mathematics

Ravi Vakil

Ravi Vakil 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 Ravi Vakil rather than just read about it. In short: Ravi D. Vakil (born February 22, 1970) is a Canadian-American mathematician working in algebraic geometry.

Key takeaways

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

Reference excerpt

Ravi D. Vakil (born February 22, 1970) is a Canadian-American mathematician working in algebraic geometry. He is the current president of the American Mathematical Society.

Education and career Vakil was born on February 22, 1970. His father was a professor of preventative medicine at the University of Toronto and his mother was a high school math teacher. He later attended high school at Martingrove Collegiate Institute in Etobicoke, Ontario, where he won several mathematical contests and olympiads. After earning a BSc and MSc from the University of Toronto in 1992, he completed a PhD in mathematics at Harvard University in 1997 under Joe Harris. He has since been an instructor at both Princeton University and MIT. Since the fall of 2001, he has taught at Stanford University, becoming a full professor in 2007. The Rising Sea: Foundations of Algebraic Geometry, a mathematical textbook about algebraic geometry by Ravi Vakil, was published in 2025, although drafts were available online ever since he began to write it in 2010.

Contributions Vakil is an algebraic geometer and his research work spans over enumerative geometry, topology, Gromov–Witten theory, and classical algebraic geometry. He has solved several old problems in Schubert calculus. Among other results, he proved that all Schubert problems are enumerative over the real numbers, a result that resolves an issue mathematicians have worked on for at least two decades.

Awards and honors Vakil has received many awards, including an NSF CAREER Fellowship, a Sloan Research Fellowship, an American Mathematical Society Centennial Fellowship, a G. de B. Robinson prize for the best paper published (2000) in the Canadian Journal of Mathematics and the Canadian Mathematical Bulletin, and the André-Aisenstadt Prize from the Centre de Recherches Mathématiques at the Université de Montréal (2005), and the Chauvenet Prize (2014). In 2013 he became a fellow of the American Mathematical Society. Vakil was elected as its president in 2024 and began his two-year term on 1 February 2025.

Mathematics contests He was a member of the Canadian team in three International Mathematical Olympiads, winning silver, gold (perfect score), and gold in 1986, 1987, and 1988 respectively. He was also the fourth person to be a four-time Putnam Fellow in the history of the contest. Also, he has been the coordinator of weekly Putnam preparation seminars at Stanford.

References

External links Ravi Vakil's Home Page Ravi Vakil at the Mathematics Genealogy Project Ravi Vakil's results at International Mathematical Olympiad The Rising Sea | Ravi's notes on algebraic geometry

Illustrations

Worked examples

Example 1 — a first encounter with Ravi Vakil

Start with the simplest possible case. Write down what Ravi Vakil 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 Ravi Vakil 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 Ravi Vakil 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 Ravi Vakil

In research: Ravi Vakil 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 Ravi Vakil 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: Ravi Vakil is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1970 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Ravi Vakil 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.

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How to study Ravi Vakil in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Ravi Vakil 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 Ravi Vakil out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Ravi Vakil in simple terms?

Ravi D. Vakil (born February 22, 1970) is a Canadian-American mathematician working in algebraic geometry.

Why does Ravi Vakil 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 Ravi Vakil?

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 Ravi Vakil.