Ravi Vakil
Ravi D. Vakil is a Canadian-American mathematician and a leading figure in algebraic geometry. Born in 1970, the Toronto-raised scholar is the Robert Grimmett Professor of Mathematics at Stanford University and, as of February 2025, the president of the American Mathematical Society. Vakil is renowned for his deep contributions to enumerative geometry and Schubert calculus, and for his influential textbook, The Rising Sea: Foundations of Algebraic Geometry, published in 2025. His exceptional early career as a multiple gold medalist in the International Mathematical Olympiad and a four-time Putnam Fellow established him as one of Canada's most celebrated mathematical prodigies.
Early Life and Education in Canada
Ravi Vakil was born on February 22, 1970, into an academic family in Toronto. His father was a professor of preventative medicine at the University of Toronto, and his mother taught high school mathematics. This environment fostered an early and strong interest in the subject, which flourished at Martingrove Collegiate Institute in Etobicoke, Ontario. His mathematical talent became unmistakably clear through his success in national and international contests, setting the stage for his future career and providing an early indication of the problem-solving prowess that would define his research.
After completing high school, Vakil pursued his undergraduate and master's degrees at the University of Toronto, graduating in 1992. He then moved to Harvard University for his doctoral studies, where he worked under the supervision of distinguished algebraic geometer Joe Harris. Vakil earned his PhD in 1997 with a dissertation that foreshadowed his future work in the complex structures of algebraic geometry. His educational path from a Toronto high school to the pinnacle of American graduate studies illustrates a classic trajectory for top Canadian mathematical talent.
Academic Career and Research
Following his PhD, Vakil held instructor positions at Princeton University and the Massachusetts Institute of Technology. In the fall of 2001, he joined the faculty at Stanford University, where he has remained for the core of his career. He was promoted to full professor in 2007 and now holds the title of Robert Grimmett Professor of Mathematics. His research is centred in algebraic geometry, a field that uses abstract algebra to study geometric objects defined by polynomial equations. Vakil's work has made significant advances across several subfields, including enumerative geometry, topology, and Gromov-Witten theory. One of his most celebrated results solved a long-standing problem in Schubert calculus, a branch of mathematics concerned with counting geometric configurations.
Ravi Vakil proved that all Schubert problems are enumerative over the real numbers. This result resolved an issue mathematicians had worked on for at least two decades. His research spans enumerative geometry, topology, Gromov-Witten theory, and classical algebraic geometry. Beyond research, he coordinates weekly Putnam preparation seminars at Stanford University.
The Rising Sea and Scholarly Influence
A major part of Vakil's contribution to mathematics is his comprehensive textbook, The Rising Sea: Foundations of Algebraic Geometry. He began writing the work in 2010, sharing drafts freely online for over a decade as a dynamic resource for students and researchers worldwide. The book was formally published in 2025, offering a rigorous and modern treatment of the subject's foundations. Its online-first development model made it an influential and widely used reference long before its print release, reflecting Vakil's commitment to open and accessible scholarship. Vakil also maintains a significant digital presence through his conference listing pages, which serve the mathematical community.
For years, he personally maintained a widely used list of upcoming conferences in algebraic geometry. As of 2026, this resource, now powered by MathMeetings.net, is co-maintained with Kristin DeVleming. These lists are essential tools for researchers planning their travel and staying current with developments in the field. His stewardship of these communal resources highlights his role as an organizer and connector within the global mathematics community.
Leadership and Recognition
Ravi Vakil's leadership within the mathematical community reached a peak with his election as president of the American Mathematical Society (AMS). He began his two-year term on February 1, 2025. In this role, he represents one of the world's foremost professional organizations for mathematicians and helps guide its policies and initiatives. His presidency coincides with a period of rapid change in the field, particularly regarding the role of artificial intelligence, a topic on which he has spoken publicly, including at the International Congress of Mathematicians in 2026. His research and exposition have been recognized with numerous prestigious awards throughout his career. These honours reflect both the quality of his mathematical output and his skill in communication.
- NSF CAREER Fellowship (early career award).
- American Mathematical Society Centennial Fellowship.
- G. de B. Robinson Prize (2000) for the best paper in the Canadian Journal of Mathematics and the Canadian Mathematical Bulletin.
- André-Aisenstadt Prize from the Centre de Recherches Mathématiques at the Université de Montréal (2005).
- Chauvenet Prize (2014) for outstanding mathematical exposition.
- Elected Fellow of the American Mathematical Society (2013).
These awards span Canadian, American, and international institutions. For example, he received the André-Aisenstadt Prize from the Centre de Recherches Mathématiques at the Université de Montréal. He also received the Chauvenet Prize from the United States. This highlights the broad respect he commands across the mathematical world.
Mathematical Olympiad and Contest Legacy
Long before his professional career, Ravi Vakil established himself as one of Canada's most accomplished participants in mathematical competitions. He represented Canada in three consecutive International Mathematical Olympiads (IMO), achieving remarkable success. In 1986, he won a silver medal. He followed this with a gold medal in 1987, and in 1988 he achieved a perfect score to win a second gold medal. These results placed him among the elite high school mathematicians in the world and brought recognition to Canada's mathematical training programs. His excellence continued at the university level with the William Lowell Putnam Mathematical Competition, the premier contest for undergraduate mathematics in the United States and Canada.
Ravi Vakil is the fourth person to be a four-time Putnam Fellow in the history of the contest. This distinction is awarded to the top five scorers each year. This rare feat cemented his reputation as a problem-solver of extraordinary ability. His ongoing involvement includes coordinating weekly Putnam preparation seminars at Stanford University.
Engagement with Artificial Intelligence in Mathematics
As president of the AMS, Vakil has been a prominent voice in discussions about the impact of artificial intelligence on mathematical research. In July 2026, he participated in a live podcast recorded at the International Congress of Mathematicians in Philadelphia, alongside mathematicians Akshay Venkatesh and Alex Kontorovich. The discussion, titled "What Is Math For in the Age of AI?", grappled with the major shifts occurring as AI systems begin to produce proofs and solve longstanding problems. Vakil brought a measured perspective to the conversation, acknowledging both the milestones achieved and their potential misinterpretation. He specifically referenced the performance of AI at the International Mathematical Olympiad, where models like AlphaProof won a silver medal in 2024 and DeepThink achieved gold in 2025.
Ravi Vakil noted that AI achievements in competitions were exciting proofs of concept. He emphasized that the true value of such competitions lies in how they encourage millions of students to hone their reasoning skills. His commentary reflects a leader's view on the rise of AI in mathematics. He has discussed the importance of creativity, understanding, and storytelling in the field.
Questions about Ravi Vakil
Where is Ravi Vakil from?
Ravi Vakil is from Toronto, Canada. He was born on February 22, 1970, and attended Martingrove Collegiate Institute in Etobicoke, Ontario. His parents were both educators. His father was a professor at the University of Toronto and his mother was a high school math teacher. Vakil completed his BSc and MSc degrees at the University of Toronto before moving to the United States for his PhD.
What is Ravi Vakil known for?
Ravi Vakil is known for his work in algebraic geometry, particularly in Schubert calculus and enumerative geometry. He proved that all Schubert problems are enumerative over the real numbers, solving a decades-old problem. He is also the author of the influential textbook The Rising Sea: Foundations of Algebraic Geometry. He is celebrated for his exceptional performance as a youth in mathematical contests, winning multiple International Mathematical Olympiad medals.
What is Ravi Vakil's role at the American Mathematical Society?
Ravi Vakil is the president of the American Mathematical Society (AMS). He was elected to this position in 2024 and began his two-year term on February 1, 2025. As president, he leads one of the world's primary professional organizations for mathematicians. In this capacity, he helps shape the society's direction and has been a key voice in contemporary discussions, such as the impact of artificial intelligence on mathematical research.
What awards has Ravi Vakil won?
Ravi Vakil has won many awards. These include an NSF CAREER Fellowship, a Sloan Research Fellowship, and an American Mathematical Society Centennial Fellowship. He won the G. de B. Robinson prize in 2000 and the André-Aisenstadt Prize in 2005. He also received the Chauvenet Prize in 2014 and became a fellow of the American Mathematical Society in 2013.
How did Ravi Vakil perform in math competitions?
Ravi Vakil performed exceptionally well in math competitions. He was a member of the Canadian team in three International Mathematical Olympiads. He won a silver medal in 1986 and gold medals in 1987 and 1988, with a perfect score in 1988. He is also the fourth person to be a four-time Putnam Fellow in the history of that contest.
What is 'The Rising Sea' by Ravi Vakil?
The Rising Sea: Foundations of Algebraic Geometry is a major textbook written by Ravi Vakil. He began writing it in 2010 and made drafts freely available online for over a decade, where it became a widely used resource. The book was formally published in 2025. It provides a comprehensive and modern treatment of the foundations of algebraic geometry and is considered a significant contribution to the mathematical literature and pedagogy.
Sources and further reading
- Ravi Vakil (Wikipedia)
- Topology from Algebraic Geometry by Ravi Vakil (Stanford) (math.uconn.edu)
Checked by the Your Space Hamilton desk. Last updated 2026-10-24.
