mathematics

William Messing

William Messing 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 William Messing rather than just read about it. In short: William Messing is an American mathematician who works in the field of arithmetic algebraic geometry. Messing received his doctorate in 1971 at Princeton University under the supervisions of Alexander Grothendieck (and Nicholas Katz) with his thesis The Crystals Associated to Barsotti–Tate Groups: With Applications to Abelian Schemes.

Key takeaways

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

Reference excerpt

William Messing is an American mathematician who works in the field of arithmetic algebraic geometry. Messing received his doctorate in 1971 at Princeton University under the supervisions of Alexander Grothendieck (and Nicholas Katz) with his thesis The Crystals Associated to Barsotti–Tate Groups: With Applications to Abelian Schemes. In 1972, he was a C.L.E. Moore instructor at Massachusetts Institute of Technology. He is currently professor emeritus at the University of Minnesota (Minneapolis). In his thesis, Messing elaborated on Grothendieck's 1970 lecture at the International Congress of Mathematicians in Nice on p-divisible groups (Barsotti–Tate groups) that are important in algebraic geometry in prime characteristic, which were introduced in the 1950s by Dieudonné in his study of Lie algebras over fields of finite characteristic. Messing worked together with Pierre Berthelot, Barry Mazur, and Aise Johan de Jong.

Writings Pierre Berthelot, Messing, Theorie de Dieudonné cristalline I, Journées de Geometrie Algebrique de Rennes, 1978, volume 1, pp. 17–37, Asterisque, volume 63, 1979 Pierre Berthelot, Lawrence Breen, Messing, Theorie de Dieudonné cristalline II, Springer Lecture Notes in Mathematics, Volume 930, 1982 With Berthelot, Theorie de Dieudonné cristalline III, in Paul Cartier and others, Grothendieck Festschrift, Volume 1, 1990, Springer, p. 173 Barry Mazur, Messing, Universal extensions and one dimensional cristalline cohomology, Springer Lecture Notes in Mathematics, Volume 370, 1974 Messing, The crystals associated to Barsotti–Tate groups: with applications to abelian schemes, Springer Lecture Notes in Mathematics, Volume 264, 1972

References The original article was a Google-aided translation of the corresponding article in German Wikipedia.

External links Homepage

Illustrations

Worked examples

Example 1 — a first encounter with William Messing

Start with the simplest possible case. Write down what William Messing 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 William Messing 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 William Messing 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 William Messing

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

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

Frequently asked questions

What is William Messing in simple terms?

Why does William Messing 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 William Messing?

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 William Messing.