mathematics

Peter Scholze

Peter Scholze 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 Scholze rather than just read about it. In short: Peter Scholze (German pronunciation: [ˈpeːtɐ ˈʃɔltsə] ; born 11 December 1987) is a German mathematician known for his work in arithmetic geometry. He has been a professor in the University of Bonn since 2012 and co-director at the Max Planck Institute for Mathematics since 2018.

Key takeaways

Peter Scholze 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 Scholze to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Peter Scholze from memory before moving on to harder problems.

Reference excerpt

Peter Scholze (German pronunciation: [ˈpeːtɐ ˈʃɔltsə] ; born 11 December 1987) is a German mathematician known for his work in arithmetic geometry. He has been a professor in the University of Bonn since 2012 and co-director at the Max Planck Institute for Mathematics since 2018. He has been called one of the leading mathematicians in the world. In 2018, he won the Fields Medal, an award regarded as the highest professional honor in mathematics.

Early life and education Scholze was born in Dresden and grew up in Berlin. His father is a physicist, his mother a computer scientist, and his sister studied chemistry. He attended the Heinrich-Hertz-Gymnasium in Berlin-Friedrichshain, a gymnasium devoted to mathematics and science. As a student, Scholze participated in the International Mathematical Olympiad, winning three gold medals and one silver medal. He studied at the University of Bonn and completed his bachelor's degree in three semesters and his master's degree in two further semesters. He obtained his Ph.D. in 2012 under the supervision of Michael Rapoport. Scholze was a student of Rapoport, who was a student of Deligne, who was a student of Grothendieck, who was a student of Schwartz; in this chain, Scholze, Deligne, Grothendieck, and Schwartz are all Fields medallists.

Career From July 2011 until 2016, Scholze was a research fellow of the Clay Mathematics Institute in New Hampshire. In 2012, shortly after completing his PhD, he was made full professor in the University of Bonn, becoming at the age of 24 the youngest full professor in Germany. In fall 2014, Scholze was appointed a chancellor's professor in the University of California, Berkeley, where he taught a course on p-adic geometry. In 2018, Scholze was appointed as a director of the Max Planck Institute for Mathematics in Bonn.

Work Peter Scholze's work focuses on local aspects of p-adic algebraic geometry. He presented in a more compact form some of the previous fundamental theories pioneered by Gerd Faltings, Jean-Marc Fontaine and later by Kiran Kedlaya. His PhD thesis on perfectoid spaces yields the solution to a special case of the weight-monodromy conjecture. Scholze and Bhargav Bhatt have developed a theory of prismatic cohomology, which has been described as progress towards motivic cohomology by unifying singular cohomology, de Rham cohomology, ℓ-adic cohomology, and crystalline cohomology. Scholze and Dustin Clausen proposed a program for condensed mathematics.

Awards In 2012, he was awarded the Prix and Cours Peccot. He was awarded the 2013 SASTRA Ramanujan Prize. In 2014, he received the Clay Research Award. In 2015, he was awarded the Cole Prize in Algebra, and the Ostrowski Prize. He received the Fermat Prize 2015 from the Institut de Mathématiques de Toulouse. In 2016, he was awarded the Leibniz Prize 2016 by the German Research Foundation. He declined the $100,000 "New Horizons in Mathematics Prize" of the 2016 Breakthrough Prizes. His turning down of the prize received some media attention. In 2017 he became a member of the German Academy of Sciences Leopoldina. In 2018, at thirty years old, Scholze, who was at the time serving as a mathematics professor in the University of Bonn, became one of the youngest mathematicians ever to be awarded the Fields Medal for "transforming arithmetic algebraic geometry over p-adic fields through his introduction of perfectoid spaces, with application to Galois representations, and for the development of new cohomology theories." In 2019, Scholze received the Great Cross of Merit of the Order of Merit of the Federal Republic of Germany. In 2022 he became a foreign member of the Royal Society and was awarded the Pius XI Medal from the Pontifical Academy of Sciences.

Personal life Scholze is married to a fellow mathematician and has a daughter.

References

External links Prof. Dr. Peter Scholze, University of Bonn (in German) Prof. Dr. Peter Scholze, Hausdorff Center for Mathematics Prof. Dr. Peter Scholze, Academy of Sciences Leopoldina (in German) Peter Scholze's results at International Mathematical Olympiad Klarreich, Erica (28 June 2016), "The Oracle of Arithmetic", Quanta Magazine ("Peter Scholze And The Future of Arithmetic Geometry") Scopus preview – Scholze, Peter – Author details – Scopus Hesse, Michael (16 August 2018), "Interview mit Peter Scholze "Mathematiker brauchen eine hohe Frustrationstoleranz"", Berliner Zeitung Annual Report 2012: Interview with Research Fellow Peter Scholze (PDF), Clay Mathematics Institute, 2012, pp. 12–14

Illustrations

Worked examples

Example 1 — a first encounter with Peter Scholze

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

In research: Peter Scholze 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 Scholze 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 Scholze is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1987 births, 21st-century German mathematicians, Academic staff of the University of Bonn, so understanding it makes those chapters shorter.
In everyday life: Look for Peter Scholze 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 Scholze in 20 minutes

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

Frequently asked questions

What is Peter Scholze in simple terms?

Why does Peter Scholze 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 Scholze?

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 Scholze.