mathematics

Peter Hintz

Peter Hintz 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 Peter Hintz rather than just read about it. In short: Peter Hintz (born 1991 in Kassel, Germany) is a German mathematician working in the areas of partial differential equations, microlocal analysis, scattering theory and general relativity. He is currently a professor of mathematics at Pennsylvania State University.

Key takeaways

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

Reference excerpt

Peter Hintz (born 1991 in Kassel, Germany) is a German mathematician working in the areas of partial differential equations, microlocal analysis, scattering theory and general relativity. He is currently a professor of mathematics at Pennsylvania State University.

Education and career Hintz graduated with a BSc in mathematics and a BSc in physics from the University of Göttingen in 2011. He obtained his PhD in 2015 at Stanford University under the supervision of András Vasy. After his postdoctoral appointments at the Miller Institute and Clay Mathematics Institute, he joined the faculty of the Massachusetts Institute of Technology as an assistant professor in 2019, later becoming an associate professor. In 2021, he moved to ETH Zürich as an associate professor of mathematics and physics. As of Fall 2025, he is a full professor of mathematics at Pennsylvania State University.

Awards and honors Hintz was Miller Research Fellow from 2015 to 2017, where he was mentored by Maciej Zworski. He subsequently was a Clay Research Fellow from 2017 to 2020. During his time as a faculty member of the Massachusetts Institute of Technology, he was an Alfred P. Sloan Research Fellow from 2020 to 2022. In 2021, he delivered a plenary lecture at the 20th International Congress on Mathematical Physics. The following year, Hintz gave a special invited lecture at the International Congress of Mathematicians together with Gustav Holzegel (de). In 2022, he was awarded the Golden Owl for excellence in teaching at ETH Zürich. He received a Frontiers of Science Award in 2023 and the IAMP Early Career Award in 2024.

Research Hintz's work applies methods from microlocal analysis as well as scattering and spectral theory to hyperbolic partial differential equations arising in Einstein's theory of general relativity. In collaboration with András Vasy, he proved the nonlinear stability of the Kerr-de Sitter family of black holes. He also co-authored a paper on possible violations of Sir Roger Penrose's strong cosmic censorship conjecture. Among his other contributions is a proof of Price's law on the rate of decay of waves on Kerr black hole spacetimes.

Books Hintz, Peter (October 2025). An Introduction to Microlocal Analysis. Graduate Texts in Mathematics. Vol. 304. Springer-Verlag, Cham. doi:10.1007/978-3-031-90706-7. ISBN 978-3-031-90705-0.

References

Worked examples

Example 1 — a first encounter with Peter Hintz

Start with the simplest possible case. Write down what Peter Hintz 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 Peter Hintz 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 Peter Hintz 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 Peter Hintz

In research: Peter Hintz 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 Peter Hintz 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: Peter Hintz is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1991 births, 21st-century German mathematicians, German relativity theorists, so understanding it makes those chapters shorter.
In everyday life: Look for Peter Hintz 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 Peter Hintz in 20 minutes

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

Frequently asked questions

What is Peter Hintz in simple terms?

Why does Peter Hintz 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 Peter Hintz?

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 Peter Hintz.