June Huh

June Huh
Huh at the 2018 International Congress of Mathematicians
June Huh
Born	09 06, 1983
Birthplace	Stanford, California, U.S.
Nationality	American
Occupation	Mathematician, professor
Employer	Princeton University
Known for	Resolution of the Heron–Rota–Welsh conjecture; connections between algebraic geometry and combinatorics
Education	Ph.D., University of Michigan (2014)
Spouse(s)	Nayoung Kim
Children	2
Awards	Fields Medal (2022) MacArthur Fellowship (2022) New Horizons in Mathematics Prize (2019)
Website	[https://web.math.princeton.edu/~huh/ Official site]

June Huh (Template:Lang-ko; born June 9, 1983) is an American mathematician and professor at Princeton University whose work has forged deep and unexpected connections between algebraic geometry and combinatorics. Born in Stanford, California, and raised in South Korea, Huh's path to mathematics was notably unconventional—he aspired first to become a poet and then a science journalist, and did not develop a serious interest in mathematics until his final year as an undergraduate at Seoul National University. A chance encounter with the legendary mathematician Heisuke Hironaka during a lecture series at Seoul National University redirected his academic life entirely. Huh received the Fields Medal in 2022, one of the highest honors in mathematics, for his work applying methods from algebraic geometry to resolve longstanding conjectures in combinatorics, most notably the Heron–Rota–Welsh conjecture. In the same year, he was named a MacArthur Fellow.

Early Life

June Huh was born on June 9, 1983, in Stanford, California, where his parents were residing at the time. He grew up in South Korea, where he attended school. By his own account, Huh showed little early aptitude or interest in mathematics. During his youth, he was drawn to writing and the humanities, harboring ambitions of becoming a poet. His academic trajectory was far from the prodigy narrative commonly associated with Fields Medal recipients; he has been described as a late bloomer whose unconventional journey has challenged assumptions about the typical path to mathematical achievement.

Huh reportedly dropped out of high school at one point, a detail that became part of the broader narrative surrounding his Fields Medal award. He did not follow a conventional academic path through secondary education, and his early educational experiences were marked by a lack of engagement with formal mathematical study. His interests during adolescence and early adulthood centered on writing and literary pursuits rather than the sciences.

It was not until Huh enrolled at Seoul National University that the trajectory of his life began to shift. Even then, he spent an extended period as an undergraduate—approximately six years—before discovering mathematics as a vocation. His transition from aspiring poet and journalist to mathematician was catalyzed by a specific and formative academic encounter that would alter the course of his career.

Education

Huh attended Seoul National University as an undergraduate, where he initially pursued interests outside of mathematics. During what has been described as his sixth year of college, he encountered the work of Heisuke Hironaka, a Japanese mathematician who had won the Fields Medal in 1970 for his resolution of singularities in algebraic geometry. Hironaka was giving a series of lectures at Seoul National University, and Huh, who had been considering a career in science journalism, attended the lectures with the initial intention of writing about Hironaka. The experience instead ignited a deep interest in mathematics itself.

Huh began studying mathematics seriously under Hironaka's mentorship. Despite his nontraditional background, he was accepted into the graduate program in mathematics at the University of Michigan, where he worked under the supervision of Mircea Mustață, a Romanian-American mathematician specializing in algebraic geometry and commutative algebra. Huh completed his doctoral dissertation in 2014, titled Rota's conjecture and positivity of algebraic cycles in permutohedral varieties. The dissertation addressed a central conjecture in combinatorics using techniques drawn from algebraic geometry, foreshadowing the approach that would define much of his subsequent career.

Career

Early research and the chromatic polynomial

Huh's mathematical career began to attract attention even before the completion of his doctoral degree. While still working with Hironaka, he made progress on a conjecture related to the chromatic polynomial of graphs, a foundational object in combinatorics that counts the number of ways to color the vertices of a graph such that no two adjacent vertices share the same color. The conjecture, originally posed by the mathematician Ronald Read in 1968, stated that the absolute values of the coefficients of the chromatic polynomial of any graph form a log-concave sequence—meaning that each coefficient is at least as large as the geometric mean of its neighbors.

Using methods inspired by algebraic geometry, Huh proved Read's conjecture for a broad class of graphs. This result was striking not only for its mathematical content but also for the methods employed: Huh brought techniques from a seemingly distant area of mathematics—algebraic geometry—to bear on a problem in combinatorics, a field more commonly associated with discrete and enumerative reasoning. This early work established the methodological signature that would characterize Huh's subsequent contributions.

The Heron–Rota–Welsh conjecture

The central achievement for which Huh received the Fields Medal was his work, conducted with collaborators, on the Heron–Rota–Welsh conjecture. This conjecture, formulated independently by several mathematicians including Gian-Carlo Rota and Dominic Welsh, concerned the log-concavity of the characteristic polynomial of matroids, which are abstract combinatorial structures that generalize the notion of linear independence from linear algebra.

The conjecture had resisted proof for decades and was considered one of the major open problems in combinatorics. Huh's approach was to establish an analogy between the combinatorial properties of matroids and the geometric properties of algebraic varieties—specifically, to construct algebraic-geometric objects whose properties could be analyzed using tools such as Hodge theory, which originated in the study of the topology of complex algebraic varieties.

In a series of papers, Huh and his collaborators—including Karim Adiprasito and Eric Katz—developed a combinatorial Hodge theory that applied to matroids, even those that do not arise from any geometric or linear-algebraic setting (so-called non-representable matroids). This work culminated in the full resolution of the Heron–Rota–Welsh conjecture, establishing that the coefficients of the characteristic polynomial of any matroid form a log-concave sequence.

The significance of this achievement was twofold. First, it resolved a major conjecture that had been open for more than forty years. Second, and perhaps more fundamentally, it demonstrated that deep structural properties of algebraic geometry—properties that had been thought to depend on the existence of an underlying geometric space—could be extended to purely combinatorial settings. This conceptual advance opened new avenues of research and suggested that the boundary between geometry and combinatorics was more porous than previously understood.

Academic positions

Following the completion of his Ph.D. at the University of Michigan in 2014, Huh held several academic positions. He was a member of the Institute for Advanced Study in Princeton, New Jersey, a research institution that has hosted many of the world's leading mathematicians and scientists. He subsequently joined the faculty of Princeton University as a professor of mathematics, the position he held at the time of his Fields Medal award in 2022. He also held a professorship at Stanford University.

Subsequent research directions

In the years following his Fields Medal, Huh has continued to broaden his research interests. In a 2025 interview, he discussed the evolving landscape of mathematics and artificial intelligence, noting that an "AI that doesn't understand everyday conversation is evolving in a different direction than humanity." Huh has indicated that in the period since receiving the Fields Medal, he has worked to shed the pressure associated with the award and to broaden his research horizons.

Mathematical approach and methodology

Huh's work has been characterized by an approach that draws on deep analogies between disparate branches of mathematics. His use of algebraic geometry—particularly Hodge theory and the theory of algebraic cycles—to address problems in combinatorics represented a methodological innovation that has influenced the work of other researchers in both fields. Professor Sang-il Oum, a colleague at the Korea Advanced Institute of Science and Technology, described Huh's contribution as solving "intractable combinatorial problems with algebraic geometry," emphasizing the originality of Huh's interdisciplinary approach.

Rather than working within the established frameworks of either algebraic geometry or combinatorics in isolation, Huh developed new theoretical infrastructure—most notably a version of Hodge theory applicable to combinatorial settings—that allowed the transfer of ideas between the two fields. This approach has been described as yielding "profound insights" into the structural properties shared by geometric and combinatorial objects.

Personal Life

Huh is married to Nayoung Kim. The couple has two children. Huh has spoken publicly about his unconventional path to mathematics, including his early aspirations in writing and his extended undergraduate career. His personal narrative—from high school dropout and aspiring poet to Fields Medalist—has received considerable attention in media coverage of his achievements, and he has been cited as an example challenging the stereotype that mathematical talent must manifest early in life.

In interviews, Huh has described his working style as slow and contemplative, preferring to think deeply about a small number of problems rather than working rapidly across many areas. He has noted that he finds inspiration in the aesthetic qualities of mathematical structures and in the unexpected connections between seemingly unrelated areas of mathematics.

Recognition

Huh has received several major awards and honors for his mathematical work.

In 2019, he received the New Horizons in Mathematics Prize, awarded by the Breakthrough Prize foundation to early-career researchers who have made significant contributions to mathematics.

In July 2022, the International Mathematical Union awarded Huh the Fields Medal at the International Congress of Mathematicians. The Fields Medal, awarded every four years to mathematicians under the age of 40, is one of the most prestigious distinctions in the discipline. The citation recognized Huh's work in "bringing the ideas of Hodge theory to combinatorics, the ## of log-concavity of the characteristic polynomial of matroids, and the development of Lorentzian polynomials." Huh was one of four recipients of the Fields Medal in 2022; the award ceremony was noted for also including Maryna Viazovska, only the second woman to receive the honor.

In October 2022, the John D. and Catherine T. MacArthur Foundation named Huh a MacArthur Fellow, recognizing his "creative approaches to mathematical puzzles" and his innovative use of geometric methods to solve combinatorial problems. The MacArthur Fellowship, colloquially known as the "genius grant," provides unrestricted funding to individuals who have demonstrated exceptional creativity in their fields.

Legacy

Huh's contributions to mathematics have had a significant impact on the fields of algebraic geometry and combinatorics. His resolution of the Heron–Rota–Welsh conjecture, in collaboration with Adiprasito and Katz, demonstrated that techniques from Hodge theory—previously thought to be applicable only in geometric contexts—could be extended to purely combinatorial settings. This conceptual breakthrough has opened new research directions and has inspired further work exploring the boundary between algebraic geometry and discrete mathematics.

Beyond his specific mathematical results, Huh's career trajectory has attracted attention as a counterexample to the prevailing narrative in mathematics that significant contributions require early exposure and prodigious talent from childhood. His path from a student with little interest in mathematics to a Fields Medalist has been cited in discussions about the diversity of pathways into mathematical research and the role of mentorship in nurturing mathematical talent. His encounter with Hironaka at Seoul National University has been described as a pivotal moment, illustrating how exposure to mathematical ideas at any stage can catalyze a productive career.

Huh's methodological approach—building bridges between algebraic geometry and combinatorics through the development of new theoretical tools such as combinatorial Hodge theory and Lorentzian polynomials—has been recognized as a model for interdisciplinary work within mathematics. The International Mathematical Union's laudatio for his Fields Medal emphasized the "surprising and deep" nature of the connections he established between these fields. His work continues to influence ongoing research in both algebraic geometry and combinatorics, and the tools he developed are being applied by other mathematicians to related problems.