What benchmarks show GPT-5's extended reasoning outperforming GPT-4 on math and coding

Mathematical Reasoning Benchmarks

Recent GPT-5 evaluations show a leap in performance on premier competition and research-level math tasks. According to OpenAI's official data, GPT-5 achieves an outstanding 94.6% accuracy on the AIME 2025 (American Invitational Mathematics Examination) without the use of external tools—a domain previously seen as prohibitive for language models due to its complex context, solution creativity, and the need for error minimization. Similarly, on the USAMO and AIME suite, GPT-5 Pro with Python tools scores 100% accuracy, while standard GPT-5 with Python tools attains 96.7%, and even without any tool augmentation, attains 93.3%—rivaling top mathematical competitors and demonstrating expert-level problem-solving.

A notable aspect of these results involves the Harvard-MIT Mathematics Tournament (HMMT) and the even more challenging FrontierMath benchmarks, which push up against the limits of mathematical reasoning for AI. On the FrontierMath Tier 1–3 tasks, GPT-5 Pro reaches 32.1% (at least twice as good as prior state-of-the-art baselines), with notable improvements attributed to its enhanced capabilities for stepwise deduction and complex proof construction. Standard GPT-5 similarly far surpasses prior models, validating its upgrade in both foundational math skills and deep problem-solving.

The GPQA (Graduate Pharmacology and Quantitative Analysis) diamond benchmark, known for requiring long-form, multi-step, graduate-level reasoning, records GPT-5 Pro as the first model to surpass 88% accuracy without tools, compared with previous top scores in the low 70s for prior GPT-4-based models.

In practical mathematical reasoning, GPT-5 exhibits:
- Extensive proficiency in stepwise, multi-variable reasoning (handling multi-step derivations, recursive logic, and variable substitution efficiently).
- The ability to integrate Python or symbolic tools natively for even stronger performance, with the best accuracy seen when using code or tool-augmented reasoning.
- Dramatically reduced hallucination and error rates on long and open-ended factual math problems, with about 80% fewer factual errors reported during “thinking” mode compared to previous generations.

Coding Benchmarks and Programming Reasoning

On software engineering benchmarks, GPT-5 sets a new state of the art. SWE-bench Verified, a highly regarded test in the open-source community that measures the ability of an AI to autonomously understand, fix, and validate real-world GitHub issues, credits GPT-5 with a score of 74.9%. This is a striking jump up from GPT-4.1, which tops out at 54.6%, and GPT-4.5, which manages just 38%. Contemporary competitors (such as o3) generally fall in the 69.1%–71.7% range, while GPT-4o lags even further behind. These metrics aren't mere artifacts of toy problems—SWE-bench tasks reflect actual multi-file, cross-codebase defects and bugfixes as faced by working engineers.

Another key measure, Aider Polyglot, specifically examines an AI's capabilities to make code edits across diverse programming languages and ensure correctness. Here, GPT-5 again leads with an 88% score under “thinking” mode, a considerable leap over GPT-4.1's 76.9% and GPT-4.5's 45%.

Qualitative testing and third-party benchmarks further confirm that GPT-5's edge is most prominent on tasks demanding:
- Multi-file reasoning, such as tracing a bug that propagates through several interdependent modules or APIs.
- Debugging larger repositories, including open-source libraries with minimal documentation, where strategy and context retention are crucial.
- Cross-modal development, such as integrating screenshots of stack traces, frontend bug images, or diagrams into coding workflows. GPT-5 reliably interprets and acts on these inputs, while GPT-4 requires more manual effort.

Real-World Coding Impact

In the coding workflow, these benchmark gains translate to tangible developer advantages:
- Faster, context-aware pair programming—autocompletions, bugfixes, and test scaffolding are more accurate and need less back-and-forth.
- PR summarization and code review acceleration—GPT-5 generates focused, prioritized change lists and edge-case detection with fewer hallucinations or missed cross-cutting issues.
- Smarter integration with CI/CD pipelines and code hosting platforms, reducing human bottlenecks on mechanical reviews and opening space for more strategic, human-led code design.

Moreover, GPT-5's internal API allows for mini and “thinking” variants to be dynamically routed based on query complexity—affording cost and speed optimizations without sacrificing quality.

Extended Reasoning, Hallucination, and Factual Accuracy

GPT-5's extended reasoning mode, internally dubbed “thinking,” catalyzes large gains not only in accuracy but also in the interpretability of long and ambiguous queries. Chain-of-thought approaches, which prompt the model to clarify its logic before proposing an answer, see boost results of 20–60 percentage points in both math and code benchmarks relative to non-reasoning baselines. For instance, SWE-bench gains up to 22.1% and Aider Polyglot up to 61.3% when reasoning is enabled. This shows that the core leap isn't just raw parameter count but new meta-learning techniques and prompt architectures.

Key advances in GPT-5 include:
- Significantly fewer hallucinations: The hallucination rate on open-ended fact-seeking benchmarks (e.g., LongFact, FActScore) is ~6 times lower in GPT-5 than o3 and notably lower than GPT-4. Many failure classes—such as claiming to fix non-existent APIs or misreporting type signatures—are greatly reduced.
- Greater honesty: Where earlier models would confidently assert the completion of impossible or underspecified tasks, GPT-5 more reliably admits limitations—vital for production-grade coding use where silent failures are unacceptable.
- Decreased sycophancy: Benchmark tests aimed at eliciting over-agreement or excessive flattery show GPT-5 is less likely to give spurious affirmations, with sycophantic completions dropping from 14.5% to below 6%.

The impact on real-world workflows is clear: less time spent checking for “AI mistakes,” more reliable code and reasoning drafts, and less risk of critical errors in mission-critical domains.

Multimodal and Cross-Disciplinary Reasoning

GPT-5's design incorporates much deeper multimodality. It can fluently process and synthesize context that spans source code, annotated diagrams, tabular data, and even visual puzzles—a previously elusive AI goal often called “cross-domain agentic reasoning”. In practice, this augments debugging and code comprehension in complex codebases where unit tests, stack traces, screenshots, and architecture diagrams all need to be reasoned over simultaneously.

A developer can, for example:
- Submit screenshots and associated code, obtaining both a fix and an explanation that ties visual context to code logic.
- Provide database schemas, API documentation, and logs; receive not just suggested patches, but end-to-end integration tests and clarifying commentary.
- Ask for explanations accounting for past bug history, version diff context, and requirements gathering in long product cycles—a task that evaded previous models due to context window and retention limitations.

The increase in token and output capacity (up to 400,000 for input, 128,000 for output with Pro access) means that huge projects and entire repositories can fit in a single window for holistic reasoning—a distinct practical improvement for enterprise and research use.

Performance in Research, Education, and Theory

While GPT-5's utility in commercial and enterprise coding is now widely acknowledged, its impact on research mathematics, university STEM education, and theoretical fields is equally significant. Teachers, researchers, and competition solvers report that GPT-5:
- Offers stepwise explanations for advanced math olympiad problems, with accurate use of symbolic notation and clear justification—a step up from GPT-4, which often skipped steps or introduced errors when forced beyond memory.
- Consistently proposes cleaner and more usable scripts in open-source research software, survey analysis, and data engineering contexts, helping newcomers and experts alike focus on concept mastery rather than battling obscure code errors.

For graduate-level science and engineering, extended benchmarks such as GPQA now spotlight GPT-5's ability to pass or best human-level performance in content areas like physics derivations, advanced statistics, and algorithm complexity analysis—many of which previously required expert human oversight.

Areas of Ongoing Limitation

Not every area sees uniform progress with GPT-5, as noted by reviewers and developers. Specific weaknesses include:
- For highly creative or UI-heavy implementations, GPT-5 may still output skeleton code requiring considerable human refinement—a limitation shared with prior generations.
- In edge-case programming domains or with highly specialized stacks, GPT-5 sometimes regresses in stylistic or convention-heavy outputs, especially compared to new-surge specialized models (such as some iterations of Anthropic and Sonnet-4).
- Areas such as speculative design, jazz-like or intentionally ambiguous logic, or novel code idioms may still require close human supervision and iterative prompt engineering.

Practical Takeaways for Power Users

The net result for advanced users in mathematics and coding:
- Upgrade to GPT-5 for workloads demanding robust, end-to-end cognitive assistance: vast codebases, critical bug triage, multi-modal debugging, and complex mathematical work get easier and more accurate.
- Leverage the “thinking” variant for all high-value, multi-step, or open-ended queries in mathematics and engineering to maximize factual accuracy and minimize hallucinations.
- Use mini and tool-aided variants for cost-sensitive, high-throughput, or bulk-code-generation workflows.

For researchers, power-coders, and theorists, GPT-5 represents a concrete step toward AI as an agentic partner, not just a suggestion engine—able to reason, critique, and build in collaboration with users at or above the level of specialist practitioners in core STEM fields.