mathematics

The Mathematical Experience

The Mathematical Experience 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 The Mathematical Experience rather than just read about it. In short: The Mathematical Experience (1981) is a book by Philip J. Davis and Reuben Hersh that discusses the practice of modern mathematics from a historical and philosophical perspective.

Key takeaways

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

Reference excerpt

The Mathematical Experience (1981) is a book by Philip J. Davis and Reuben Hersh that discusses the practice of modern mathematics from a historical and philosophical perspective. The book discusses the psychology of mathematicians, and gives examples of famous proofs and outstanding problems. It goes on to speculate about what a proof really means, in relationship to actual truth. Other topics include mathematics in education and some of the math that occurs in computer science. The first paperback edition won a U.S. National Book Award in Science. It is cited by some mathematicians as influential in their decision to continue their studies in graduate school; and has been hailed as a classic of mathematical literature. On the other hand, Martin Gardner disagreed with some of the authors' philosophical opinions. A new edition, published in 1995, includes exercises and problems, making the book more suitable for classrooms. There is also The Companion Guide to The Mathematical Experience, Study Edition. Both were co-authored with Elena Marchisotto. Davis and Hersh wrote a follow-up book, Descartes' Dream: The World According to Mathematics (Harcourt, 1986), and each has written other books with related themes, such as Mathematics And Common Sense: A Case of Creative Tension by Davis and What is Mathematics, Really? by Hersh.

Notes

References

External links

Book Review of the 1995 edition, by Kenneth C. Millett at the American Mathematical Society. The Mathematical Experience from the Internet Archive

Illustrations

Worked examples

Example 1 — a first encounter with The Mathematical Experience

Start with the simplest possible case. Write down what The Mathematical Experience 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 The Mathematical Experience 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 The Mathematical Experience 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 The Mathematical Experience

In research: The Mathematical Experience 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 The Mathematical Experience 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: The Mathematical Experience is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1981 non-fiction books, Books about mathematics, Collaborative non-fiction books, so understanding it makes those chapters shorter.
In everyday life: Look for The Mathematical Experience 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “The Mathematical Experience” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study The Mathematical Experience in 20 minutes

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

Frequently asked questions

What is The Mathematical Experience in simple terms?

The Mathematical Experience (1981) is a book by Philip J. Davis and Reuben Hersh that discusses the practice of modern mathematics from a historical and philosophical perspective.

Why does The Mathematical Experience 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 The Mathematical Experience?

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 The Mathematical Experience.