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 variety, alg ...

. He has been a professor at the

University of Bonn The Rhenish Friedrich Wilhelm University of Bonn (german: Rheinische Friedrich-Wilhelms-Universität Bonn) is a public research university located in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the ( en, Rhine U ...

since 2012 and director at the

Max Planck Institute for Mathematics The Max Planck Institute for Mathematics (german: Max-Planck-Institut für Mathematik, MPIM) is a prestigious research institute located in Bonn, Germany. It is named in honor of the German physicist Max Planck and forms part of the Max Planck S ...

since 2018. He has been called one of the leading mathematicians in the world. 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 the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

in 2018, which is regarded as the highest professional honor in mathematics.

Early life and education

Scholze was born in

Dresden Dresden (, ; Upper Saxon: ''Dräsdn''; wen, label=Upper Sorbian, Drježdźany) is the capital city of the German state of Saxony and its second most populous city, after Leipzig. It is the 12th most populous city of Germany, the fourth larg ...

and grew up in

Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...

. 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 caus ...

, his mother a

computer scientist A computer scientist is a person who is trained in the academic study of computer science. Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus (al ...

, and his sister studied

chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...

. 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. The first IMO was held in Romania in 1959. It has since been held annually, except i ...

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

and completed his

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

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 Univ ...

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 (nonprofit), foundation dedicated to increasing and disseminating mathematics, mathematical knowledge. Formerly based in Peterborough, New Hampshire, the corporate address i ...

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 land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

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

in Bonn.

Work

Scholze's work has concentrated on purely local aspects of

such as ''p''-adic geometry and its applications. 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. In 1978 he received his PhD in mathema ...

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 Écol ...

and later by Kiran Kedlaya. His PhD thesis on

perfectoid space In mathematics, perfectoid spaces are adic spaces of special kind, which occur in the study of problems of "mixed characteristic", such as local fields of characteristic zero which have residue fields of characteristic prime ''p''. A perfecto ...

s 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 geo ...

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, 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—a project to unify various mathematical subfields, including

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

and

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

Awards

In 2012, he was awarded the Prix and Cours Peccot. He was awarded the 2013

SASTRA Ramanujan Prize The SASTRA Ramanujan Prize, founded by Shanmugha Arts, Science, Technology & Research Academy (SASTRA) located near Kumbakonam, India, Srinivasa Ramanujan's hometown, is awarded every year to a young mathematician judged to have done outstanding ...

. In 2014, he received the

Clay Research Award __NOTOC__ The Clay Research Award is an annual award given by the Oxford-based Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research. The following mathematicians have received the award: {, class=" ...

. In 2015, he was awarded the Frank Nelson Cole Prize in Algebra, and the

Ostrowski Prize The Ostrowski Prize is a mathematics award given every odd year for outstanding mathematical achievement judged by an international jury from the universities of Basel, Jerusalem, Waterloo and the academies of Denmark and the Netherlands. Alexand ...

. He received the

Fermat Prize The Fermat prize of 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 geometry * Numb ...

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

Leibniz Prize The Gottfried Wilhelm Leibniz Prize (german: link=no, Förderpreis für deutsche Wissenschaftler im Gottfried Wilhelm Leibniz-Programm der Deutschen Forschungsgemeinschaft), in short Leibniz Prize, is awarded by the German Research Foundation to ...

2016 by the

German Research Foundation The German Research Foundation (german: Deutsche Forschungsgemeinschaft ; 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 Germ ...

. 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 Mi ...

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

German Academy of Sciences Leopoldina The German National Academy of Sciences Leopoldina (german: Deutsche Akademie der Naturforscher Leopoldina – Nationale Akademie der Wissenschaften), short Leopoldina, is the national academy of Germany, and is located in Halle (Saale). Founded ...

. 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, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

over ''p''-adic fields through his introduction of

s, with application to Galois representations, 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 viewe ...

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 (german: Verdienstorden der Bundesrepublik Deutschland, or , BVO) is the only federal decoration of Germany. It is awarded for special achievements in political, economic, cultural, intellect ...

. 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 The Pius XI Medal is an award presented every second year by the Pontifical Academy of Sciences to a promising scientist under the age of 45. Winners of the Pius XI Medal (1939-2020) * 1939 Corneille Heymans (Belgium) Physiology * 1942 Harlow Sh ...

from the

Pontifical Academy of Sciences The Pontifical Academy of Sciences ( it, Pontificia accademia delle scienze, la, Pontificia Academia Scientiarum) is a scientific academy of the Vatican City, established in 1936 by Pope Pius XI. Its aim is to promote the progress of the math ...

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 ...

Prof. Dr. Peter Scholze

Academy of Sciences Leopoldina The German National Academy of Sciences Leopoldina (german: Deutsche Akademie der Naturforscher Leopoldina – Nationale Akademie der Wissenschaften), short Leopoldina, is the national academy of Germany, and is located in Halle (Saale). Founded ...

* * ("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 Scientists from Berlin International Mathematical Olympiad participants Commanders Crosses of the Order of Merit of the Federal Republic of Germany University of Bonn faculty University of Bonn alumni Arithmetic geometers People from Friedrichshain-Kreuzberg Members of the German Academy of Sciences Leopoldina Foreign Members of the Royal Society Max Planck Institute directors