PeopleofSuperintelligence

Researcher

Levent Alpöge

Also known as Levent Hasan Ali Alpöge, Levent Alpoge

Levent Alpöge is a number theorist who has worked with AI tools on mathematical problems. He was named a Churchill Scholar in 2014 and completed a Princeton thesis, Points on Curves, in 2020. From 2021 to 2025 he was a Junior Fellow in the Harvard Society of Fellows, and in 2022 he, Manjul Bhargava, and Ari Shnidman showed that at least about 9.5% of whole numbers are sums of two rational cubes. In July 2026 he presented an explicit counterexample to the Jacobian conjecture, found with AI tools, and in August 2026 he examined Claude's work on the Riemann zeta function. As of October 2026, he is a member of the technical staff at Anthropic.

Timeline

  1. 2014

    A Churchill Scholarship

    He is named a Churchill Scholar in 2014 and plans a year of research in analytic number theory at the University of Cambridge.

  2. 2020

    A Princeton thesis on curves

    His Princeton dissertation, Points on Curves, is completed in 2020 under Manjul Bhargava.

  3. 2021–2025

    Junior Fellow at Harvard

    In 2021 he joins the Harvard Society of Fellows as a Junior Fellow, a post he holds until 2025.

  4. 2022

    Sums of two rational cubes

    In number theory, he, Manjul Bhargava, and Ari Shnidman show that at least about 9.5% and at most about 83% of whole numbers are sums of two rational cubes.

  5. January 2025

    Hilbert's tenth problem over rings

    In a paper with Bhargava, Wei Ho, and Ari Shnidman, he posts a result that implies a negative answer to Hilbert's tenth problem over the ring of integers of any number field.

  6. July 2026

    A Jacobian conjecture counterexample

    Using AI tools, he presents an explicit counterexample to the Jacobian conjecture, a problem posed in 1939.

  7. August 2026

    A Riemann zeta lower bound

    Alongside Ralph Furman, he examines Claude's work, which raises the lower bound on the fraction of Riemann zeta zeros that satisfy the Riemann hypothesis from 41.6% to 67.2%.

  8. As of October 2026

    Technical staff at Anthropic

    He works at Anthropic as a member of the technical staff.

Sources and credits

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  1. Senior wins Churchill Scholarship — Harvard Gazette news.harvard.edu. Checked 14 October 2026.
  2. Levent Alpöge - The Mathematics Genealogy Project mathgenealogy.org. Checked 14 October 2026.
  3. Levent Alpöge - Wikipedia en.wikipedia.org. Checked 14 October 2026.
  4. Mathematical Trio Advances Centuries-Old Number Theory Problem | Quanta Magazine quantamagazine.org. Checked 14 October 2026.
  5. Integers expressible as the sum of two rational cubes arxiv.org. Checked 14 October 2026.
  6. Rank stability in quadratic extensions and Hilbert’s tenth problem for the ring of integers of a number field arxiv.org. Checked 14 October 2026.
  7. Türk Matematikçi Levent Alpöge Kimdir - Borsa Gundem | Finans, Ekonomi, Bitcoin ve Kripto Gündem Haberleri borsagundem.com.tr. Checked 14 October 2026.
  8. Claude has improved on a longstanding lower bound for the fraction of zeros of the Riemann zeta function that satisfy the Riemann hypothesis \ Anthropic anthropic.com. Checked 14 October 2026.
  9. Levent Alpöge alpo.ge. Checked 14 October 2026.