Math and logic are one of the areas where AI model capability has genuinely improved the most, and also one of the areas where a wrong answer is easiest to state with total confidence. Evaluating an AI for math and logic work needs a different lens than evaluating one for open-ended writing, because there's usually an actual right answer to check against. That's an advantage, and a trap if you don't actually check.
Why math and logic performance is genuinely uneven across problem types
A model can perform very well on a certain class of problem and poorly on a structurally similar one, particularly once a problem requires holding many steps of reasoning in a specific order without an arithmetic or logical slip anywhere in the chain. Reasoning models, which work through problems step by step before answering, tend to perform meaningfully better on genuinely multi-step problems than models optimized purely for fast response. That makes reasoning depth the single most important evaluation axis for this category.
What to actually evaluate
Reasoning depth versus problem complexity
For simple, single-step calculations, most current models perform reliably. For problems requiring many chained logical or mathematical steps, performance drops off more sharply and unpredictably. That's why testing against your actual problem complexity matters more than a general reputation for "being good at math."
Whether it shows its work, and whether that work is actually checkable
A model that shows its reasoning step by step lets you verify where, if anywhere, it went wrong. That's far more useful for real work than a model that outputs only a final answer with no reasoning to audit. This matters even more than raw accuracy for any use case where a wrong answer has real consequences.
Consistency across repeated attempts at the same problem
The same model, given the same problem, can sometimes reach different answers on different attempts, particularly for genuinely difficult problems near the edge of its reliable capability. If a use case is sensitive to this kind of variance, testing consistency across multiple runs matters as much as testing single-run accuracy.
Whether the specific reasoning effort setting was actually tuned for the task
We've covered this directly in choosing a reasoning effort budget, but it's especially relevant here: a model running at a low reasoning effort setting can underperform its own capability on a hard problem. A fair evaluation has to check that reasoning effort was configured appropriately for the difficulty of what's being tested.
The verification discipline this category specifically needs
Because math and logic problems usually have an objectively checkable answer, this is one of the categories where it's most worth building a verification step: check the model's answer against a known-correct method or a second, independent calculation rather than trusting a single confident output. A wrong mathematical or logical conclusion stated confidently is one of the more consequential failure modes, precisely because confidence is easy to mistake for correctness.
How we approach this
We test math and logic-heavy AI use cases against known-correct answers at the actual complexity level the real work requires, tune reasoning effort deliberately rather than accepting a default, and build in independent verification wherever a wrong answer would have real consequences.