mathematics

John Pardon

John Pardon is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand John Pardon rather than just read about it. In short: John Vincent Pardon (born June 1989) is an American mathematician who works on geometry and topology. He is primarily known for having solved Gromov's problem on distortion of knots, for which he received the 2012 Morgan Prize.

Key takeaways

John Pardon belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect John Pardon to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of John Pardon from memory before moving on to harder problems.

Reference excerpt

John Vincent Pardon (born June 1989) is an American mathematician who works on geometry and topology. He is primarily known for having solved Gromov's problem on distortion of knots, for which he received the 2012 Morgan Prize. He is a permanent member of the Simons Center for Geometry and Physics in Stony Brook, New York. He was awarded the Fields Medal in 2026.

Early life Pardon's mother, Joyce Eileen Maggio Pardon, was a math teacher. She introduced him to basic arithmetic, trigonometry, and calculus. His father, William Pardon, was a mathematics professor at Duke University. Pardon was a three-time gold medalist at the International Olympiad in Informatics, in 2005, 2006, and 2007. In 2007, he placed second in the Intel Science Talent Search competition, with a generalization to rectifiable curves of the carpenter's rule problem for polygons. In the project, he showed that every rectifiable Jordan curve in the plane can be continuously deformed into a convex curve without changing its length and without ever allowing any two points of the curve to get closer to each other. He published this research in the Transactions of the American Mathematical Society in 2009. After high school, Pardon attended Princeton University, where, after his sophomore year, he began taking graduate-level mathematics classes. As a student there, he solved a problem in knot theory posed by Mikhail Gromov in 1983 about whether every knot can be embedded into three-dimensional space with bounded stretch factor. He showed that on the contrary, the stretch factor of certain torus knots could be arbitrarily large. His proof was published in the Annals of Mathematics in 2011, and it earned him the Morgan Prize of 2012. In college, Pardon became fluent in Chinese. He later recalled, "I was signing up for classes as a freshman in college, and I heard Chinese was pretty difficult, so I wanted a challenge." He participated in a Chinese-language immersion program at Princeton and represented the university in an international debate competition in Singapore, broadcast on Chinese television. As a cello player, he was a two-time winner of the Princeton Sinfonia concerto competition. He graduated in 2011 and was the valedictorian of his class. He then went to Stanford University for his graduate studies. His accomplishments there included solving the three-dimensional case of the Hilbert–Smith conjecture. He completed his Ph.D. in 2015, under the supervision of Yakov Eliashberg. In 2015, he was also appointed to a five-year term as a Clay Research Fellow.

Career In the fall of 2016, he became a full professor of Mathematics at Princeton University. He is currently a permanent member of the Simons Center for Geometry and Physics in Stony Brook, New York. In 2023, he proved the Maulik–Nekrasov–Okounkov–Pandharipande (MNOP) conjecture, which posited an equivalence between two different curve enumeration invariants of Calabi–Yau threefolds. He is currently working on a book about the foundations of symplectic geometry.

Awards and honors In 2017, Pardon received the National Science Foundation's Alan T. Waterman Award for his contributions to geometry and topology. He was elected to the 2018 class of fellows of the American Mathematical Society. Also in 2018 he was an invited speaker at the International Congress of Mathematicians (ICM) in Rio de Janeiro. In 2022 he was awarded the Clay Research Award. In 2025, he was awarded the New Horizons in Mathematics Prize. Pardon was awarded the Fields Medal at ICM Philadelphia 2026 for "achievements in symplectic geometry including new approaches to virtual fundamental cycles, Fukaya categories of certain manifolds and counting holomorphic curves, and for his contributions to other areas of geometry and topology, including group actions on 3-manifolds and knot theory".

Personal life Pardon has two sons, Alexandros and Andreas. In the Fields Medal award video produced by the Simons Foundation, Pardon said he quizzes them in Chinese: "I talk to them in Chinese a lot. We learn the characters. I read to them. I make them read to me."

Selected publications Pardon, John (2009), "On the unfolding of simple closed curves" (PDF), Transactions of the American Mathematical Society, 361 (4): 1749–1764, arXiv:0809.1404, doi:10.1090/S0002-9947-08-04781-8, MR 2465815, S2CID 230031 Pardon, John (2011), "On the distortion of knots on embedded surfaces" (PDF), Annals of Mathematics, Second Series, 174 (1): 637–646, arXiv:1010.1972, doi:10.4007/annals.2011.174.1.21, MR 2811613, S2CID 55567836 Pardon, John (2011), "Central limit theorems for random polygons in an arbitrary convex set", Annals of Probability, 39 (3): 881–903, arXiv:1003.4209, doi:10.1214/10-AOP568, MR 2789578 Pardon, John (2013), "The Hilbert–Smith conjecture for three-manifolds" (PDF), Journal of the American Mathematical Society, 26 (3): 879–899, arXiv:1112.2324, doi:10.1090/S0894-0347-2013-00766-3, MR 3037790, S2CID 96422853 Pardon, John (2016). "An algebraic approach to virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves". Geometry & Topology. 20 (2): 779–1034. arXiv:1309.2370. doi:10.2140/gt.2016.20.779. MR 3493097. S2CID 119171219. Pardon, John (2019). "Contact homology and virtual fundamental cycles". Journal of the American Mathematical Society. 32 (3): 825–919. arXiv:1508.03873. doi:10.1090/jams/924. MR 3981989. S2CID 119335098. Pardon, John (2023). "Universally counting curves in Calabi--Yau threefolds". arXiv:2308.02948 [math.AG].

References

External links Home page of John Pardon at Princeton 21 Questions With … John Pardon '11, University Press Club, Princeton

Illustrations

Worked examples

Example 1 — a first encounter with John Pardon

Start with the simplest possible case. Write down what John Pardon claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to John Pardon before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about John Pardon ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of John Pardon

In research: John Pardon appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses John Pardon in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: John Pardon is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1989 births, 21st-century American mathematicians, American geometers, so understanding it makes those chapters shorter.
In everyday life: Look for John Pardon outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study John Pardon in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what John Pardon means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain John Pardon out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is John Pardon in simple terms?

Why does John Pardon matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study John Pardon?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on John Pardon.