mathematics

John Hammersley

John Hammersley 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 John Hammersley rather than just read about it. In short: John Michael Hammersley, (21 March 1920 – 2 May 2004) was a British mathematician best known for his foundational work in the theory of self-avoiding walks and percolation theory. Early life and education Hammersley was born in Helensburgh in Dunbartonshire, and educated at Sedbergh School.

Key takeaways

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

Reference excerpt

John Michael Hammersley, (21 March 1920 – 2 May 2004) was a British mathematician best known for his foundational work in the theory of self-avoiding walks and percolation theory.

Early life and education Hammersley was born in Helensburgh in Dunbartonshire, and educated at Sedbergh School. He started reading mathematics at Emmanuel College, Cambridge but was called up to join the Royal Artillery in 1941. During his time in the army he worked on ballistics. He graduated in mathematics in 1948. He never studied for a PhD but was awarded an ScD by Cambridge University and a DSc by Oxford University in 1959.

Academic career

With Jillian Beardwood and J.H. Halton, Hammersley is known for the Beardwood-Halton-Hammersley Theorem. Published by the Cambridge Philosophical Society in a 1959 article entitled “The Shortest Path Through Many Points,” the theorem provides a practical solution to the “traveling salesman problem.” He held a number of positions, both in and outside academia. His book Monte Carlo Methods with David Handscomb was published in 1964. He is known for devising an early solution to the moving sofa problem in 1968. He was an advocate of problem solving, and an opponent of abstraction in mathematics, taking part in the New Math debate. He was a fellow (later professorial fellow) of Trinity College, Oxford, from 1961, reader in mathematical statistics at Oxford University from 1969, and elected Fellow of the Royal Society (FRS) in 1976.

See also Hammersley set Hammersley–Clifford theorem Low-discrepancy sequence

References

Illustrations

Worked examples

Example 1 — a first encounter with John Hammersley

Start with the simplest possible case. Write down what John Hammersley 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 John Hammersley 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 John Hammersley 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 John Hammersley

In research: John Hammersley 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 John Hammersley 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: John Hammersley is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1920 births, 2004 deaths, Alumni of Emmanuel College, Cambridge, so understanding it makes those chapters shorter.
In everyday life: Look for John Hammersley 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 John Hammersley in 20 minutes

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

Frequently asked questions

What is John Hammersley in simple terms?

John Michael Hammersley, (21 March 1920 – 2 May 2004) was a British mathematician best known for his foundational work in the theory of self-avoiding walks and percolation theory. Early life and education Hammersley was born in Helensburgh in Dunbartonshire, and educated at Sedbergh School.

Why does John Hammersley 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 John Hammersley?

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 John Hammersley.