mathematics

Matthias Aschenbrenner

Matthias Aschenbrenner 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 Matthias Aschenbrenner rather than just read about it. In short: Matthias Aschenbrenner (born 1972 in Bad Kötzting) is a German-American mathematician. He is a professor of mathematics and director of the logic group at the University of Vienna.

Key takeaways

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

Reference excerpt

Matthias Aschenbrenner (born 1972 in Bad Kötzting) is a German-American mathematician. He is a professor of mathematics and director of the logic group at the University of Vienna. His research interests include differential algebra and model theory.

Career Aschenbrenner earned his "Vordiplom" at the University of Passau in 1996. In 2001, he received his Ph.D. from the University of Illinois at Urbana–Champaign, where he was a student of Lou van den Dries. For his dissertation, he was awarded the 2001 Sacks Prize by the Association for Symbolic Logic. After a visiting position at the University of California, Berkeley, Aschenbrenner joined the faculty at the University of Illinois at Chicago in 2003, moving to the University of California, Los Angeles in 2007. In 2012, Aschenbrenner became a Fellow of the American Mathematical Society. He was jointly awarded the 2018 Karp Prize with Lou van den Dries and Joris van der Hoeven "for their work in model theory, especially on asymptotic differential algebra and the model theory of transseries". In 2018, Aschenbrenner was an invited speaker at the International Congress of Mathematicians in Rio de Janeiro. Aschenbrenner moved to the University of Vienna in 2020, where he is also director of the logic group.

References

Illustrations

Worked examples

Example 1 — a first encounter with Matthias Aschenbrenner

Start with the simplest possible case. Write down what Matthias Aschenbrenner 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 Matthias Aschenbrenner 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 Matthias Aschenbrenner 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 Matthias Aschenbrenner

In research: Matthias Aschenbrenner 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 Matthias Aschenbrenner 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: Matthias Aschenbrenner is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1972 births, 21st-century American mathematicians, Academic staff of the University of Vienna, so understanding it makes those chapters shorter.
In everyday life: Look for Matthias Aschenbrenner 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 Matthias Aschenbrenner in 20 minutes

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

Frequently asked questions

What is Matthias Aschenbrenner in simple terms?

Matthias Aschenbrenner (born 1972 in Bad Kötzting) is a German-American mathematician. He is a professor of mathematics and director of the logic group at the University of Vienna.

Why does Matthias Aschenbrenner 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 Matthias Aschenbrenner?

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 Matthias Aschenbrenner.