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The abc conjecture remains unproven and disputed among mathematicians.

The Claim

The abc conjecture in number theory is true.

Verified by Lenz ·

The Short Version

The abc conjecture has not been established as true. Mainstream mathematics continues to treat it as an open problem because Mochizuki’s proposed proof remains disputed, and recent verification efforts report unresolved issues. This verdict concerns the unsupported assertion of settled truth; no counterexample has proved the conjecture mathematically false.

Caveats

  • “Unproven” does not mean the conjecture has been disproved or that a counterexample exists.
  • Results showing that abc holds “almost always” are weaker than the full universal conjecture.
  • Mochizuki’s publications and affiliated verification efforts are not substitutes for broad independent acceptance of the proof.

The Receipts

  1. A new lower bound in the $abc$ conjecture | Canadian Mathematical Bulletin | Cambridge Core

    cambridge.org

  2. The 𝑎⁢𝑏⁢𝑐 conjecture is true almost always

    arxiv.org

  3. zbmath.org

    zbmath.org

  4. Why is still a conjecture

    math.uni-bonn.de

  5. $1 Million Will Go to the Mathematician Who Busts the 'ABC Conjecture' Theory | Scientific American

    scientificamerican.com

  6. Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

    quantamagazine.org

  7. Effort to solve biggest controversy in mathematics has made no progress | New Scientist

    newscientist.com

  8. ABC conjecture: Mathematicians are bitterly divided over a controversial proof | New Scientist

    newscientist.com

  9. The Weakly Special Conjecture contradicts Orbifold Mordell, and hence the abc conjecture | EMS Press

    ems.press

  10. ABC is Still a Conjecture | Not Even Wrong - Columbia Math Department

    math.columbia.edu

+ 27 more sources — see the full list on Lenz

Filed Under

ABC conjecture

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