mathematics

Kathryn Hess

Kathryn Hess 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 Kathryn Hess rather than just read about it. In short: Kathryn Pamela Hess (born 1967) is an American mathematician who has served as professor of mathematics at École Polytechnique Fédérale de Lausanne (EPFL) since 1999. She is known for her work on homotopy theory, category theory, and algebraic topology, both pure and applied.

Key takeaways

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

Reference excerpt

Kathryn Pamela Hess (born 1967) is an American mathematician who has served as professor of mathematics at École Polytechnique Fédérale de Lausanne (EPFL) since 1999. She is known for her work on homotopy theory, category theory, and algebraic topology, both pure and applied. In particular, she applies the methods of algebraic topology to the study of neuroscience, cancer biology, and materials science. She is a fellow of the American Mathematical Society.

Life Kathryn Hess was born 21 September 1967 in Bryn Mawr, Pennsylvania. She began to accelerate in mathematics in 1979, thanks to the Mathematical Talent Development Project (MTDP) set up in Eau Claire, Wisconsin, by her parents, through the Association for High Potential Children, which they also founded. Both programs are currently defunct. Hess earned a BSc with honors in mathematics from the University of Wisconsin–Madison in 1985. She received her doctorate in mathematics from the Massachusetts Institute of Technology in 1989 under the direction of David J. Anick. Her dissertation was entitled A Proof of Ganea's Conjecture for Rational Spaces.[H91]

Work Hess has worked and written extensively on topics in algebraic topology including homotopy theory, model categories[H02] and algebraic K-theory.[HS] She has also used the methods of algebraic topology and category theory to investigate homotopical generalizations of descent theory[H10] and Hopf–Galois extensions.[H09] In particular, she has studied generalizations of these structures for ring spectra and differential graded algebras. She has more recently used algebraic topology to understand structures in neurology[KDS][DHL] and materials science.[LBD] As of March 2025, she has been the principal academic advisor for 21 mathematics PhDs at EPFL, including 9 women.

Awards and honors In addition to her strong publication record, Hess has been widely recognized for her pedagogical abilities. She received the Agepoly prize for best teacher in the Basic Sciences Faculty in 2005, the Credit Suisse prize for best EPFL teacher in 2012, and the "Polysphere d'Or" Agepoly prize for best teacher at EPFL in 2013. She was named an individual member of the Swiss Academy of Engineering Sciences in 2016 and a fellow of the American Mathematical Society for "contributions to homotopy theory, applications of topology to the analysis of biological data, and service to the mathematical community" in 2017. In 2017, she received an award as a distinguished speaker of the European Mathematical Society. She delivered one of the public lectures during the Eighth European Congress of Mathematics on 21 June 2021. Hess was named a fellow of the Association for Women in Mathematics in the class of 2024 "for her support of women in mathematics via innovative and impactful programs, including her role in founding and sustaining the Women in Topology program; for her exceptional mentoring; and for her commitment to gender diversity throughout her many leadership roles in the mathematics profession." She was a visiting member of the IBS Center for Geometry and Physics.

Selected publications

References

External links Videos. Women Inspire Innovation: Kathryn Hess Bellwald, EPFL

Illustrations

Worked examples

Example 1 — a first encounter with Kathryn Hess

Start with the simplest possible case. Write down what Kathryn Hess 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 Kathryn Hess 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 Kathryn Hess 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 Kathryn Hess

In research: Kathryn Hess 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 Kathryn Hess 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: Kathryn Hess is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1967 births, 20th-century American mathematicians, 20th-century American women mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Kathryn Hess 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.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Kathryn Hess in 20 minutes

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

Frequently asked questions

What is Kathryn Hess in simple terms?

Why does Kathryn Hess 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 Kathryn Hess?

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 Kathryn Hess.