mathematics

Mary Tiles

Mary Tiles 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 Mary Tiles rather than just read about it. In short: Mary Tiles (born March 6, 1946) is an American philosopher and historian of mathematics and science. From 2006 until 2009, she served as chair of the philosophy department of the University of Hawaii at Manoa.

Key takeaways

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

Reference excerpt

Mary Tiles (born March 6, 1946) is an American philosopher and historian of mathematics and science. From 2006 until 2009, she served as chair of the philosophy department of the University of Hawaii at Manoa. She retired in 2009.

Life At Bristol University, Tiles obtained her B.A. in philosophy and mathematics in 1967, and her Ph.D. in philosophy in 1973, followed by a B.Phil. in philosophy in 1974 at Oxford and a M.A. in 1978 at Cambridge. After positions as lecturer and visiting associate professor at different institutions, Tiles became associate professor of philosophy at University of Hawaii at Manoa in 1989, and full professor in 1992.

Work Tiles' area of work is primarily philosophy and history of logic, mathematics and science, with a special emphasis on French contributions to this area, e.g. by Gaston Bachelard, Georges Canguilhem, Bruno Latour, Michel Foucault, Pierre Bourdieu, Michel Serres, Jean-Claude Martzloff, Karine Chemla, Catherine Jami, and François Jullien. One of her publications is the 1989 book The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise. As the subtitle suggests, it is an example of a book that treats the philosophy of mathematics as inseparable from historical concerns. Despite some criticisms, for its lack of technical detail and correctness, and for pressing the author's philosophical agenda on its readers, it has been recommended as an introductory textbook for undergraduates interested in the philosophy of mathematics.

Bibliography with Hans Oberdiek, Living in a Technological Culture: Human Tools and Human Values, Routledge 1995. with Jim Tiles, An Introduction to Historical Epistemology: The Authority of Knowledge, Oxford 1993. Mathematics and the Image of Reason, Routledge 1991. The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise, Blackwell 1989; reprinted by Dover 2004. Bachelard: Science and Objectivity, Cambridge University Press 1984.

References

Worked examples

Example 1 — a first encounter with Mary Tiles

Start with the simplest possible case. Write down what Mary Tiles 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 Mary Tiles 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 Mary Tiles 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 Mary Tiles

In research: Mary Tiles 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 Mary Tiles 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: Mary Tiles is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1946 births, 20th-century American mathematicians, 20th-century American women mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Mary Tiles 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 Mary Tiles in 20 minutes

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

Frequently asked questions

What is Mary Tiles in simple terms?

Why does Mary Tiles 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 Mary Tiles?

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 Mary Tiles.