mathematics

James Arthur (mathematician)

James Arthur (mathematician) 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 James Arthur (mathematician) rather than just read about it. In short: James Greig Arthur (born May 18, 1944) is a Canadian mathematician working on automorphic forms, and former President of the American Mathematical Society. He is a Mossman Chair and University Professor Emeritus at the University of Toronto Department of Mathematics.

Key takeaways

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

Reference excerpt

James Greig Arthur (born May 18, 1944) is a Canadian mathematician working on automorphic forms, and former President of the American Mathematical Society. He is a Mossman Chair and University Professor Emeritus at the University of Toronto Department of Mathematics. He won the Wolf Prize in 2015 "for his monumental work on the trace formula and his fundamental contributions to the theory of automorphic representations of reductive groups".

Education and career Born in Hamilton, Ontario, Arthur graduated from Upper Canada College in 1962, received a BSc from the University of Toronto in 1966, and a MSc from the same institution in 1967. He received his PhD from Yale University in 1970. He was a student of Robert Langlands; his dissertation was Analysis of Tempered Distributions on Semisimple Lie Groups of Real Rank One. Arthur taught at Yale from 1970 until 1976. He joined the faculty of Duke University in 1976. He has been a professor at the University of Toronto since 1978. He was four times a visiting scholar at the Institute for Advanced Study between 1976 and 2002.

Contributions Arthur is known for the Arthur–Selberg trace formula, generalizing the Selberg trace formula from the rank-one case (due to Selberg himself) to general reductive groups, one of the most important tools for research on the Langlands program. He also introduced the Arthur conjectures. His seminal 2013 book The endoscopic classification of representations—orthogonal and symplectic groups uses the trace formula to establish important special cases of the Langlands Functoriality Principle.

Recognition Arthur was elected a Fellow of the Royal Society of Canada in 1981 and a Fellow of the Royal Society in 1992. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 2003. In 2012 he became a fellow of the American Mathematical Society. He was elected as a fellow of the Canadian Mathematical Society in 2019.

References

Further reading Langlands, Robert P. (2001). "The trace formula and its applications: an introduction to the work of James Arthur". Canadian Mathematical Bulletin. 44 (2): 160–209. doi:10.4153/CMB-2001-020-8. ISSN 0008-4395. MR 1827854. S2CID 124942105.

External links James Arthur at the Mathematics Genealogy Project Collected works of James Arthur at the Clay institute, with full text of all articles Archive of Collected Works of James Arthur at the University of Toronto Department of Mathematics Wolf Prizes 2015 Author profile in the database zbMATH

Worked examples

Example 1 — a first encounter with James Arthur (mathematician)

Start with the simplest possible case. Write down what James Arthur (mathematician) 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 James Arthur (mathematician) 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 James Arthur (mathematician) 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 James Arthur (mathematician)

In research: James Arthur (mathematician) 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 James Arthur (mathematician) 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: James Arthur (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1944 births, 20th-century Canadian mathematicians, 21st-century Canadian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for James Arthur (mathematician) 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 James Arthur (mathematician) in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what James Arthur (mathematician) 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.
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Frequently asked questions

What is James Arthur (mathematician) in simple terms?

Why does James Arthur (mathematician) 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 James Arthur (mathematician)?

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 James Arthur (mathematician).