mathematics

Norman Routledge

Norman Routledge 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 Norman Routledge rather than just read about it. In short: Norman Arthur Routledge (7 March 1928 – 27 April 2013) was a British mathematician and schoolteacher. He was a personal friend of fellow mathematician Alan Turing (1912–1954).

Key takeaways

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

Reference excerpt

Norman Arthur Routledge (7 March 1928 – 27 April 2013) was a British mathematician and schoolteacher. He was a personal friend of fellow mathematician Alan Turing (1912–1954).

Life and career Norman Routledge was born near Alexandra Park, north London, England. He was about to begin secondary education at Glendale County School, Wood Green, in 1939, when the outbreak of World War II intervened. He was evacuated with his mother, going to live in Letchworth with an aunt, and attending Letchworth Grammar School, where he was taught mathematics by George Braithwaite. In 1946 Routledge matriculated with a scholarship at King's College, Cambridge, where he read mathematics. He was supervised by Albert Ingham and Philip Hall. He gained a first class degree in 1949 and went on to research in recursion theory. It resulted in the papers Ordinal recursion (1953) and Concerning definable sets (1954). Routledge taught as a scientific officer at the Royal Aircraft Establishment, RAE Farnborough. He went on to the National Physical Laboratory (NPL), Teddington. These were placements to fulfil the requirements for his compulsory national service. At the NPL in 1952 he was able to become an operator of an early version of the Automatic Computing Engine: the Pilot ACE project supported by Harry Huskey's prototype assembler. Returning to academia, Routledge became a research Fellow in mathematics at King's College, Cambridge. He taught college undergraduates, and after a time was a director of studies. In 1957, he was photographed by Antony Barrington Brown. The photograph is now in the collection of the National Portrait Gallery, London. In 1959, Robert Birley, Headmaster at Eton College, asked Routledge for a recommendation of some promising student for a mathematics teaching post; and he suggested himself. He taught mathematics at the school for some years and was later a housemaster. He was considered an inspirational teacher, teaching among other Etonians Simon P. Norton, Timothy Gowers and Stephen Wolfram. Later in his life, he taught music for the Salvation Army community in Bermondsey, southeast London. Routledge was a raconteur, including on his personal life. In retirement towards the end of his own life, he was able to be more openly gay. In Turing's biography, Routledge is described as "clever, flamboyant and sometimes outrageous".

Association with Alan Turing Routledge was a friend of the mathematician and codebreaker Alan Turing, whom he met after World War II, when Turing was in Cambridge to study physiology. Turing wrote personal letters to Routledge towards the end of his life. After his arrest and before his trial, he sent the following cryptic syllogism to Routledge in 1952:

Turing believes that machines thinkTuring lies with menTherefore machines cannot think The 1992 documentary programme The Strange Life and Death of Dr Turing had Routledge as one of the interviewees.

Selected publications Routledge, N. A. (1952). "A result in Hilbert space". The Quarterly Journal of Mathematics. 3 (1): 12–18. doi:10.1093/qmath/3.1.12. Routledge, N. A. (April 1953). "Ordinal recursion". Mathematical Proceedings of the Cambridge Philosophical Society. 49 (2): 175–182. Bibcode:1953PCPS...49..175R. doi:10.1017/S0305004100028255. S2CID 251094316.

References

Bibliography Copeland, B. Jack; Bowen, Jonathan P.; Wilson, Robin; Sprevak, Mark (2017). The Turing Guide. Oxford University Press. pp. 37, 44, 471. ISBN 978-0-19-874783-3. Hodges, Andrew (1983). Alan Turing: The Enigma. Simon & Schuster. pp. 372, 395, 476, 483. ISBN 0-671-49207-1. Leavitt, David (2006). The Man Who Knew Too Much: Alan Turing and the Invention of the Computer. Weidenfeld & Nicolson. pp. 5, 25, 265, 268, 270, 271. ISBN 978-0-7538-2200-5. Turing, Dermot (2015). Alan Turing Decoded. The History Press. pp. 246–247. ISBN 978-1-84165-643-4.

External links Norman Routledge (Teacher), Web of Stories – Life Stories of Remarkable People, YouTube Norman Routledge, Saucy Raconteur, Remembers His Friend Alan Turing, Nassau Hedron, The Turing Centenary (+ Bicentennial), 18 October 2011

Worked examples

Example 1 — a first encounter with Norman Routledge

Start with the simplest possible case. Write down what Norman Routledge 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 Norman Routledge 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 Norman Routledge 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 Norman Routledge

In research: Norman Routledge 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 Norman Routledge 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: Norman Routledge is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1928 births, 2013 deaths, 20th-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Norman Routledge 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 Norman Routledge in 20 minutes

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

Frequently asked questions

What is Norman Routledge in simple terms?

Norman Arthur Routledge (7 March 1928 – 27 April 2013) was a British mathematician and schoolteacher. He was a personal friend of fellow mathematician Alan Turing (1912–1954).

Why does Norman Routledge 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 Norman Routledge?

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 Norman Routledge.