Copilot Needs Stronger Mathematical Rigor

I’ve submitted this note via Feedback Hub and are sharing it here to invite discussion or visibility.

As a user who values mathematical precision and structural fidelity, I’ve encountered recurring issues with Copilot’s handling of advanced mathematical topics—especially in algebraic frameworks involving Galois theory, resolvents, and group actions. While Copilot excels in linguistic creativity and dialectal nuance, its mathematical reasoning often includes invented logic, vague generalizations, and unjustified steps.

More concerningly, Copilot can contradict itself within the same chat. The standard disclaimer that “AI can make mistakes” doesn’t begin to capture how wrong the answers can be—especially when the errors are not just factual but structural, undermining the logic of the entire framework. This inconsistency makes it difficult to trust Copilot as a mathematical collaborator.

By contrast, Gemini—while also disclaiming fallibility—often delivers correct, elegant, and structurally sound mathematical responses. I’ve tested both systems side-by-side and can provide examples where Gemini maintains closure and fidelity, while Copilot improvises or contradicts itself.

Specific areas where Copilot needs improvement:

• Explicit group-theoretic formalization, e.g., distinguishing C3 vs S3; providing the correct Galois group of a quartic D4 instead of V4; Using Galois’ approach, when asked, instead of responding with the modern, Artin’s style, field automorphisms fixing the base field; etc.
• Step-by-step logical closure in algebraic derivations
• Minimal counterexample reasoning to trap structure
• Historical fidelity in methods like Cardano and Lagrange resolvents
• Internal consistency across turns and within the same session

Copilot has enormous potential to be a world-class mathematical companion. I’m passionate about using it for deep mathematical exploration, and I hope Microsoft will prioritize tightening the math engine—especially for users who demand rigor, not just fluency. It can be done as Gemini proves.

Thank you for your work and openness to feedback.

—Victor