Joshua Evan Greene

Joshua Greene
Greene outside the Simons-Laufer Mathematical Sciences Institute
Born1981
Alma materPrinceton University (PhD)
University of Chicago (MSc)
Harvey Mudd College (BSc)
Known forLow-dimensional topology
AwardsFrontiers of Science Award (2025)
Levi L. Conant Prize (2023)
Morgan Prize (2002)
Scientific career
FieldsMathematics, geometric topology
InstitutionsBoston College
Columbia University
Thesis Donaldson's Theorem, Heegaard Floer Homology, and Results on Knots (2009)
Doctoral advisorZoltán Szabó
Websitesites.google.com/bc.edu/joshua-e-greene

Joshua Evan Greene (born in 1981) is a mathematician whose primary area of research is low-dimensional topology. He is a professor at Boston College. Greene solved the lens space realization problem, while he and a co-author have made notable advances in the understanding of the inscribed square problem.[1]

Education and career

Greene completed his undergraduate studies at Harvey Mudd College[2] and at the University of Chicago. He received his PhD in mathematics from Princeton University in 2009,[3] with Zoltán Szabó as advisor (thesis: Donaldson's Theorem, Heegaard Floer Homology, and Results on Knots).[4]

After completing his doctoral degree, Greene worked as a NSF Postdoctoral Fellow from 2009 to 2011 at Columbia University. Greene is currently a professor at Boston College.[5]

Mathematical work

In early work, Greene solved the lens space realization problem for knot surgery.[6]

In 2020, together with Andrew Lobb, Greene proved the rectangular peg conjecture.[5][7][8] Later they resolved the cyclic quadrilateral peg problem[7][9][10]


Awards and honors

Greene was awarded the 2002 Morgan Prize for his simple topological proof of Kneser's conjecture. He received the Levi L. Conant Prize in 2023 for his article in the Notices of the American Mathematical Society. His work was featured in the 2021 Current Events Bulletin of the American Mathematical Society.[11] He was a 2024 Simons Fellow in mathematics.[12] Together with Andrew Lobb, in 2025 Greene won a Frontiers of Science Award[13] for their work resolving the rectangular peg problem.


Selected publications

  • Greene, Joshua; Lobb, Andrew (2023). "Cyclic quadrilaterals and smooth Jordan curves". Inventiones Mathematicae. 234: 931–935. doi:10.1007/s00222-023-01212-6.

Further reading


References

  1. ^ "This open problem taught me what topology is". youtube.com.
  2. ^ "Joshua Greene '02 to Receive 2023 Levi L. Conant Prize". www.hmc.edu.
  3. ^ "Alum Joshua Greene *09 to Receive 2023 Conant Prize". www.math.princeton.edu. Retrieved 2025-06-20.
  4. ^ "Joshua Greene - The Mathematics Genealogy Project". www.mathgenealogy.org. Retrieved 2025-06-20.
  5. ^ a b Kevin Hartnett (June 25, 2020), "New Geometric Perspective Cracks Old Problem About Rectangles" (Quanta Magazine) https://www.quantamagazine.org/new-geometric-perspective-cracks-old-problem-about-rectangles-20200625/
  6. ^ "The lens space realization problem" (PDF). annals.math.princeton.edu.
  7. ^ a b "A survey on the square peg problem" (PDF). www.ams.org.
  8. ^ "The rectangular peg problem". annals.math.princeton.edu. 2021.
  9. ^ "What's Happening in the Mathematical Sciences, volume 12". bookstore.ams.org.
  10. ^ "Cyclic quadrilaterals and smooth Jordan curves". springer.com.
  11. ^ "Current Events Bulletin of the AMS 2021" (PDF). www.ams.org.
  12. ^ "2024 Simons Fellows in Mathematics". www.simonsfoundation.org.
  13. ^ "The Frontiers of Science Award 2025". www.icbs.cn.
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