mathematics

Nancy Hingston

Nancy Hingston 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 Nancy Hingston rather than just read about it. In short: Nancy Burgess Hingston is a mathematician working in algebraic topology and differential geometry. She is a professor emerita of mathematics at The College of New Jersey.

Key takeaways

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

Reference excerpt

Nancy Burgess Hingston is a mathematician working in algebraic topology and differential geometry. She is a professor emerita of mathematics at The College of New Jersey.

Early life and education Nancy Hingston's father William Hingston was superintendent of the Central Bucks School District in Pennsylvania; her mother was a high school mathematics and computer science teacher. She graduated from the University of Pennsylvania with a double major in mathematics and physics. After a year studying physics as a graduate student, she switched to mathematics, and completed her PhD in 1981 from Harvard University under the supervision of Raoul Bott.

Career Before joining TCNJ, she taught at the University of Pennsylvania. She has also been a frequent visitor to the Institute for Advanced Study, and has been involved with the Program for Women and Mathematics at the Institute for Advanced Study since its founding in 1994.

Contributions Nancy Hingston made major contributions in Riemannian geometry and Hamiltonian dynamics, and more specifically in the study of closed geodesics and, more generally, periodic orbits of Hamiltonian systems. In her very first paper, she proved that a generic Riemannian metric on a closed manifold possesses infinitely many closed geodesics. In the 1990s, she proved that the growth rate of closed geodesics in Riemannian 2-spheres is at least the one of prime numbers. In the years 2000s, she proved the long-standing Conley conjecture from symplectic geometry: every Hamiltonian diffeomorphism of a standard symplectic torus of any even dimension possesses infinitely many periodic points (the result was subsequently extended by Viktor Ginzburg to more general symplectic manifolds).

Recognition Nancy Hingston was an invited speaker at the International Congress of Mathematicians in 2014. She is a fellow of the American Mathematical Society, for "contributions to differential geometry and the study of closed geodesics."

Personal Her husband, Jovi Tenev, is a lawyer. She has three children.

References

Worked examples

Example 1 — a first encounter with Nancy Hingston

Start with the simplest possible case. Write down what Nancy Hingston 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 Nancy Hingston 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 Nancy Hingston 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 Nancy Hingston

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

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

Frequently asked questions

What is Nancy Hingston in simple terms?

Nancy Burgess Hingston is a mathematician working in algebraic topology and differential geometry. She is a professor emerita of mathematics at The College of New Jersey.

Why does Nancy Hingston 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 Nancy Hingston?

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 Nancy Hingston.