mathematics

Neil Sloane

Neil Sloane 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 Neil Sloane rather than just read about it. In short: Neil James Alexander Sloane FLSW (born October 10, 1939) is a British-American mathematician. His major contributions are in the fields of combinatorics, error-correcting codes, and sphere packing.

Key takeaways

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

Reference excerpt

Neil James Alexander Sloane FLSW (born October 10, 1939) is a British-American mathematician. His major contributions are in the fields of combinatorics, error-correcting codes, and sphere packing. Sloane is best known for being the creator and maintainer of the On-Line Encyclopedia of Integer Sequences (OEIS).

Biography Sloane was born in Beaumaris, Anglesey, Wales, in 1939, moving to Cowes, Isle of Wight, England in 1946. The family emigrated to Australia, arriving at the start of 1949. Sloane then moved from Melbourne to the United States in 1961. He studied at Cornell University under Nick DeClaris, Frank Rosenblatt, Frederick Jelinek and Wolfgang Heinrich Johannes Fuchs, receiving his Ph.D. in 1967. His doctoral dissertation was titled Lengths of Cycle Times in Random Neural Networks. Sloane joined Bell Labs in 1968 and retired from its successor AT&T Labs in 2012. He became an AT&T Fellow in 1998. He is also a Fellow of the Learned Society of Wales, an IEEE Fellow, a Fellow of the American Mathematical Society, and a member of the National Academy of Engineering. He is a winner of a Lester R. Ford Award in 1978 and the Chauvenet Prize in 1979. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. In 2005 Sloane received the IEEE Richard W. Hamming Medal. In 2008 he received the Mathematical Association of America David P. Robbins Prize, and in 2013 the George Pólya Award. In 2014, to celebrate his 75th birthday, Sloane shared some of his favorite integer sequences. Besides mathematics, he loves rock climbing and has authored two rock-climbing guides to New Jersey. He regularly appears in videos for Brady Haran's YouTube channel Numberphile.

Selected publications Neil James Alexander Sloane, A Handbook of Integer Sequences, Academic Press, NY, 1973. Florence Jessie MacWilliams and Neil James Alexander Sloane, The Theory of Error-Correcting Codes, Elsevier/North-Holland, Amsterdam, 1977. M. Harwit and Neil James Alexander Sloane, Hadamard Transform Optics, Academic Press, San Diego CA, 1979. Neil James Alexander Sloane and A. D. Wyner, editors, Claude Elwood Shannon: Collected Papers, IEEE Press, NY, 1993. Neil James Alexander Sloane and S. Plouffe, The Encyclopedia of Integer Sequences, Academic Press, San Diego, 1995. J. H. Conway and Neil James Alexander Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, NY, 1st edn., 1988; 2nd edn., 1993; 3rd ed., 1998. A. S. Hedayat, Neil James Alexander Sloane and J. Stufken, Orthogonal Arrays: Theory and Applications, Springer-Verlag, NY, 1999. G. Nebe, E. M. Rains and Neil James Alexander Sloane, Self-Dual Codes and Invariant Theory, Springer-Verlag, 2006.

See also Reeds–Sloane algorithm Sloane's gap

References

External links Neil Sloane at the Mathematics Genealogy Project IEEE Richard W. Hamming Medal Recipients, 2005 – Neil J. A. Sloane Neil Sloane's entry in the Numericana Hall of Fame "The pattern collector", Science News Doron Zeilberger, Opinion 124: A Database is Worth a Thousand Mathematical Articles Confessions of a Sequence Addict: Neil Sloane My Favorite Integer Sequences: Neil Sloane

Illustrations

Worked examples

Example 1 — a first encounter with Neil Sloane

Start with the simplest possible case. Write down what Neil Sloane 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 Neil Sloane 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 Neil Sloane 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 Neil Sloane

In research: Neil Sloane 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 Neil Sloane 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: Neil Sloane is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1939 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Neil Sloane 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 Neil Sloane in 20 minutes

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

Frequently asked questions

What is Neil Sloane in simple terms?

Neil James Alexander Sloane FLSW (born October 10, 1939) is a British-American mathematician. His major contributions are in the fields of combinatorics, error-correcting codes, and sphere packing.

Why does Neil Sloane 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 Neil Sloane?

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 Neil Sloane.