mathematics

Paul T. Bateman

Paul T. Bateman 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 Paul T. Bateman rather than just read about it. In short: Paul Trevier Bateman (June 6, 1919 – December 26, 2012) was an American number theorist, known for formulating the Bateman–Horn conjecture on the density of prime number values generated by systems of polynomials and the New Mersenne conjecture relating the occurrences of Mersenne primes and Wagstaff primes. Born in Philadelphia, Bateman received his Ph.D. from the University of Pennsylvania in 1946, under the super…

Key takeaways

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

Reference excerpt

Paul Trevier Bateman (June 6, 1919 – December 26, 2012) was an American number theorist, known for formulating the Bateman–Horn conjecture on the density of prime number values generated by systems of polynomials and the New Mersenne conjecture relating the occurrences of Mersenne primes and Wagstaff primes. Born in Philadelphia, Bateman received his Ph.D. from the University of Pennsylvania in 1946, under the supervision of Hans Rademacher. After temporary positions at Yale University and the Institute for Advanced Study, he joined in 1950 the mathematics department at the University of Illinois at Urbana-Champaign, where he was department chair for 15 years and was subsequently an emeritus professor. He was the doctoral advisor of 20 students, including Marvin Knopp, Kevin McCurley, George B. Purdy, and Claudia Spiro. Bateman was a member of the American Mathematical Society for 71 years. He served as an associate secretary for 16 years, a member of the board of trustees for 4 years, and a member of the Mathematical Reviews Committee for 5 years.

Textbooks Bateman was a coauthor of Analytic Number Theory: An Introductory Course. He was also a contributor to the second edition of the textbook Elementary Number Theory, a translation into English of Edmund Landau's German language text Elementare Zahlentheorie.

Personal information Bateman attended Upper Moreland High School, which recognized his accomplishments by inducting him into its Hall of Fame in 1999. He was department head at the University of Illinois at Urbana-Champaign for 15 years, and had a flair for the dramatic, which led to his being called P. T. Barnum. In the Christmas skit one year the students had a character called Batman, with aluminum foil on his head to simulate baldness. Not to be outdone, at the following year's skit Bateman himself appeared in a Batman costume. As department head, Bateman was a great believer in the committee of one because it made committee meetings unnecessary. Ph.D. candidates had to pass an oral exam in either German, Russian or French. It happened that Philippe Tondeur was fluent in those three languages, and so Bateman gave him the job of examining all the candidates. Bateman served as Problems editor of The American Mathematical Monthly from 1986 to 1991. His first act was to solve all the problems in the backlog. He visited the Institute for Advanced Study three times.

References

Worked examples

Example 1 — a first encounter with Paul T. Bateman

Start with the simplest possible case. Write down what Paul T. Bateman 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 Paul T. Bateman 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 Paul T. Bateman 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 Paul T. Bateman

In research: Paul T. Bateman 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 Paul T. Bateman 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: Paul T. Bateman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1919 births, 2012 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Paul T. Bateman 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 Paul T. Bateman in 20 minutes

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

Frequently asked questions

What is Paul T. Bateman in simple terms?

Why does Paul T. Bateman 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 Paul T. Bateman?

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 Paul T. Bateman.