mathematics

John Stillwell

John Stillwell 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 Stillwell rather than just read about it. In short: John Colin Stillwell (born 1942) is an Australian mathematician on the faculties of the University of San Francisco and Monash University. Biography He was born in Melbourne, Australia and lived there until he went to the Massachusetts Institute of Technology for his doctorate.

Key takeaways

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

Reference excerpt

John Colin Stillwell (born 1942) is an Australian mathematician on the faculties of the University of San Francisco and Monash University.

Biography He was born in Melbourne, Australia and lived there until he went to the Massachusetts Institute of Technology for his doctorate. He received his PhD from MIT in 1970, working under Hartley Rogers, Jr, who had himself worked under Alonzo Church. From 1970 until 2001, he taught at Monash University back in Australia and in 2002 began teaching in San Francisco.

Honors In 2005, Stillwell was the recipient of the Mathematical Association of America's prestigious Chauvenet Prize for his article "The Story of the 120-Cell," Notices of the AMS, January 2001, pp. 17–24. In 2012, he became a fellow of the American Mathematical Society.

Works

Books Stillwell is the author of many textbooks and other books on mathematics including:

Classical Topology and Combinatorial Group Theory, 1980, ISBN 0-387-97970-0 2012 pbk reprint of 1993 2nd edition ISBN 978-0-387-97970-0 Mathematics and Its History, 1989, pbk reprint of 2nd edition 2002; 3rd edition 2010, ISBN 0-387-95336-1 Geometry of Surfaces, 1992, ISBN 0-387-97743-0; 2012 pbk reprint of 1st edition Elements of Algebra: Geometry, Numbers, Equations, 1994, ISBN 0-387-94290-4 Numbers and Geometry, 1998, ISBN 0-387-98289-2 Elements of Number Theory, 2003, ISBN 0-387-95587-9 The Four Pillars of Geometry, 2005, ISBN 0-387-25530-3 Yearning for the Impossible: The Surprising Truths of Mathematics, 2006, ISBN 1-56881-254-X Naive Lie Theory, 2008, ISBN 0-387-98289-2 Roads to Infinity, 2010, ISBN 978-1-56881-466-7 The Real Numbers: An Introduction to Set Theory and Analysis, 2013, ISBN 978-3319015767 Elements of Mathematics: From Euclid to Gödel, 2016, ISBN 978-0691171685 Reverse Mathematics: Proofs from the Inside Out, 2018, ISBN 978-0691177175 A Concise History of Mathematics for Philosophers, 2019, ISBN 978-1108610124 The Story of Proof: Logic and the History of Mathematics, 2022, ISBN 978-0691234366

Selected articles Stillwell, John (1982). "The word problem and the isomorphism problem for groups". Bulletin of the American Mathematical Society. (N.S.). 6 (1): 33–56. doi:10.1090/s0273-0979-1982-14963-1. MR 0634433. Stillwell, John (1983). "Efficient computations in groups and simplicial complexes". Transactions of the American Mathematical Society. 276 (2): 715–727. doi:10.1090/s0002-9947-1983-0688973-8. MR 0688973. Lenard, Andrew; Stillwell, John (1983). "An algorithmically unsolvable problem in analysis". Proceedings of the American Mathematical Society. 88 (1): 129–130. doi:10.1090/s0002-9939-1983-0691292-2. MR 0691292. Stillwell, John (1987). "The occurrence problem for mapping class groups". Proceedings of the American Mathematical Society. 101 (3): 411–416. doi:10.1090/s0002-9939-1987-0908639-5. MR 0908639. Stillwell, John (January 2001). "The Story of the 120-Cell" (PDF). Notices of the AMS. 48 (1): 17–25. Stillwell, John (2012). "Poincaré and the early history of 3-manifolds" (PDF). Bulletin of the American Mathematical Society. (N.S.). 49 (4): 555–576. doi:10.1090/s0273-0979-2012-01385-x.

References

Illustrations

Worked examples

Example 1 — a first encounter with John Stillwell

Start with the simplest possible case. Write down what John Stillwell 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 Stillwell 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 Stillwell 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 Stillwell

In research: John Stillwell 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 Stillwell 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 Stillwell is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1942 births, Academic staff of Monash University, Academics from Melbourne, so understanding it makes those chapters shorter.
In everyday life: Look for John Stillwell 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 Stillwell in 20 minutes

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

Frequently asked questions

What is John Stillwell in simple terms?

John Colin Stillwell (born 1942) is an Australian mathematician on the faculties of the University of San Francisco and Monash University. Biography He was born in Melbourne, Australia and lived there until he went to the Massachusetts Institute of Technology for his doctorate.

Why does John Stillwell 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 Stillwell?

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 Stillwell.