mathematics

Leonard Soicher

Leonard Soicher 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 Leonard Soicher rather than just read about it. In short: Leonard Hyman Soicher is a British-Canadian mathematician who worked in algebraic graph theory, group theory, combinatorial design theory, and discrete computational mathematics. He is an Emeritus Professor of Mathematics at Queen Mary University of London.

Key takeaways

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

Reference excerpt

Leonard Hyman Soicher is a British-Canadian mathematician who worked in algebraic graph theory, group theory, combinatorial design theory, and discrete computational mathematics. He is an Emeritus Professor of Mathematics at Queen Mary University of London.

Education Soicher earned a BSc in mathematics in 1978 and a Master of Computer Science in 1981, both from Concordia University in Montreal, Canada. His master's thesis, titled “The Computation of Galois groups”, was supervised by John McKay. He won a Commonwealth Scholarship to pursue a doctorate from the University of Cambridge, with John H. Conway as his supervisor. Soicher was awarded his PhD in 1985, with a PhD thesis titled “Presentations of Some Finite Groups” that focused on sporadic simple groups.

Career Soicher has worked across a range of fields as a professional pure mathematician. After his doctorate, he worked again with John McKay as a postdoc at Concordia University in Canada. He then joined Queen Mary University of London in 1987, where he remained until retirement in 2018, becoming a Professor in 2007. Soicher is most known for his early work on presentations of sporadic simple groups; his contribution to the ATLAS of Finite Groups; the Bimonster group; work with Charles Leedham-Green developing “collection from the left” and the product replacement algorithm. in computational group theory; his research on distance-regular graphs (especially the three so-called Soicher graphs and the Moscow-Soicher graph); and his long-term and ongoing authorship and development of the GRAPE package for GAP. Soicher is also a co-creator and maintainer of the website designtheory.org. Soicher has co-published with notable mathematicians, including Peter Cameron, John Conway, Simon P. Norton, Cheryl Praeger, and Sarah Rees

GAP Soicher has been a member of the council of the computer algebra system GAP since June 1997, and was its chair from March 2009 until September 2021. He is the author of the GRAPE and DESIGN packages for GAP. A special session in honour of Soicher's 70th birthday was held at the GAP Days Summer 2025 workshop in Koper, Slovenia.

Selected publications with John McKay: Computing Galois groups over the rationals, Journal of Number Theory (1985). with John H. Conway, Simon P. Norton: The Bimonster, the group Y555, and the projective plane of order 3, Computers in Algebra (1988). with Rosemary A. Bailey, Peter J. Cameron, Peter Dobcsányi, John P. Morgan: Designs on the web, Discrete Mathematics (2006). with Cheryl E. Praeger: Low rank representations and graphs for sporadic groups, Cambridge University Press (1996).

References

Illustrations

Worked examples

Example 1 — a first encounter with Leonard Soicher

Start with the simplest possible case. Write down what Leonard Soicher 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 Leonard Soicher 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 Leonard Soicher 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 Leonard Soicher

In research: Leonard Soicher 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 Leonard Soicher 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: Leonard Soicher is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1955 births, 20th-century Canadian mathematicians, 21st-century Canadian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Leonard Soicher 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 Leonard Soicher in 20 minutes

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

Frequently asked questions

What is Leonard Soicher in simple terms?

Why does Leonard Soicher 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 Leonard Soicher?

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 Leonard Soicher.