mathematics

John H. Coates

John H. Coates 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 H. Coates rather than just read about it. In short: John Henry Coates (26 January 1945 – 9 May 2022) was an Australian mathematician who was the Sadleirian professor of pure mathematics at the University of Cambridge in the United Kingdom from 1986 to 2012. Early life and education Coates was born the son of J.

Key takeaways

John H. Coates 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 H. Coates to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of John H. Coates from memory before moving on to harder problems.

Reference excerpt

John Henry Coates (26 January 1945 – 9 May 2022) was an Australian mathematician who was the Sadleirian professor of pure mathematics at the University of Cambridge in the United Kingdom from 1986 to 2012.

Early life and education Coates was born the son of J. H. Coates and B. L. Lee on 26 January 1945 and grew up in Possum Brush (near Taree) in New South Wales, Australia. Coates Road in Possum Brush is named after the family farm on which he grew up. Before university he spent a summer working for BHP in Newcastle, New South Wales, though he was not successful in gaining a university scholarship with the company. Coates attended Australian National University on scholarship as one of the first undergraduates, from which he gained a BSc degree. He then moved to France, doing further study at the École Normale Supérieure in Paris, before moving again, this time to England.

Career In England he did postgraduate research at the University of Cambridge, his doctoral dissertation being on p-adic analogues of Baker's method. In 1969, Coates was appointed assistant professor of mathematics at Harvard University in the United States, before moving again in 1972 to Stanford University where he became an associate professor. In 1975, he returned to England, where he was made a fellow of Emmanuel College, and took up a lectureship. Here he supervised the PhD of Andrew Wiles, and together they proved a partial case of the Birch and Swinnerton-Dyer conjecture for elliptic curves with complex multiplication. In 1977, Coates moved back to Australia, becoming a professor at the Australian National University, where he had been an undergraduate. The following year, he moved back to France, taking up a professorship at the University of Paris XI at Orsay. In 1985, he returned to the École Normale Supérieure, this time as professor and director of mathematics. From 1986 until his death, Coates worked in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) of the University of Cambridge. He was head of DPMMS from 1991 to 1997. His research interests included Iwasawa theory, number theory and arithmetical algebraic geometry. He served on the Mathematical Sciences jury for the Infosys Prize in 2009.

Awards and honours Coates was elected a fellow of the Royal Society of London in 1985, and was President of the London Mathematical Society from 1988 to 1990. The latter organisation awarded him the Senior Whitehead Prize in 1997, for "his fundamental research in number theory and for his many contributions to mathematical life both in the UK and internationally". His nomination for the Royal Society reads:

Distinguished for his contributions to the theory of numbers, in particular to the study of transcendence, cyclotomic fields and elliptic curves. In addition to his own important contributions he has been a stimulating influence on colleagues and students. Together with his pupil A. Wiles he achieved the first major breakthrough towards a proof of the Birch-Swinnerton-Dyer conjectures.

Personal life and death Coates married Julie Turner in 1966, with whom he had three sons. He collected Japanese pottery and porcelain. He died at his home in Cambridge, on 9 May 2022, at the age of 77.

References

External links Mazur, Barry; Lichtenbaum, Stephen; Wiles, Andrew; Schneps, Leila; Sujatha; Kakde, Mahesh (January 2024). "John Coates (1945–2022): Celebration of a Life" (PDF). Notices of the American Mathematical Society. 71 (1): 46–56. doi:10.1090/noti2844.

Illustrations

Worked examples

Example 1 — a first encounter with John H. Coates

Start with the simplest possible case. Write down what John H. Coates 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 H. Coates 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 H. Coates 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 H. Coates

In research: John H. Coates 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 H. Coates 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 H. Coates is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1945 births, 2022 deaths, 20th-century Australian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for John H. Coates 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 H. Coates in 20 minutes

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

Frequently asked questions

What is John H. Coates in simple terms?

Why does John H. Coates 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 H. Coates?

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 H. Coates.