mathematics

Stanley Skewes

Stanley Skewes 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 Stanley Skewes rather than just read about it. In short: Stanley Skewes (; 1899–1988) was a South African mathematician, best known for his discovery of the Skewes's number in 1933. He was one of John Edensor Littlewood's students at Cambridge University.

Key takeaways

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

Reference excerpt

Stanley Skewes (; 1899–1988) was a South African mathematician, best known for his discovery of the Skewes's number in 1933. He was one of John Edensor Littlewood's students at Cambridge University. Skewes's numbers contributed to the refinement of the theory of prime numbers.

Academic career Skewes obtained a degree in civil engineering from the University of Cape Town before emigrating to England. He studied mathematics at Cambridge University and obtained a PhD in mathematics in 1938. He discovered the first Skewes's number in 1933. This is also referred to as the Riemann true Skewes's number owing to its relationship to the Riemann hypothesis as related to prime number theory. He discovered the second Skewes's number in 1955. This number was applicable if the Riemann hypothesis is false. Since his original discovery the numbers have been further refined.

Publications Skewes, S. (1933). "On the difference π(x) − Li(x) (I)". Journal of the London Mathematical Society. 8 (4): 277–283. doi:10.1112/jlms/s1-8.4.277. Archived 19 May 2007 at the Wayback Machine Skewes, S. (1955). "On the difference π(x) − Li(x) (II)". Proceedings of the London Mathematical Society. 5 (17): 48–70. doi:10.1112/plms/s3-5.1.48. Archived 19 May 2007 at the Wayback Machine

Personal life

Stanley Skewes was born in Germiston, South Africa in 1899. His parents were Henry (Harry) Skewes, a tin miner and assayer from Cury, Cornwall, England and Emily Moyle, who was American by birth. His parents moved from Redruth, Cornwall in 1894 to the Transvaal, South Africa. He married Ena Allen. She was the daughter of the head chef at King's College, Cambridge, and a talented opera singer. Among his contemporaries at Cambridge was Alan Turing. They rowed together at Cambridge. Although Skewes returned to South Africa, he revisited Cambridge and Cornwall. He was also a keen rugby player in his youth. Skewes and his number are discussed by Isaac Asimov in his book Of Matters Great and Small and in the 20th edition of the Guinness Book of Records. A memorandum written by Skewes on his retirement was kept in a glass case in the department of mathematics at the University of Cape Town. The memorandum discuses Skewes's number and further development of it. He died in 1988 in Cape Town, South Africa.

References

Illustrations

Worked examples

Example 1 — a first encounter with Stanley Skewes

Start with the simplest possible case. Write down what Stanley Skewes 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 Stanley Skewes 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 Stanley Skewes 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 Stanley Skewes

In research: Stanley Skewes 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 Stanley Skewes 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: Stanley Skewes is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1899 births, 1988 deaths, 20th-century South African mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Stanley Skewes 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 Stanley Skewes in 20 minutes

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

Frequently asked questions

What is Stanley Skewes in simple terms?

Why does Stanley Skewes 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 Stanley Skewes?

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 Stanley Skewes.