mathematics

Paul Vojta

Paul Vojta 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 Vojta rather than just read about it. In short: Paul Alan Vojta (born September 30, 1957) is an American mathematician, known for his work in number theory on Diophantine geometry and Diophantine approximation. Contributions In formulating Vojta's conjecture, he pointed out the possible existence of parallels between the Nevanlinna theory of complex analysis, and diophantine analysis in the circle of ideas around the Mordell conjecture and abc conjecture.

Key takeaways

Paul Vojta 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 Vojta to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Paul Vojta from memory before moving on to harder problems.

Reference excerpt

Paul Alan Vojta (born September 30, 1957) is an American mathematician, known for his work in number theory on Diophantine geometry and Diophantine approximation.

Contributions In formulating Vojta's conjecture, he pointed out the possible existence of parallels between the Nevanlinna theory of complex analysis, and diophantine analysis in the circle of ideas around the Mordell conjecture and abc conjecture. This suggested the importance of the integer solutions (affine space) aspect of diophantine equations. Vojta wrote the .dvi-previewer xdvi. He also wrote a vi clone.

Education and career He was an undergraduate student at the University of Minnesota, where he became a Putnam Fellow in 1977, and a doctoral student at Harvard University (1983). He currently is a professor in the Department of Mathematics at the University of California, Berkeley.

Awards and honors In 2012 he became a fellow of the American Mathematical Society.

Selected publications Diophantine Approximations and Value Distribution Theory, Lecture Notes in Mathematics 1239, Springer Verlag, 1987, ISBN 978-3-540-17551-3

References

External links Vojta's home page Paul Vojta's results at International Mathematical Olympiad

Illustrations

Worked examples

Example 1 — a first encounter with Paul Vojta

Start with the simplest possible case. Write down what Paul Vojta 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 Vojta 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 Vojta 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 Vojta

In research: Paul Vojta 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 Vojta 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 Vojta 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 Paul Vojta 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 Vojta in 20 minutes

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

Frequently asked questions

What is Paul Vojta in simple terms?

Paul Alan Vojta (born September 30, 1957) is an American mathematician, known for his work in number theory on Diophantine geometry and Diophantine approximation. Contributions In formulating Vojta's conjecture, he pointed out the possible existence of parallels between the Nevanlinna theory of com…

Why does Paul Vojta 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 Vojta?

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 Vojta.