On this article, you’ll learn the way GPT-5 handles intermediate to superior mathematical reasoning, together with fixing methods of equations and establishing clear, textbook-style proofs.
Matters we’ll cowl embody:
- A fast, methodical warmup on fixing a 2×2 linear system.
- Proofs about monotonicity and performance ranges, written clearly and rigorously.
- Dialogue of response high quality, tone, and the place the mannequin nonetheless feels mechanical.
Let’s get proper to it.
Is ChatGPT-5 Capable of Present Proofs for Superior Arithmetic?
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Introduction
One of many claims made by OpenAI concerning its newest mannequin, GPT-5, is a breakthrough in reasoning for math and logic, with the flexibility to “suppose” extra deeply when a immediate advantages from cautious evaluation. This contains advanced, human-like reasoning settings corresponding to coding, science questions, synthesizing data, or analyzing monetary knowledge. In arithmetic, the mannequin reportedly achieved a 94.6% success fee on math downside fixing on the AIME 2025 worldwide convention, with out counting on exterior instruments, demonstrating vital enhancements over earlier variations.
This text showcases — by examples of intermediate to superior mathematical reasoning — how the newest model of ChatGPT tackles advanced mathematical issues with sturdy accuracy and a notably methodical analytical method. We additionally present a quick dialogue concerning the habits exhibited within the responses obtained.
Disclaimer: whereas the intention right here is to not go so far as proven on this Reddit publish that claims ChatGPT-5 innovated by creating “new math,” we’ll briefly analyze the mannequin’s capabilities to construct elaborate, stable proofs for a wide range of issues.
Warmup: Fixing a System of Linear Equations
We are going to begin with one thing light and purely methodological earlier than transferring to a more difficult downside: fixing a system of two linear equations with two variables, x
and y
.
The system is as follows (taken from these lecture notes):
5x − 2y = 7 −2x + y = 3 |
And the immediate is straightforward, leaving the mannequin free to decide on its reasoning method:
Remedy the next system of linear equations: (adopted by the above system as such)
That is the response ChatGPT returns:

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Not solely did the mannequin clear up the system accurately, with x = 13
and y = 29
because the true answer—it additionally confirmed a transparent step-by-step technique (e.g. substitution or elimination) and saved the algebra tidy.
Apparently, if we additionally ask ChatGPT to decide on probably the most environment friendly technique from the accessible ones to unravel the system—and to justify the selection — it’d (and did, in my case) produce two potential solutions and allow you to choose your most well-liked one.

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Each solutions resort to the identical technique — elimination — which reveals how ChatGPT stays prompt-oriented and logically constant fairly than “artistic” for its personal sake (for instance, by deliberately producing two completely different strategies). The step-by-step reasoning can also be comparable in each circumstances, with the primary distinction being the fashion used to justify elimination.
A Bit Extra Problem: Examples of Mathematical Proofs
Shifting into extra superior, university-level math, we requested ChatGPT to assemble proofs with out offering particular instance features:
Show that the composition of any two reducing features is rising.
With out explicitly activating one in every of ChatGPT’s latest modalities, known as the suppose longer mode, the app supplied a convincing response that reads like a self-contained proof.

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It may be simply verified—through options accessible on the Internet, corresponding to this instance—that GPT-5 dealt with this problem cleanly.
Right here’s one other instance.
Let g(x) = 2x + 3x for |x| ≤ 1. (So the area of g is [−1, 1].) Show that the vary of g is precisely [5/6, 5].

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And the proof is, certainly, annoyingly right! There’s nothing incorrect with it, and there’s little to nitpick. General, the proof construction is full and flows logically. Additional, it accurately identifies the important thing properties of g(x): monotonicity, continuity, and differentiability. If we wished to be choosy, the narrative stays considerably mechanical and low-engagement (e.g. it may embody pleasant signposts corresponding to “right here comes the tough half” or “the subsequent step is simple to digest”). To be honest, although, a proper, impartial tone is commonly acceptable for presenting a proof. Past tone, there’s little to query from a mathematical standpoint.
Wrapping Up
This text illustrated intermediate to superior mathematical reasoning and problem-solving by OpenAI’s latest mannequin, GPT-5. By means of a couple of examples, the mannequin’s accuracy and methodical depth have been on show, adopted by temporary reflections on its outcomes and the method used to generate them.