mathematics

Jeffrey Lagarias

Jeffrey Lagarias 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 Jeffrey Lagarias rather than just read about it. In short: Jeffrey Clark Lagarias (born November 16, 1949) is a mathematician and professor at the University of Michigan. Education While in high school in 1966, Lagarias studied astronomy at the Summer Science Program.

Key takeaways

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

Reference excerpt

Jeffrey Clark Lagarias (born November 16, 1949) is a mathematician and professor at the University of Michigan.

Education While in high school in 1966, Lagarias studied astronomy at the Summer Science Program. He completed an S.B. and S.M. in Mathematics at the Massachusetts Institute of Technology in 1972. The title of his thesis was "Evaluation of certain character sums". He was a Putnam Fellow at MIT in 1970. He received his Ph.D. in Mathematics from MIT for his thesis "The 4-part of the class group of a quadratic field", in 1974. His advisor for both his masters and Ph.D. was Harold Stark.

Career In 1974, he joined AT&T Bell Laboratories and eventually became a member of technical staff. From 1995 to 2004, he was a Technology Consultant at AT&T Research Laboratories. In 2004, he moved to the University of Michigan as a professor of mathematics.

Research Lagarias originally worked in analytic algebraic number theory. His later work has been in theoretical computer science. Lagarias discovered an elementary problem that is equivalent to the Riemann hypothesis, namely whether for all n > 0, we have

σ ( n ) ≤ H n + e H n ln ⁡ H n {\displaystyle \sigma (n)\leq H_{n}+e^{H_{n}}\ln H_{n}}

with equality only when n = 1. Here Hn is the nth harmonic number, the sum of the reciprocals of the first n {\displaystyle n} positive integers, and σ(n) is the divisor function, the sum of the positive divisors of n. He disproved Keller's conjecture in dimensions at least 10. Lagarias has also done work on the Collatz conjecture and Li's criterion and has written several highly cited papers in symbolic computation with Dave Bayer.

Awards and honors Lagarias received in 1986 a Lester R. Ford award from the Mathematical Association of America and again in 2007. In 2012, he became a fellow of the American Mathematical Society. In 2024 he was elected as a member of the National Academy of Sciences.

References

External links

Jeffrey Lagarias at the Mathematics Genealogy Project Jeffrey Clark Lagarias homepage, University of Michigan

Worked examples

Example 1 — a first encounter with Jeffrey Lagarias

Start with the simplest possible case. Write down what Jeffrey Lagarias 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 Jeffrey Lagarias 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 Jeffrey Lagarias 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 Jeffrey Lagarias

In research: Jeffrey Lagarias 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 Jeffrey Lagarias 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: Jeffrey Lagarias is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1949 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Jeffrey Lagarias 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 Jeffrey Lagarias in 20 minutes

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

Frequently asked questions

What is Jeffrey Lagarias in simple terms?

Jeffrey Clark Lagarias (born November 16, 1949) is a mathematician and professor at the University of Michigan. Education While in high school in 1966, Lagarias studied astronomy at the Summer Science Program.

Why does Jeffrey Lagarias 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 Jeffrey Lagarias?

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 Jeffrey Lagarias.