mathematics

Myles Tierney

Myles Tierney 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 Myles Tierney rather than just read about it. In short: Myles Tierney (September 1937 – 5 October 2017) was an American mathematician and Professor at Rutgers University who founded the theory of elementary toposes with William Lawvere. Tierney obtained his B.A. from Brown University in 1959 and his Ph.D. from Columbia University in 1965.

Key takeaways

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

Reference excerpt

Myles Tierney (September 1937 – 5 October 2017) was an American mathematician and Professor at Rutgers University who founded the theory of elementary toposes with William Lawvere. Tierney obtained his B.A. from Brown University in 1959 and his Ph.D. from Columbia University in 1965. His dissertation, On the classifying spaces for K-Theory mod p, was written under the supervision of Samuel Eilenberg. Following positions at Rice University (1965–66) and ETH Zurich (1966–68), he became an associate professor at Rutgers in 1968. Tierney was named a Fellow of the American Mathematical Society.

Publications Myles Tierney, On the Spectrum of a Ringed Topos, Algebra, Topology and Category Theory, (1976) doi:10.1016/B978-0-12-339050-9.50020-1 André Joyal, Myles Tierney, An extension of the Galois theory of Grothendieck, Memoirs of the American Mathematical Society 51 (1984), no. 309. doi:10.1090/memo/0309 MR 0756176 André Joyal, Myles Tierney, Strong stacks and classifying space, Category theory (Como, 1990), 213—236, Lecture Notes in Math. 1488, Springer 1991. André Joyal, Myles Tierney, On the theory of path groupoids, Journal of Pure and Applied Algebra 149 (2000), no. 1, 69—100, doi:10.1016/S0022-4049(98)00164-9. André Joyal, Myles Tierney, Quasi-categories vs Segal spaces, Categories in algebra, geometry and mathematical physics, 277—326, Contemporary Mathematics 431, American Mathematical Society, Providence, RI, 2007.

Worked examples

Example 1 — a first encounter with Myles Tierney

Start with the simplest possible case. Write down what Myles Tierney 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 Myles Tierney 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 Myles Tierney 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 Myles Tierney

In research: Myles Tierney 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 Myles Tierney 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: Myles Tierney is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1937 births, 2017 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Myles Tierney 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 Myles Tierney in 20 minutes

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

Frequently asked questions

What is Myles Tierney in simple terms?

Why does Myles Tierney 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 Myles Tierney?

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 Myles Tierney.