mathematics

John G. Thompson

John G. Thompson 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 John G. Thompson rather than just read about it. In short: John Griggs Thompson (born October 13, 1932) is an American mathematician at the University of Florida noted for his work in the field of finite groups. He was awarded the Fields Medal in 1970, the Wolf Prize in 1992, and the Abel Prize in 2008.

Key takeaways

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

Reference excerpt

John Griggs Thompson (born October 13, 1932) is an American mathematician at the University of Florida noted for his work in the field of finite groups. He was awarded the Fields Medal in 1970, the Wolf Prize in 1992, and the Abel Prize in 2008.

Biography Thompson received his Bachelor of Arts from Yale University in 1955 and his doctorate from the University of Chicago in 1959 under the supervision of Saunders Mac Lane. After spending some time on the mathematics faculty at the University of Chicago, he moved to the UK, in 1970, to take up the Rouse Ball Professorship in Mathematics at the University of Cambridge and later moved to the Mathematics Department of the University of Florida as a Graduate Research Professor. He is currently a professor emeritus of pure mathematics at the University of Cambridge, and a professor of mathematics at the University of Florida. He received the Abel Prize in 2008 together with Jacques Tits.

Academic career Thompson's doctoral thesis introduced new techniques and included the solution of a problem in finite group theory which had stood for around sixty years: the nilpotency of Frobenius kernels. At the time, this achievement was noted in The New York Times. Thompson became a figure in the progress toward the classification of finite simple groups. In 1963, he and Walter Feit proved that all nonabelian finite simple groups are of even order (the Odd Order Paper, filling a whole issue of the Pacific Journal of Mathematics). This work was recognised by the award of the 1965 Cole Prize in Algebra of the American Mathematical Society. His N-group papers classified all finite simple groups for which the normalizer of every non-identity solvable subgroup is solvable. This included, as a by-product, the classification of all minimal finite simple groups (simple groups for which every proper subgroup is solvable). This work had some influence on later developments in the classification of finite simple groups, and was quoted in the citation by Richard Brauer for the award of Thompson's Fields Medal in 1970 (Proceedings of the International Congress of Mathematicians, Nice, France, 1970). The Thompson group Th is one of the 26 sporadic finite simple groups. Thompson also made major contributions to the inverse Galois problem. He found a criterion for a finite group to be a Galois group, that in particular implies that the monster simple group is a Galois group.

Awards In 1971, Thompson was elected to the United States National Academy of Sciences. In 1982, he was awarded the Senior Berwick Prize of the London Mathematical Society, and, in 1988, he received the honorary degree of Doctor of Science from the University of Oxford. In 1992 he was awarded the Wolf Prize in Mathematics. Thompson was awarded the United States National Medal of Science in 2000. He is a Fellow of the Royal Society and a recipient of its Sylvester Medal in 1985. He is a member of the Norwegian Academy of Science and Letters.

See also Feit–Thompson theorem McKay–Thompson series Quadratic pair Thompson factorization Thompson order formula Thompson subgroup Thompson transitivity theorem Thompson uniqueness theorem

References

External links O'Connor, John J.; Robertson, Edmund F., "John G. Thompson", MacTutor History of Mathematics Archive, University of St Andrews John G. Thompson at the Mathematics Genealogy Project List of mathematical articles by John G. Thompson Biography from the Abel Prize center Archived 2016-06-11 at the Wayback Machine

Illustrations

Worked examples

Example 1 — a first encounter with John G. Thompson

Start with the simplest possible case. Write down what John G. Thompson 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 John G. Thompson 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 John G. Thompson 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 John G. Thompson

In research: John G. Thompson 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 John G. Thompson 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: John G. Thompson is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1932 births, 20th-century American mathematicians, Abel Prize laureates, so understanding it makes those chapters shorter.
In everyday life: Look for John G. Thompson 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 John G. Thompson in 20 minutes

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

Frequently asked questions

What is John G. Thompson in simple terms?

Why does John G. Thompson 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 John G. Thompson?

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 John G. Thompson.