Scholze was born in Dresden and grew up in Berlin.^[10] His father is a physicist, his mother a computer scientist, and his sister studied chemistry.^[11] He attended the Heinrich-Hertz-Gymnasium [de] in Berlin-Friedrichshain, a gymnasium devoted to mathematics and science.^[12] As a student, Scholze participated in the International Mathematical Olympiad, winning three gold medals and one silver medal.^[13]

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.^[14] He obtained his Ph.D. in 2012 under the supervision of Michael Rapoport.^[1]

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.

From July 2011 until 2016, Scholze was a Research Fellow of the Clay Mathematics Institute in New Hampshire.^[15] 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.^{[3][14][16][17]}

In fall 2014, Scholze was appointed the Chancellor's Professor at University of California, Berkeley, where he taught a course on p-adic geometry.^[18][19]

In 2018, Scholze was appointed as a director of the Max Planck Institute for Mathematics in Bonn.^[20]

Peter Scholze is an Algebraic Geometer at heart and many of his works focus 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^[21] yields the solution to a special case of the weight-monodromy conjecture.^[22]

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.^[23][24]

Scholze and Dustin Clausen proposed a program for condensed mathematics.

In 2012, he was awarded the Prix and Cours Peccot.^[25] He was awarded the 2013 SASTRA Ramanujan Prize.^[26] In 2014, he received the Clay Research Award.^[27] In 2015, he was awarded the Frank Nelson Cole Prize in Algebra,^[28] and the Ostrowski Prize.^[29][30]

He received the Fermat Prize 2015 from the Institut de Mathématiques de Toulouse.^[31] In 2016, he was awarded the Leibniz Prize 2016 by the German Research Foundation.^[32] He declined the $100,000 "New Horizons in Mathematics Prize" of the 2016 Breakthrough Prizes.^[33] His turning down of the prize received some media attention.^[34]

In 2017 he became a member of the German Academy of Sciences Leopoldina.^[35]

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 Fields Medal^[36][37] 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".^[38]

In 2019, Scholze received the Great Cross of Merit of the Order of Merit of the Federal Republic of Germany.^[39][40][41]

In 2022 he became a foreign member of the Royal Society^[42] and was awarded the Pius XI Medal from the Pontifical Academy of Sciences.^[43]

Scholze is married to a fellow mathematician^[44] and has a daughter.^[45]

• 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