mathematics

Richard Borcherds

Richard Borcherds 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 Richard Borcherds rather than just read about it. In short: Richard Ewen Borcherds (; born 29 November 1959) is a British mathematician currently working in quantum field theory. He is known for his work in lattices, group theory, and infinite-dimensional algebras, for which he was awarded the Fields Medal in 1998.

Key takeaways

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

Reference excerpt

Richard Ewen Borcherds (; born 29 November 1959) is a British mathematician currently working in quantum field theory. He is known for his work in lattices, group theory, and infinite-dimensional algebras, for which he was awarded the Fields Medal in 1998. He is well known for his proof of monstrous moonshine using ideas from string theory.

Early life and education Borcherds was born in Cape Town, South Africa, but the family moved to Birmingham in the United Kingdom when he was six months old. Borcherds was educated at King Edward's School, Birmingham. As a student, Borcherds won a gold medal, silver medal, and special prize in the International Mathematical Olympiad. He attended university at Trinity College, Cambridge, where he studied under John Horton Conway.

Career After receiving his doctorate in 1985, Borcherds has held various alternating positions at Cambridge and the University of California, Berkeley, serving as Morrey assistant professor of mathematics at Berkeley from 1987 to 1988. He was a Royal Society University Research Fellow. From 1996 he held a Royal Society Research Professorship at Cambridge before returning to Berkeley in 1999 as professor of mathematics.

Mathematical work He did notable work on the Monstrous moonshine theory. He introduced vertex algebras.

Autism An interview with Simon Singh for The Guardian, in which Borcherds suggested he might have some sort of traits possibly associated with Asperger syndrome, led to a chapter about him in a book on autism by Simon Baron-Cohen. Baron-Cohen insinuated that while Borcherds may have had autistic traits, he did not meet a formal diagnosis of Asperger's syndrome.

Awards and honours In 1992 Borcherds was one of the first recipients of the EMS prizes awarded at the first European Congress of Mathematics in Paris, and in 1994 he was an invited speaker at the International Congress of Mathematicians in Zurich. In 1994, he was elected to be a Fellow of the Royal Society. In 1998 at the 23rd International Congress of Mathematicians in Berlin, Germany he received the Fields Medal together with Maxim Kontsevich, William Timothy Gowers and Curtis T. McMullen. The award cited him "for his contributions to algebra, the theory of automorphic forms, and mathematical physics, including the introduction of vertex algebras and Borcherds' Lie algebras, the proof of the Conway-Norton moonshine conjecture and the discovery of a new class of automorphic infinite products." In 2012 he became a fellow of the American Mathematical Society, and in 2014 he was elected to the National Academy of Sciences.

References

Further reading Conway and Sloane, Sphere Packings, Lattices and Groups, Third Edition, Springer, 1998 ISBN 0-387-98585-9. Frenkel, Lepowsky and Meurman, Vertex Operator Algebras and the Monster, Academic Press, 1988 ISBN 0-12-267065-5. Kac, Victor, Vertex Algebras for Beginners, Second Edition, AMS 1997 ISBN 0-8218-0643-2. O'Connor, John J.; Robertson, Edmund F., "Richard Borcherds", MacTutor History of Mathematics Archive, University of St Andrews Mark Ronan (2007), Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics, Oxford University Press.

External links

Richard Borcherds's publications indexed by the Scopus bibliographic database. (subscription required) Richard Borcherds's results at International Mathematical Olympiad Richard E Borcherds' channel at YouTube

Illustrations

Worked examples

Example 1 — a first encounter with Richard Borcherds

Start with the simplest possible case. Write down what Richard Borcherds 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 Richard Borcherds 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 Richard Borcherds 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 Richard Borcherds

In research: Richard Borcherds 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 Richard Borcherds 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: Richard Borcherds is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1959 births, 20th-century British mathematicians, 21st-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Richard Borcherds 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 Richard Borcherds in 20 minutes

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

Frequently asked questions

What is Richard Borcherds in simple terms?

Why does Richard Borcherds 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 Richard Borcherds?

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 Richard Borcherds.