mathematics

Paul Althaus Smith

Paul Althaus Smith 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 Paul Althaus Smith rather than just read about it. In short: Paul Althaus Smith (May 18, 1900 – June 13, 1980) was an American mathematician. His name occurs in two significant conjectures in geometric topology: the Smith conjecture, which is now a theorem, and the Hilbert–Smith conjecture, which was proved in dimension 3 in 2013.

Key takeaways

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

Reference excerpt

Paul Althaus Smith (May 18, 1900 – June 13, 1980) was an American mathematician. His name occurs in two significant conjectures in geometric topology: the Smith conjecture, which is now a theorem, and the Hilbert–Smith conjecture, which was proved in dimension 3 in 2013. Smith theory is a theory about homeomorphisms of finite order of manifolds, particularly spheres. Smith was a student of Solomon Lefschetz at the University of Kansas, moving to Princeton University with Lefschetz in the mid-1920s. He finished his doctorate at Princeton, in 1926. His Ph.D. thesis was published in the Annals of Mathematics that same year. He also worked with George David Birkhoff, with whom he wrote a 1928 paper in ergodic theory, entitled Structure analysis of surface transformations, which appeared in the Journal des Mathématiques. He subsequently became a professor at Columbia University and at Barnard College. His students at Columbia included Sherman K. Stein and Moses Richardson. He has many academic descendants through Richardson and his student Louis Billera.

Family Smith was married to the Swiss–American early music pioneer Suzanne Bloch. They had two children.

External links Approximation of curves and surfaces by algebraic curves and surfaces, Annals of Mathematics, 2nd Ser., Vol. 27, No. 3 (Mar., 1926), pp. 224–244. "Abstract of The New York Times description of his death". Paul Althaus Smith at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Paul Althaus Smith

Start with the simplest possible case. Write down what Paul Althaus Smith 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 Paul Althaus Smith 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 Paul Althaus Smith 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 Paul Althaus Smith

In research: Paul Althaus Smith 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 Paul Althaus Smith 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: Paul Althaus Smith is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1900 births, 1980 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Paul Althaus Smith 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 Paul Althaus Smith in 20 minutes

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

Frequently asked questions

What is Paul Althaus Smith in simple terms?

Why does Paul Althaus Smith 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 Paul Althaus Smith?

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 Paul Althaus Smith.