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Formula-One Prompting: Equation-First Reasoning For Applied Mathematics

Natapong Nitarach, Pittawat Taveekitworachai, Kunat Pipatanakul · Jan 27, 2026 · Citations: 0

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How to use this paper page

Coverage: Stale

Use this page to decide whether the paper is strong enough to influence an eval design. It summarizes the abstract plus available structured metadata. If the signal is thin, use it as background context and compare it against stronger hub pages before making protocol choices.

Best use

Background context only

Metadata: Stale

Trust level

Low

Signals: Stale

What still needs checking

Extraction flags indicate low-signal or possible false-positive protocol mapping.

Signal confidence: 0.25

Abstract

LLMs encode vast mathematical knowledge including governing equations from pretraining on equation-rich corpora, yet existing prompting methods, including Chain-of-Thought (CoT) and Program-of-Thought (PoT), do not explicitly elicit equation formulation as a reasoning stage. We propose Formula-One Prompting (F-1), a single-call, two-phase approach that fills this equation gap by using mathematical equations as an intermediate representation before solving through natural flow reasoning. F-1 first formulates governing equations from problem descriptions; the model then naturally selects a solving strategy among CoT, PoT, or direct computation based on the formalized equation structure, without explicit routing rules. Results across five models and four benchmarks show F-1 outperforms CoT by +5.76% and PoT by +8.42% on average, winning 53 out of 60 benchmark-model comparisons (88.3%). Gains are largest in applied domains: +13.30% on FinanceMath over CoT, and within OlympiadBench, larger gains on physics (+2.55%) than pure math (+0.44%). Per-problem analysis confirms equation formalization is the primary driver.

Use caution before copying this protocol

Use this page for context, then validate protocol choices against stronger HFEPX references before implementation decisions.

  • Extraction flags indicate low-signal or possible false-positive protocol mapping.
  • Extraction confidence is 0.25 (below strong-reference threshold).
  • No explicit evaluation mode was extracted from available metadata.
Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub

HFEPX Relevance Assessment

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

Background context only.

Main weakness

Extraction flags indicate low-signal or possible false-positive protocol mapping.

Trust level

Low

Eval-Fit Score

0/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Weak / implicit signal

HFEPX Fit

Adjacent candidate

Extraction confidence: Low

If you are doing eval pipeline work, start here:

Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub Tool-Use Eval Hub

What This Page Found In The Paper

Each field below shows whether the signal looked explicit, partial, or missing in the available metadata. Use this to judge what is safe to trust directly and what still needs full-paper validation.

Human Feedback Types

missing

None explicit

Confidence: Low Not found

No explicit feedback protocol extracted.

Evidence snippet: LLMs encode vast mathematical knowledge including governing equations from pretraining on equation-rich corpora, yet existing prompting methods, including Chain-of-Thought (CoT) and Program-of-Thought (PoT), do not explicitly elicit equation formulation as a reasoning stage.

Evaluation Modes

missing

None explicit

Confidence: Low Not found

Validate eval design from full paper text.

Evidence snippet: LLMs encode vast mathematical knowledge including governing equations from pretraining on equation-rich corpora, yet existing prompting methods, including Chain-of-Thought (CoT) and Program-of-Thought (PoT), do not explicitly elicit equation formulation as a reasoning stage.

Quality Controls

missing

Not reported

Confidence: Low Not found

No explicit QC controls found.

Evidence snippet: LLMs encode vast mathematical knowledge including governing equations from pretraining on equation-rich corpora, yet existing prompting methods, including Chain-of-Thought (CoT) and Program-of-Thought (PoT), do not explicitly elicit equation formulation as a reasoning stage.

Benchmarks / Datasets

partial

Olympiadbench

Confidence: Low Direct evidence

Useful for quick benchmark comparison.

Evidence snippet: Gains are largest in applied domains: +13.30% on FinanceMath over CoT, and within OlympiadBench, larger gains on physics (+2.55%) than pure math (+0.44%).

Reported Metrics

missing

Not extracted

Confidence: Low Not found

No metric anchors detected.

Evidence snippet: LLMs encode vast mathematical knowledge including governing equations from pretraining on equation-rich corpora, yet existing prompting methods, including Chain-of-Thought (CoT) and Program-of-Thought (PoT), do not explicitly elicit equation formulation as a reasoning stage.

Rater Population

missing

Unknown

Confidence: Low Not found

Rater source not explicitly reported.

Evidence snippet: LLMs encode vast mathematical knowledge including governing equations from pretraining on equation-rich corpora, yet existing prompting methods, including Chain-of-Thought (CoT) and Program-of-Thought (PoT), do not explicitly elicit equation formulation as a reasoning stage.

Human Data Lens

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Unknown
  • Unit of annotation: Unknown
  • Expertise required: Math
  • Signal basis: Structured extraction plus abstract evidence.

Evaluation Lens

  • Evaluation modes:
  • Agentic eval: None
  • Quality controls: Not reported
  • Signal confidence: 0.25
  • Known cautions: low_signal, possible_false_positive

Protocol And Measurement Signals

Benchmarks / Datasets

Olympiadbench

Reported Metrics

No metric terms were extracted from the available abstract.

Research Brief

Metadata summary

LLMs encode vast mathematical knowledge including governing equations from pretraining on equation-rich corpora, yet existing prompting methods, including Chain-of-Thought (CoT) and Program-of-Thought (PoT), do not explicitly elicit equation formulation as a reasoning stage.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key Takeaways

  • LLMs encode vast mathematical knowledge including governing equations from pretraining on equation-rich corpora, yet existing prompting methods, including Chain-of-Thought (CoT) and Program-of-Thought (PoT), do not explicitly elicit equation formulation as a reasoning stage.
  • We propose Formula-One Prompting (F-1), a single-call, two-phase approach that fills this equation gap by using mathematical equations as an intermediate representation before solving through natural flow reasoning.
  • F-1 first formulates governing equations from problem descriptions; the model then naturally selects a solving strategy among CoT, PoT, or direct computation based on the formalized equation structure, without explicit routing rules.

Researcher Actions

  • Compare this paper against others mentioning MATH.
  • Check the full text for explicit evaluation design choices (raters, protocol, and metrics).
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Recommended Queries

MATH

Research Summary

Contribution Summary

  • We propose Formula-One Prompting (F-1), a single-call, two-phase approach that fills this equation gap by using mathematical equations as an intermediate representation before solving through natural flow reasoning.
  • Results across five models and four benchmarks show F-1 outperforms CoT by +5.76% and PoT by +8.42% on average, winning 53 out of 60 benchmark-model comparisons (88.3%).
  • Gains are largest in applied domains: +13.30% on FinanceMath over CoT, and within OlympiadBench, larger gains on physics (+2.55%) than pure math (+0.44%).

Why It Matters For Eval

  • Results across five models and four benchmarks show F-1 outperforms CoT by +5.76% and PoT by +8.42% on average, winning 53 out of 60 benchmark-model comparisons (88.3%).

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Gap: Evaluation mode is explicit

    No clear evaluation mode extracted.

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Pass: Benchmark or dataset anchors are present

    Detected: Olympiadbench

  • Gap: Metric reporting is present

    No metric terms extracted.

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