Some theorems may only ever be provable by unintelligible case-by-case brute force; the four colour theorem still has no conceptually elegant proof.

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• A proof and an explanation are different things, and a theorem can stay an unsolved expository problem long after it is proved. GSGrant Sanderson30 Jun 2026
• Struggling with a hard problem before being shown the answer is not always the best way to learn; a hint or a worked example can beat floundering. SYScott H. Young22 Jul 2026
• On P versus NP, the evidence leans towards no, and the problem is unusual in how many approaches have been proven not to work. TTTerence Tao14 Jun 2025
• The fear that a great theorem will arrive as an incomprehensible proof is misplaced, because once the proof exists as an artifact we can analyse it. TTTerence Tao20 Mar 2026
• The twin prime conjecture is certainly true, the random model gives overwhelming odds of it, and he just cannot prove it. TTTerence Tao14 Jun 2025

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