Living in the Math World Means Threading the Needle

2 days ago

Hong Wang and Joshua Zahl proved the 3D Kakeya conjecture in 2025, a major result in harmonic analysis, geometric measure theory, and PDEs.
Wang's proof earned her numerous prizes, including the Fields Medal in 2026, making her just the third female winner in the medal's history.
Born in Guilin, China, Wang showed early mathematical talent, solving a tree-planting puzzle at age 6 and later skipping grades.
She initially struggled with self-doubt, switching to architecture briefly before recommitting to math, eventually earning a PhD at MIT under Larry Guth.
The Kakeya conjecture concerns whether sets of line segments pointing in all directions in space must occupy the full dimension of that space; Wang and Zahl proved it for 3D.
Wang's dedication to math is intense, with little time for hobbies, but she maintains balance through yoga, friends, and morning walks.
The proof used a strategy of analyzing 'sticky' Kakeya sets and an inductive argument to show all Kakeya sets are 3D.
Wang now faces increased recognition and pressure but remains focused on future problems, including the 4D Kakeya conjecture.

Chinese woman Hong Wang wins Fields Medal for the first time, marking third woman ever to win in 90 years.
Two Chinese mathematicians, Hong Wang and Yu Deng, win simultaneously, a first for China.
Award recognizes work on Kakeya conjecture (Wang) and axiomatizing physics (Deng).

A mathematician solved an 87-year-old mathematical problem (the Jacobian conjecture) with AI and announced it via tweet.
The Jacobian conjecture, set in 1939 and on a list of 21st-century tough problems, was proven false with a 216-character counterexample.
The AI used was likely Anthropic's Claude Fable 5, credited by the mathematician for helping during the World Cup final.

The Fields Medal recognizes outstanding mathematical achievement and future promise.
Funded by a trust established by J.C. Fields, with additional support for 2026 from the Fields Institute.
Awarded for work in partial differential equations, including derivation of the Boltzmann equation and wave kinetic equations.

Kepler discovered planetary motion laws through a blend of creativity and data analysis, not solely through genius.
AI reduces the cost of generating scientific ideas, shifting the bottleneck to verification and validation.
The verification loop for correct scientific theories can span decades, often with initially worse predictions.

OpenAI's unreleased Astra model solved ten major open mathematics problems, including high-dimensional sphere packing, binary codes, non-sofic groups, Connes's rigidity conjecture, arithmetic circuit complexity, quantum parallel repetition, closest vector problem, Ehrhart's volume conjecture, multicolor Ramsey numbers, and extremal number conjectures.
The results were achieved at a cost of roughly $2,000 in compute using an internal version of Astra, with Lean formalizations and human-prepared manuscripts.
Some of these problems were also solvable by earlier models like Sol and Fable when pointed to the specific questions, indicating a degree of 'mathematical proofs overhang'.

Chinese woman Hong Wang wins Fields Medal for the first time, marking third woman ever to win in 90 years.
Two Chinese mathematicians, Hong Wang and Yu Deng, win simultaneously, a first for China.
Award recognizes work on Kakeya conjecture (Wang) and axiomatizing physics (Deng).

A mathematician solved an 87-year-old mathematical problem (the Jacobian conjecture) with AI and announced it via tweet.
The Jacobian conjecture, set in 1939 and on a list of 21st-century tough problems, was proven false with a 216-character counterexample.
The AI used was likely Anthropic's Claude Fable 5, credited by the mathematician for helping during the World Cup final.

The Fields Medal recognizes outstanding mathematical achievement and future promise.
Funded by a trust established by J.C. Fields, with additional support for 2026 from the Fields Institute.
Awarded for work in partial differential equations, including derivation of the Boltzmann equation and wave kinetic equations.

Kepler discovered planetary motion laws through a blend of creativity and data analysis, not solely through genius.
AI reduces the cost of generating scientific ideas, shifting the bottleneck to verification and validation.
The verification loop for correct scientific theories can span decades, often with initially worse predictions.

OpenAI's unreleased Astra model solved ten major open mathematics problems, including high-dimensional sphere packing, binary codes, non-sofic groups, Connes's rigidity conjecture, arithmetic circuit complexity, quantum parallel repetition, closest vector problem, Ehrhart's volume conjecture, multicolor Ramsey numbers, and extremal number conjectures.
The results were achieved at a cost of roughly $2,000 in compute using an internal version of Astra, with Lean formalizations and human-prepared manuscripts.
Some of these problems were also solvable by earlier models like Sol and Fable when pointed to the specific questions, indicating a degree of 'mathematical proofs overhang'.

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