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Mathematical proof

Reasoning for mathematical statements

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Philosophy of mathematics (1)
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GPT-5.2 (1) · OpenAI (1) · Mathematical proofs (1) · Scientific research (1) · AI benchmarks (1) · GPQA Diamond (1) · FrontierMath (1) · Technology innovation (1) · mathematical proof (1) · epistemic value (1) · formal correctness (1) · automated theorem provers (1) · artificial intelligence (1) · mathematical logic (1) · arXiv paper (1) · philosophy of mathematics (1)

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A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning that establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning that establish "reasonable expectation".

📰 Related News (2)

🇺🇸 Advancing science and math with GPT-5.2 (2025-12-11)
GPT-5.2 is OpenAI’s strongest model yet for math and science, setting new state-of-the-art results on benchmarks like GPQA Diamond and FrontierMath. T...
🇺🇸 Correctness, Artificial Intelligence, and the Epistemic Value of Mathematical Proof (2026-02-16)
arXiv:2602.12463v1 Announce Type: cross Abstract: We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic val...

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