Breakthrough Tracker record
A counterexample to the Mizohata–Takeuchi conjecture
The paper constructs counterexamples for hypersurfaces not contained in a hyperplane, disproving the Mizohata–Takeuchi conjecture in its stated generality and the related formulation of Stein's conjecture discussed in the paper.
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- Stable ID
math-mizohata-takeuchi-counterexample-2025- Revision
math-mizohata-takeuchi-counterexample-2025.v1- Field
- Mathematics · Harmonic analysis
- Evidence
- Tier 1 · Peer reviewed: No
- Record state
- Current · Expert-supported preprint
- Last checked
AI role
No generative-AI role was disclosed.
Record details
- Problem or result
- Mizohata–Takeuchi conjecture
- Authors
- Hannah Mira Cairo
- Institutions
- Work developed while studying mathematics at UC Berkeley
- Result date
- Preprint submitted February 10, 2025
Why it matters
The result changes which weighted estimates researchers can plausibly pursue in Fourier restriction theory.
Limits
Stronger or more restricted replacement statements may survive. The counterexample should not be described as ending the wider restriction-theory research program.
Sources
- Primary: Hannah Mira Cairo, A Counterexample to the Mizohata–Takeuchi Conjecture
- Independent: Quanta profile and expert context
Correction and revision history
- Added on 2026-07-22 as a counterexample to the conjecture as stated, with restricted successor statements left open.
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