---
title: 'Solving Quantitative Reasoning Problems with Language Models'
license: CC-BY-4.0
license_url: https://creativecommons.org/licenses/by/4.0/
license_note: 'paper is CC BY 4.0 (verified on arXiv abs page 2026-11-11; icon by-4.0.png, http://creativecommons.org/licenses/by/4.0/); note is our own summary'
source: https://iinventedlight.com/library/notes/2206-14858-minerva.md
source_license: 'CC BY 4.0'
attribution: 'Summary by iinventedlight (AI-assisted). Source: Aitor Lewkowycz, Anders Andreassen, David Dohan, Ethan Dyer, Henryk Michalewski, Vinay Ramasesh, et al. (14 authors), Solving Quantitative Reasoning Problems with Language Models (CC BY 4.0).'
author: 'iinventedlight (AI-assisted)'
date: 2026-11-11
status: published
approved_by: "Cole Withington, 2026-11-11 20:58 PT, Grok Bot chat widget t1717s7407: \"Publish all 100 including the LLMs Encode Clinical Knowledge note\""
checked_on: 2026-11-11
as_of: 2026-11-11
confidence: medium
untested: 'Not reproduced. Abs page and HTML key sections read 2026-11-11. Named code URLs checked; code not run.'
category: arxiv
topic_area: 'ai-research: reasoning'
tags: arxiv, reasoning, quantitative
arxiv_id: 2206.14858
alias: 2206.14858-minerva
sources:
  - id: S1
    title: 'Solving Quantitative Reasoning Problems with Language Models'
    publisher: arXiv
    authors: 'Aitor Lewkowycz, Anders Andreassen, David Dohan, Ethan Dyer, Henryk Michalewski, Vinay Ramasesh, et al. (14 authors)'
    url: https://arxiv.org/abs/2206.14858
    version_read: 'v2 (1 Jul 2022)'
    accessed: 2026-11-11
    license: 'CC BY 4.0'
---
# Solving Quantitative Reasoning Problems with Language Models

## Summary
Minerva is a language model that starts from general natural-language pretraining and is then further trained on technical content. The authors report state-of-the-art performance on technical benchmarks without external tools. They also evaluate on over two hundred undergraduate-level problems in physics, biology, chemistry, economics, and other sciences, and they say the model can correctly answer nearly a third of them. [S1]

## Claims
- id: C1
  claim: 'Minerva is pretrained on general natural language data and further trained on technical content.'
  source: S1
  evidence: "pretrained on general natural language data and further trained on technical content"
- id: C2
  claim: 'They report state-of-the-art performance on technical benchmarks without external tools.'
  source: S1
  evidence: "state-of-the-art performance on technical benchmarks without the use of external tools"
- id: C3
  claim: 'They say the model can correctly answer nearly a third of over two hundred undergraduate-level quantitative problems.'
  source: S1
  evidence: "evaluate our model on over two hundred undergraduate-level problems"

## Verification
- Code available: No official code URL was named on the abs page or HTML. The authors say they plan to release problems as part of an open-source dataset in an upcoming manuscript; that later release was not verified here.
- Reproduced: not reproduced (2026-11-11). Code not run.
- Related work: Live notes 2201-11903-chain-of-thought-prompting and 2203-11171-self-consistency. This is the paper-verification note for Minerva itself.
- Limits: Headline results are from mid-2022 models further trained on technical text, without tools. 'Nearly a third' is the authors' summary of their undergraduate-level set, not a general guarantee on later exams.
- License: CC BY 4.0 on the abs page (2026-11-11; icon by-4.0.png; http://creativecommons.org/licenses/by/4.0/). Submitted 29 Jun 2022 (v1); last revised 1 Jul 2022 (v2). Sources: [S1] https://arxiv.org/abs/2206.14858, v2 (1 Jul 2022). checked_on: 2026-11-11.

## When to apply
Use when looking at continued training on scientific and mathematical text for quantitative reasoning, as distinct from tool-using program-aided methods.

## Facts
- id: F1
  claim: 'Minerva continues training a general language model on technical content.'
  confidence: medium
  date: 2026-11-11
  sources: [S1]
  license: CC BY 4.0
- id: F2
  claim: 'The authors report state-of-the-art performance on technical benchmarks without external tools.'
  confidence: medium
  date: 2026-11-11
  sources: [S1]
  license: CC BY 4.0
- id: F3
  claim: 'They report that the model correctly answers nearly a third of over two hundred undergraduate-level quantitative problems they evaluated.'
  confidence: medium
  date: 2026-11-11
  sources: [S1]
  license: CC BY 4.0

## Sources
- [S1] arXiv 2206.14858, https://arxiv.org/abs/2206.14858. License: CC BY 4.0. v2 (1 Jul 2022). Accessed 2026-11-11.

License: this note is CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Summary by iinventedlight (AI-assisted). Paper is CC BY 4.0.

---

Agents: [/agents.md](/agents.md) | [/.well-known/agent-library.json](/.well-known/agent-library.json).