mathematics

Mike Hill (mathematician)

Mike Hill (mathematician) 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 Mike Hill (mathematician) rather than just read about it. In short: Michael Anthony "Mike" Hill is an American mathematician known for his research in topology. He is a professor at the University of Minnesota.

Key takeaways

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

Reference excerpt

Michael Anthony "Mike" Hill is an American mathematician known for his research in topology. He is a professor at the University of Minnesota. Together with Michael J. Hopkins and Douglas Ravenel, he received the American Mathematical Society's Oswald Veblen Prize in Geometry in 2022 for the paper "On the nonexistence of elements of Kervaire invariant one."

Education Hill's undergraduate degree is from Harvard University. He earned a PhD in mathematics from the Massachusetts Institute of Technology in 2006. His doctoral advisor was Michael J. Hopkins. His dissertation, in algebraic topology, was titled "Computational Methods for Higher Real K-Theory with Applications to Tmf."

Career and personal life Hill earned tenure at the University of Virginia before moving to the University of California, Los Angeles in 2015. He moved to the University of Minnesota in 2024. Hill is a co-founder of Spectra, an association for LGBTQ+ mathematicians. He is also a member of the Spectra board.

References

External links profile at UCLA

Illustrations

Worked examples

Example 1 — a first encounter with Mike Hill (mathematician)

Start with the simplest possible case. Write down what Mike Hill (mathematician) 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 Mike Hill (mathematician) 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 Mike Hill (mathematician) 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 Mike Hill (mathematician)

In research: Mike Hill (mathematician) 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 Mike Hill (mathematician) 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: Mike Hill (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 21st-century American mathematicians, American LGBTQ scientists, Harvard College alumni, so understanding it makes those chapters shorter.
In everyday life: Look for Mike Hill (mathematician) 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 Mike Hill (mathematician) in 20 minutes

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

Frequently asked questions

What is Mike Hill (mathematician) in simple terms?

Michael Anthony "Mike" Hill is an American mathematician known for his research in topology. He is a professor at the University of Minnesota.

Why does Mike Hill (mathematician) 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 Mike Hill (mathematician)?

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 Mike Hill (mathematician).