Peter Scholze (; born 11 December 1987) is a German mathematician known for his work in

arithmetic geometry In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties. ...

. He has been a professor at the

University of Bonn The University of Bonn, officially the Rhenish Friedrich Wilhelm University of Bonn (), is a public research university in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the () on 18 October 1818 by Frederick Willi ...

since 2012 and co-director at the

Max Planck Institute for Mathematics The Max Planck Institute for Mathematics (, MPIM) is a research institute located in Bonn, Germany. It is named in honor of the German physicist Max Planck and forms part of the Max Planck Society (''Max-Planck-Gesellschaft''), an association o ...

since 2018. He has been called one of the leading mathematicians in the world. In 2018, he won the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...

, an award regarded as the highest professional honor in mathematics.

Early life and education

Scholze was born in

Dresden Dresden (; ; Upper Saxon German, Upper Saxon: ''Dräsdn''; , ) is the capital city of the States of Germany, German state of Saxony and its second most populous city after Leipzig. It is the List of cities in Germany by population, 12th most p ...

and grew up in

Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...

. His father is a

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...

, his mother a

computer scientist A computer scientist is a scientist who specializes in the academic study of computer science. Computer scientists typically work on the theoretical side of computation. Although computer scientists can also focus their work and research on ...

, and his sister studied

chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...

. He attended the in Berlin-Friedrichshain, a gymnasium devoted to mathematics and science. As a student, Scholze participated in the

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. It is widely regarded as the most prestigious mathematical competition in the wor ...

, winning three gold medals and one silver medal. He studied at the

and completed his

bachelor's degree A bachelor's degree (from Medieval Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate degree awarded by colleges and universities upon completion of a course of study lasting three to six years ...

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 Michael Rapoport (born 2 October 1948) is an Austrian mathematician. Career Rapoport received his PhD from Paris-Sud 11 University in 1976, under the supervision of Pierre Deligne. He held a chair for arithmetic algebraic geometry at the Uni ...

. 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 The Clay Mathematics Institute (CMI) is a private, non-profit foundation dedicated to increasing and disseminating mathematical knowledge. Formerly based in Peterborough, New Hampshire, the corporate address is now in Denver, Colorado. CMI's sc ...

in New Hampshire. In 2012, shortly after completing his PhD, he was made full professor at the University of Bonn, becoming at the age of 24 the youngest full professor in Germany. In fall 2014, Scholze was appointed the Chancellor's Professor at

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

, where he taught a course on ''p''-adic geometry. In 2018, Scholze was appointed as a director of the

in Bonn.

Work

Peter Scholze's works 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 Gerd Faltings (; born 28 July 1954) is a German mathematician known for his work in arithmetic geometry. Education From 1972 to 1978, Faltings studied mathematics and physics at the University of Münster. Interrupted by 15 months of obligatory ...

Jean-Marc Fontaine Jean-Marc Fontaine (13 March 1944 – 29 January 2019) was a French mathematician. He was one of the founders of p-adic Hodge theory. He was a professor at Paris-Sud 11 University from 1988 to his death. Life In 1962 Fontaine entered the Éco ...

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 Motivic cohomology is an invariant of algebraic varieties and of more general schemes. It is a type of cohomology related to motives and includes the Chow ring of algebraic cycles as a special case. Some of the deepest problems in algebraic geome ...

by unifying

singular cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed ...

de Rham cohomology In mathematics, de Rham cohomology (named after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic topological information about smooth manifolds in a form particularly adapte ...

, ℓ-adic cohomology, and

crystalline cohomology In mathematics, crystalline cohomology is a Weil cohomology theory for schemes ''X'' over a base field ''k''. Its values ''H'n''(''X''/''W'') are modules over the ring ''W'' of Witt vectors over ''k''. It was introduced by and developed by ...

. 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 The SASTRA Ramanujan Prize is an annual prize awarded to outstanding contributions in mathematics. It was incorporated and is awarded by the Shanmugha Arts, Science, Technology & Research Academy (SASTRA) in Thanjavur district, Tamil Nadu. The awa ...

. In 2014, he received the Clay Research Award. In 2015, he was awarded the Frank Nelson Cole Prize in Algebra, and the

Ostrowski Prize The Ostrowski Prize is a mathematics award given biennially for outstanding research accomplishments in mathematics and numerical analysis. Alexander Ostrowski, a longtime professor at the University of Basel, left his estate to the Ostrowski Found ...

. He received the

Fermat Prize The Fermat prize of mathematics, mathematical research biennially rewards research works in fields where the contributions of Pierre de Fermat have been decisive: * Statements of variational principles * Foundations of probability and analytic geo ...

2015 from the Institut de Mathématiques de Toulouse. In 2016, he was awarded the Leibniz Prize 2016 by the

German Research Foundation The German Research Foundation ( ; DFG ) is a German research funding organization, which functions as a self-governing institution for the promotion of science and research in the Federal Republic of Germany. In 2019, the DFG had a funding bud ...

. He declined the $100,000 "New Horizons in Mathematics Prize" of the 2016

Breakthrough Prize The Breakthrough Prizes are a set of international awards bestowed in three categories by the Breakthrough Prize Board in recognition of scientific advances. The awards are part of several "Breakthrough" initiatives founded and funded by Yuri M ...

s. His turning down of the prize received some media attention. In 2017 he became a member of the

German Academy of Sciences Leopoldina The German National Academy of Sciences Leopoldina (), in short Leopoldina, is the national academy of Germany, and is located in Halle (Saale). Founded on 1 January 1652, based on academic models in Italy, it was originally named the ''Academi ...

. In 2018, at thirty years old, Scholze, who was at the time serving as a mathematics professor at the University of Bonn, became one of the youngest mathematicians ever to be awarded the

for "transforming arithmetic

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

over ''p''-adic fields through his introduction of perfectoid spaces, with application to

Galois representations In mathematics, a Galois module is a ''G''-module, with ''G'' being the Galois group of some extension of fields. The term Galois representation is frequently used when the ''G''-module is a vector space over a field or a free module over a ring ...

, and for the development of new

cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed ...

theories". In 2019, Scholze received the Great Cross of Merit of the

Order of Merit of the Federal Republic of Germany The Order of Merit of the Federal Republic of Germany (, or , BVO) is the highest state decoration, federal decoration of the Federal Republic of Germany. It may be awarded for any field of endeavor. It was created by the first List of president ...

. In 2022 he became a foreign member of the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

and was awarded the Pius XI Medal from the

Pontifical Academy of Sciences The Pontifical Academy of Sciences (, ) is a Academy of sciences, scientific academy of the Vatican City, established in 1936 by Pope Pius XI. Its aim is to promote the progress of the mathematical, physical, and natural sciences and the study ...

Personal life

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

References

External links

Prof. Dr. Peter Scholze

Hausdorff Center for Mathematics The Hausdorff Center for Mathematics (HCM) is a research center in Bonn, formed by the four mathematical institutes of the Rheinische Friedrich-Wilhelms-Universität Bonn (Mathematical Institute, Institute for Applied Mathematics, Institute for Nume ...

Prof. Dr. Peter Scholze

Academy of Sciences Leopoldina The German National Academy of Sciences Leopoldina (), in short Leopoldina, is the national academy of Germany, and is located in Halle (Saale). Founded on 1 January 1652, based on academic models in Italy, it was originally named the ''Academi ...

* * ("Peter Scholze And The Future of Arithmetic Geometry")
Scopus preview – Scholze, Peter – Author details – Scopus
* * {{DEFAULTSORT:Scholze, Peter 1987 births Living people Fields Medalists 21st-century German mathematicians Mathematicians from Berlin International Mathematical Olympiad participants Commanders Crosses of the Order of Merit of the Federal Republic of Germany Academic staff of the University of Bonn University of Bonn alumni Arithmetic geometers People from Friedrichshain-Kreuzberg Members of the German National Academy of Sciences Leopoldina Foreign members of the Royal Society Max Planck Institute directors