mathematics

Michael Stillman

Michael Stillman 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 Michael Stillman rather than just read about it. In short: Michael Eugene Stillman (born March 24, 1957) is an American mathematician working in computational algebraic geometry and commutative algebra. He is a professor of mathematics at Cornell University.

Key takeaways

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

Reference excerpt

Michael Eugene Stillman (born March 24, 1957) is an American mathematician working in computational algebraic geometry and commutative algebra. He is a professor of mathematics at Cornell University. He is known for being one of the creators (with Daniel Grayson) of the Macaulay2 computer algebra system.

Education and career Michael Stillman completed his PhD at Harvard University in 1983 under the direction of David Mumford. He had postdoctoral positions at the University of Chicago, Brandeis University, and the Massachusetts Institute of Technology before moving to a permanent position at Cornell University in 1987. Stillman is best known for his work on computer algebra systems. In 1983, he began work with Dave Bayer on the Macaulay computer algebra system, which they continued to improve until 1993. To get beyond several limitations in the design of Macaulay, Stillman and Daniel Grayson began work on the Macaulay2 system in 1993. Macaulay2 remains in active development as of 2019, and has been cited in over 4350 articles. Stillman has over 30 mathematical publications, and has advised 11 PhD students.

Awards and honors In 2015 Stillman was selected as a fellow of the American Mathematical Society for his work in symbolic computation (such as that on Macaulay2). Stillman was recognized for his teaching by Business Insider in a 2013 feature on the Best Colleges in America, where he was named as one of the top 10 professors at Cornell.

References

External links Michael Stillman publications indexed by Google Scholar

Illustrations

Worked examples

Example 1 — a first encounter with Michael Stillman

Start with the simplest possible case. Write down what Michael Stillman 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 Michael Stillman 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 Michael Stillman 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 Michael Stillman

In research: Michael Stillman 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 Michael Stillman 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: Michael Stillman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1957 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Michael Stillman 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 Michael Stillman in 20 minutes

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

Frequently asked questions

What is Michael Stillman in simple terms?

Michael Eugene Stillman (born March 24, 1957) is an American mathematician working in computational algebraic geometry and commutative algebra. He is a professor of mathematics at Cornell University.

Why does Michael Stillman 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 Michael Stillman?

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 Michael Stillman.