astronomy

Jonathan Pila

Jonathan Pila is a astronomy 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 Jonathan Pila rather than just read about it. In short: Jonathan Solomon Pila (born 1962) is an Australian mathematician at the University of Oxford. He was awarded a BSc from the University of Melbourne in 1984, and a PhD from Stanford University in 1988, the latter for research supervised by Peter Sarnak.

Key takeaways

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

Reference excerpt

Jonathan Solomon Pila (born 1962) is an Australian mathematician at the University of Oxford. He was awarded a BSc from the University of Melbourne in 1984, and a PhD from Stanford University in 1988, the latter for research supervised by Peter Sarnak. His dissertation was entitled "Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields". In 2010, he received an MA from Oxford.

Career and research Research interests lie in number theory and model theory. A focus has been applying the theory of o-minimality to Diophantine problems. This work began with an early paper with Enrico Bombieri, and developed through collaborations with Alex Wilkie and Umberto Zannier. The techniques obtained have led to advances in Diophantine problems, including Pila's unconditional proof of the André–Oort conjecture for powers of the modular curve. Work by Pila and Jacob Tsimerman, demonstrated the André–Oort conjecture in the case of the Siegel modular variety. Pila has held posts at Columbia University, McGill University, the University of Bristol and (as a visiting member) the Institute for Advanced Study. Pila also took a substantial break from professional mathematics to work in his family's manufacturing business. Pila has been the Editor of Proceedings of the Edinburgh Mathematical Society, and of Algebra and Number Theory.

Awards and honours Pila was awarded a Clay Research Award for his work on the Andre-Oort conjecture in 2011. In June 2011, he was awarded the Senior Whitehead Prize by the London Mathematical Society. This prize is "awarded in recognition of work in and influence on and service to mathematics; or lecturing gifts." Specifically, the citation recognized "his startling recent work on the Andre-Oort and Manin-Mumford conjectures. The approach he and his collaborators have developed, which combines analytic ideas with model theory, is entirely new and shows great promise for further applications." In addition to the Clay and London Mathematical Society awards, Pila delivered the Arf Lecture in 2011, was awarded the Leverhulme Trust Research Fellowship 2008–2010. and received the Karp Prize in 2013. Pila was elected a Fellow of the Royal Society (FRS) in 2015. In 2022, he received the Rolf Schock Prize in the category of "Mathematics".

References

Illustrations

Worked examples

Example 1 — a first encounter with Jonathan Pila

Start with the simplest possible case. Write down what Jonathan Pila claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Jonathan Pila 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 Jonathan Pila 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 Jonathan Pila

In research: Jonathan Pila appears in astronomy 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 Jonathan Pila 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: Jonathan Pila is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1962 births, Academics of the University of Oxford, Australian fellows of the Royal Society, so understanding it makes those chapters shorter.
In everyday life: Look for Jonathan Pila 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 Jonathan Pila in 20 minutes

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

Frequently asked questions

What is Jonathan Pila in simple terms?

Why does Jonathan Pila matter?

Because it connects several astronomy 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 Jonathan Pila?

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 Jonathan Pila.