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Paper 016 / Google Research

Solving Quantitative Reasoning Problems with Language Models

Minerva further trains a large language model on technical material and uses step-by-step prompting plus answer aggregation for quantitative reasoning.

UPDATED 16 Jul 2026SOURCE-LED REVIEWRESEARCH REVIEW
01

Paper, researchers, and primary source

Major lab research / reasoning

Minerva further trains a large language model on technical material and uses step-by-step prompting plus answer aggregation for quantitative reasoning.

CONTRIBUTION / 01

Contribution 1

Specialized a general language model on scientific and mathematical text.

CONTRIBUTION / 02

Contribution 2

Combined chain-of-thought prompting with sampled solution aggregation.

CONTRIBUTION / 03

Contribution 3

Evaluated across mathematics, physics, chemistry, and related quantitative benchmarks.

02

Research context

reasoning / 2022

Solving Quantitative Reasoning Problems with Language Models places minerva inside the broader reasoning discussion at Google Research, with mathematics supplying a second analytical lens. Read together, the source records three advances: Specialized a general language model on scientific and mathematical text; Combined chain-of-thought prompting with sampled solution aggregation; and Evaluated across mathematics, physics, chemistry, and related quantitative benchmarks. Keeping those moves together prevents chain of thought from being detached from its evidence. For an implementation review, the relevant consequence is that reasoning quality can depend on domain data, prompting protocol, and decoding strategy as much as the base model.

03

Methods and evidence reading

1 cataloged method notes

METHOD / 01

Method 1

The experimental design in Solving Quantitative Reasoning Problems with Language Models tests specialized a general language model on scientific and mathematical text and combined chain-of-thought prompting with sampled solution aggregation against the paper's documented baselines, datasets, model variants, or systems workloads.

How to read the evidence

The evidentiary value of Solving Quantitative Reasoning Problems with Language Models comes from the relationship among its reported moves. Two entries define the method-level claim: Specialized a general language model on scientific and mathematical text; and Combined chain-of-thought prompting with sampled solution aggregation. The cataloged result is: Evaluated across mathematics, physics, chemistry, and related quantitative benchmarks. On that basis, reasoning quality can depend on domain data, prompting protocol, and decoding strategy as much as the base model. The catalog nevertheless records that the minerva comparison in Solving Quantitative Reasoning Problems with Language Models is interpretable only alongside contamination controls, prompt design, verifier behavior, benchmark tasks, answer extraction, and sampling policy, which limits claims about unseen deployments. Reproduction work should separate genuine minerva transfer from behavior caused by a changed mathematics setup. Evidence transfer from Solving Quantitative Reasoning Problems with Language Models should be tested by anchoring minerva, slicing on mathematics, and keeping counterexamples to Combined chain-of-thought prompting with sampled solution aggregation in the evaluation record.

04

Findings in the source record

1 paper-specific findings

  1. The reported evidence in Solving Quantitative Reasoning Problems with Language Models supports evaluated across mathematics, physics, chemistry, and related quantitative benchmarks.
05

Practical implication for AI builders

Google Research / 2022

06

Proposed BrokenGPT application

Research blueprint / proposed status

INTEGRATION POINT / 01

Proposed route placement / minerva

For a proposed BrokenGPT experiment based on Solving Quantitative Reasoning Problems with Language Models, provide a quantitative-reasoning route that samples multiple derivations, checks final-answer agreement, and records calculator verification when tools are available. Keep the minerva path isolated, versioned, and attributable to this research record.

VALIDATION METRIC / 02

Proposed acceptance test / mathematics

Validate the proposed minerva route against the paper's reported outcome: Evaluated across mathematics, physics, chemistry, and related quantitative benchmarks. Measure verifier agreement, answer correctness, and stability across samples for the Solving Quantitative Reasoning Problems with Language Models candidate, then isolate mathematics regressions before judging the proposed minerva route.

TRADEOFF / 03

Proposed decision boundary / chain of thought

Balance inference compute, faithfulness, and unresolved errors before promoting the proposed chain of thought design. Because product evidence would remain incomplete without testing unseen problem forms, open-ended conversations, domain shifts, unfaithful rationales, and language changes under the selected mathematics workload, adoption remains conditional on replay under BrokenGPT's selected model, runtime, and policy configuration.

07

Limitations, verification, and source

Boundaries recorded with the paper

Limitations

  • The minerva comparison in Solving Quantitative Reasoning Problems with Language Models is interpretable only alongside contamination controls, prompt design, verifier behavior, benchmark tasks, answer extraction, and sampling policy, which limits claims about unseen deployments.
  • Product evidence would remain incomplete without testing unseen problem forms, open-ended conversations, domain shifts, unfaithful rationales, and language changes under the selected mathematics workload.

PRIMARY SOURCES

  1. 01
    Solving Quantitative Reasoning Problems with Language Models

    Google Research — Primary primary arXiv paper / 29 June 2022 / Aitor Lewkowycz, Anders Andreassen, David Dohan, and 11 more

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STRAIGHT ANSWERS

Frequently asked questions

01What does Solving Quantitative Reasoning Problems with Language Models study?

Minerva further trains a large language model on technical material and uses step-by-step prompting plus answer aggregation for quantitative reasoning.

02Which methods does Solving Quantitative Reasoning Problems with Language Models use?

The experimental design in Solving Quantitative Reasoning Problems with Language Models tests specialized a general language model on scientific and mathematical text and combined chain-of-thought prompting with sampled solution aggregation against the paper's documented baselines, datasets, model variants, or systems workloads.

03What does Solving Quantitative Reasoning Problems with Language Models report?

The reported evidence in Solving Quantitative Reasoning Problems with Language Models supports evaluated across mathematics, physics, chemistry, and related quantitative benchmarks.

04What is the proposed BrokenGPT application for Solving Quantitative Reasoning Problems with Language Models?

Proposed: provide a quantitative-reasoning route that samples multiple derivations, checks final-answer agreement, and records calculator verification when tools are available.

MAJOR LAB RESEARCH / PAPER 016

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