mathematics

Graeme Segal

Graeme Segal 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 Graeme Segal rather than just read about it. In short: Graeme Bryce Segal FRS (born 21 December 1941) is an Australian mathematician, and professor at the University of Oxford. Biography Segal was educated at the University of Sydney, where he received his BSc degree in 1961.

Key takeaways

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

Reference excerpt

Graeme Bryce Segal FRS (born 21 December 1941) is an Australian mathematician, and professor at the University of Oxford.

Biography Segal was educated at the University of Sydney, where he received his BSc degree in 1961. He went on to receive his D.Phil. in 1967 from St Catherine's College, Oxford; his thesis, written under the supervision of Michael Atiyah, was titled Equivariant K-theory. His thesis was in the area of equivariant K-theory. The Atiyah–Segal completion theorem in that subject was a major motivation for the Segal conjecture, which he formulated. He has made many other contributions to homotopy theory in the past four decades, including an approach to infinite loop spaces. He was also a pioneer of elliptic cohomology, which is related to his interest in topological quantum field theory. Segal was an Invited Speaker at the ICM in 1970 in Nice and in 1990 in Kyoto. He taught at Oxford University from 1964 to 1990, then became the Lowndean Professor of Astronomy and Geometry at the University of Cambridge from 1990 to 1999, and then a Senior Research Fellow of All Souls College, Oxford from 1999 to 2009. He was elected the President of the London Mathematical Society in 2011. He was elected a Fellow of the Royal Society in 1982 and was awarded the Sylvester Medal by the Royal Society in 2010. At the 2026 ICM, Segal was awarded the Chern Medal "for his visionary mathematical insights that have had an enduring influence in a wide range of fields, including topology, mathematical physics, representation theory and category theory." He is married to writer Marina Warner. They live in London.

Books Loop Groups (Oxford Mathematical Monographs). New ed. Clarendon Press, Oxford 2003, ISBN 0-19-853561-9 (with Andrew Pressley). Lectures on Lie groups and Lie algebras (London Mathematical Society Student texts Vol. 32). 5th ed. Cambridge University Press, Cambridge 2006, ISBN 0-521-49579-2 (with Ian G. Macdonald and Roger Carter).

References

External links Dr Graeme Segal FRS Archived 28 September 2013 at the Wayback Machine, Mathematical Institute, University of Oxford Dr Graeme Segal, All Souls College Graeme Segal at the Mathematics Genealogy Project Topology, Geometry and Quantum Field Theory. Proceedings of the 2002 Oxford Symposium in Honour of the 60th Birthday of Graeme Segal.

Illustrations

Worked examples

Example 1 — a first encounter with Graeme Segal

Start with the simplest possible case. Write down what Graeme Segal 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 Graeme Segal 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 Graeme Segal 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 Graeme Segal

In research: Graeme Segal 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 Graeme Segal 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: Graeme Segal is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1942 births, 20th-century British mathematicians, 21st-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Graeme Segal 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 Graeme Segal in 20 minutes

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

Frequently asked questions

What is Graeme Segal in simple terms?

Graeme Bryce Segal FRS (born 21 December 1941) is an Australian mathematician, and professor at the University of Oxford. Biography Segal was educated at the University of Sydney, where he received his BSc degree in 1961.

Why does Graeme Segal 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 Graeme Segal?

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 Graeme Segal.