formal theorem provers, but the trade-off is answers cannot be machine-verified the way Coq or Lean proofs can.
Researchers studying quantitative reasoning in language models use Minerva as a reference point for STEM benchmark performance. The public sample explorer hosts 110 solved problems across algebra, physics, chemistry, and other topics, so anyone can read through how the model arrived at each answer. Educators and ML engineers reviewing benchmark methodology will find the published MATH, MMLU-STEM, GSM8k, and OCWCourses scores useful for comparing against newer models.
Built on PaLM with 118GB of arXiv papers and math-formatted web pages in training data
Scores 50.3% on the MATH benchmark at 540B parameters, up from a prior best of 6.9%
Generates solutions with arithmetic and symbolic steps without calling a calculator or Python interpreter
Uses chain-of-thought prompting, few-shot examples, and majority voting across sampled outputs
Public sample explorer shows 110 worked problems across 11 topics including algebra, physics, and chemistry
Reaches 75% on MMLU-STEM and 78.5% on GSM8k, both ahead of published prior state of the art
Hits 50.3% on MATH without relying on external calculator or Python tools at inference time.
Preserves LaTeX and MathJax notation in training data instead of stripping mathematical symbols.
Free sample explorer lets you inspect 110 worked solutions across 11 STEM subject areas.
Majority voting across sampled outputs improves accuracy over taking a single greedy answer.
Not available as a public API, downloadable weights, or commercial product.
Answers cannot be automatically verified like formal proof systems such as Coq or Lean.
Can produce correct final answers with incorrect intermediate reasoning steps.
Research project announced in 2022 with no published product roadmap for public access.
What is Minerva?
Minerva is a Google Research language model trained to solve mathematical and scientific questions with step-by-step written reasoning. It builds on the Pathways Language Model (PaLM) and was further trained on arXiv papers and web pages containing LaTeX and MathJax notation.
How does Minerva solve math without a calculator?
Minerva writes out full solutions in natural language mixed with mathematical notation, performing arithmetic and symbolic manipulation inside the model. At inference it uses chain-of-thought prompting and majority voting across multiple sampled answers to pick the most common result.
What benchmark scores did Minerva achieve?
Minerva 540B scored 50.3% on MATH, 75% on MMLU-STEM, 30.8% on OCWCourses, and 78.5% on GSM8k. Each score beat the published state of the art at the time, with MATH improving from 6.9% to 50.3%.
Can I use Minerva as a product or API?
Minerva is a research model, not a commercial product with a public API or download. Google Research published the paper and hosts a free sample explorer at minerva-demo.github.io where you can browse 110 solved example problems.
What are Minerva's main limitations?
Minerva uses informal natural-language reasoning rather than formal proof systems, so its answers cannot be automatically verified. About half of its errors are calculation mistakes and half are faulty reasoning chains, and it can sometimes reach a correct final answer through incorrect intermediate steps.
What STEM topics does the Minerva demo cover?
The Minerva sample explorer at minerva-demo.github.io covers 110 problems across algebra, probability, physics, number theory, precalculus, geometry, biology, electrical engineering, chemistry, astronomy, and machine learning.