A 2025 Jacobian Conjecture paper revives a long-running open problem in algebra

littmath · x · 2026-07-22

• The post links to a 2025 paper by El Hilany about the Jacobian Conjecture.
• The attached excerpt says the conjecture is true for n = 1 because linear functions have no critical points, but for higher dimensions it remains very hard and there is no consensus on whether it is true.
• The text also notes that several incorrect proofs were published in the 1950s and 1960s, after which the topic went quiet until renewed interest in the 1980s.
• The follow-up links point to a paper by van Essen, a Peter Woit blog post, and a MathOverflow comment from Moh arguing the conjecture may plausibly be false.

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