Press releases

Peter Scholze, director at the Max Planck Institute for Mathematics and professor at the University of Bonn, was awarded the Pius XI Gold Medal 2020 by the Pontifical Academy of Sciences. The medal is awarded every two years to a young scientist under the age of 45, chosen for his or her exceptional promise. After Luis A. Caffarelli (1988), Laure Saint-Raymond (2004), and Cédric Villani (2014), Peter Scholze is only the fourth mathematician to receive this honor.

Peter Scholze was born in 1987. Studies of Mathematics at the University of Bonn, Master 2010, PhD 2012. Clay Research Fellow 2011-2016. Chancellor's Professor, UC Berkeley, Fall 2014. Hausdorff Chair, University of Bonn, since October 2012. Scientific Member and Director, MPI for Mathematics, since July 2018. Awards (selection): 2014 Clay Research Award, 2015 Ostrowski Prize, 2016 Leibniz Prize of the DFG, 2018 Fields Medal, 2019 Great Cross of Merit of Germany, 2022 Foreign Member of the Royal Society.

The Pontifical Academy of Sciences is the only supranational academy of sciences in the world. Founded in Rome in 1603 as the first exclusively scientific academy in the world with the name Linceorum Academia, to which Galileo Galilei was appointed member in 1610, it was reestablished in 1847 by Pius IX with the name Pontificia Accademia dei Nuovi Lincei. It was moved to its current headquarters in the Vatican Gardens in 1922, and given its current name and statutes by Pius XI in 1936. Its mission is to honor pure science wherever it may be found, ensure its freedom, and encourage research for the progress of science. Its 80 Pontifical Academicians are appointed for life by the Holy Father following proposals by the academic body and chosen without any form of ethnic or religious discrimination from the most eminent scientists and scholars of the mathematical and experimental sciences of every country of the world.

(Source: The Pontifical Academy of Sciences, Photo credit: Barbara Frommann)

The Fields Medal is considered the Nobel Prize of mathematics, and this year the International Mathematical Union chose to award it to Peter Scholze. The professor at the University of Bonn’s Hausdorff Center for Mathematics and Director at the Max Planck Institute for Mathematics was presented with the award during the International Congress of Mathematicians in Rio de Janeiro. The 30-year-old is only the second German to ever receive this prize.

“I am grateful for the extraordinary honour, bestowed upon me with the Fields Medal,” says Peter Scholze. The first German mathematician to be awarded the prize was Gerd Faltings in 1986, who is also a Director at the Max Planck Institute for Mathematics and a professor at the Hausdorff Centre for Mathematics. The Fields Medal is awarded every four years to recognize ‘outstanding mathematical achievement for existing work and for the promise of future achievement’. Recipients must be no more than 40 years of age. The other three fields medals of 2018 went to Caucher Birkar (Cambridge University), Alessio Figalli (ETH Zurich), and Akshay Venkatesh (Stanford University and IAS Princeton).

These type of age limits have never been an issue for Peter Scholze: Right after his doctorate in 2012 at the age of 24 he became the youngest full professor at a German university, taking over one of the prestigious Hausdorff Chairs of the Hausdorff Centre at the University of Bonn. Even at this young age, he was considered one of the most brilliant mathematicians in his field. Now, at 30 years of age, Peter Scholze can already look back on an outstanding career and numerous awards, including the Leibniz Prize from the German Research Foundation. “I am delighted that we were able to attract Peter Scholze to the Max Planck Institute for Mathematics, and that together with the University of Bonn we have been able to keep him in Germany,” says Martin Stratmann, President of the Max Planck Society.

Groundbreaking methods at the intersection between number theory and geometry

With the Fields Medal, the International Mathematical Union acknowledges Peter Scholze’s groundbreaking contributions to arithmetic geometry. Number theory and geometry come together in this field of mathematics, which means that the properties of integral numbers are explored using geometric methods. In the past, this approach has allowed for century old problems – such as Fermat’s Last Theorem – to be proven, which could not be solved with purely number theoretic methods. The field also provides for the basic principles of many modern encryption methods.

The objective of number theory is to answer questions about integral numbers, for example whether there is an infinite number of twin primes such as 3 and 5, 5 and 7, 11 and 13, etc. Or the question, how prime numbers are distributed along the number line. Geometry is dedicated to studying such objects as knots, planes, or higher-dimensional spaces. One important issue is the question, when two geometrical shapes are equivalent, that is when their essential geometric properties are the same. Mathematicians develop procedures for finding out, for example, whether two knots that initially appear to be different may still have been formed based on the same knotting rule. In arithmetic geometry, numbers are themselves understood as points in larger geometric spaces.

Entirely new possibilities for number theorists

Peter Scholze has discovered a new class of geometric structures, known as perfectoid spaces. These spaces are very large and complex, but they possess geometric properties that are useful for many problems. Several old and difficult problems of number theory could now be solved, with the help of perfectoid spaces.

“The award and Peter Scholze’s personal success are of great importance, also for the University of Bonn,” says Michael Hoch, Rector of the University of Bonn. “He will, without a doubt, continue to contribute greatly to shaping mathematical research in the future.” Peter Scholze is going to continue his research in Bonn: “The working conditions here in Bonn are excellent, and the international atmosphere is very inspiring,” says the researcher. In addition to his chair at the University’s Hausdorff Centre for Mathematics, he has only recently become Director of the Max Planck Institute for Mathematics. “The Max-Planck-Gesellschaft strives to provide the best resources available to support his research,” says Martin Stratmann. This means that Peter Scholze is able to fully devote himself to his next breakthroughs in mathematics.

A press conference with Peter Scholze is held at the Hausdorff Centre for Mathematics on Endenicher Allee 60 in Bonn, at 10:00 a.m. on Tuesday, 7 August 2018.

The Max Planck Institute for Mathematics in Bonn is one of 82 research institutes of the Max Planck Society. The Institute was founded in 1980, and has soon become one of the world’s most prestigious research institutes for mathematics. It is managed by Directors Don Zagier, Gerd Faltings, Werner Ballmann, Peter Teichner and the newest addition to the Board of Directors, Peter Scholze. With only a small number of permanent research and administrative staff, the Institute’s guest program attracts over 400 research mathematicians from around the globe every year. The Institute is home to around 100 long-term guest researchers at all times. Research at the Institute covers most areas of pure mathematics. The Max Planck Institute for Mathematics is one of the six Institutes of the Hausdorff Center of Mathematics.

For further information about Peter Scholze, please visit:
http://www.hcm.uni-bonn.de/scholze-background

Media contact person:
Christian Blohmann
Max Planck Institute for Mathematics, Bonn
Phone: +49-228-402302
Email: blohmann@mpim-bonn.mpg.de

Photo credit:
Volker Lannert / University of Bonn

Danylo Radchenko, PhD student at the Max Planck Institute for Mathematics and the Bonn International Graduate School for Mathematics, on the famous sphere packing problem, his contribution to the proof in dimension 24, and on being a PhD student in Bonn.

You are co-author of a paper about the sphere packaging problem in dimension 24. Let’s start from the scratch: What’s the sphere packing problem about?

This problem goes way back to 1611 when Johannes Kepler discussed the question how to stack cannon balls most efficiently. He found the answer, but he couldn’t prove it. This is why it’s called the “Kepler conjecture”. Since then, physicists have been working with his solution. But for mathematicians it’s not enough to know the answer, we also have to find a way to deduce logically why it is indeed correct. The solution is actually pretty simple. Almost everyone will find it intuitively if you give them a bunch of balls and some time. But the mathematical proof of this is highly complex. Even for a normal three dimensional room, the proof was found only in 1998 by Thomas Hales.

And how did you get from there to dimension 24?
We did not start working on this problem with any particular dimension in mind. However, it was known for some time, from the work of Cohn and Elkies that the sphere packing problem in dimensions 8 and 24 is rather special, and the solution could follow in these dimensions from the existence of certain mysterious functions. Therefore, we were always focused on these special dimensions and the properties of those mysterious functions.

How did you solve this problem?

We have been working on it for several years already. There were phases when we were more focused on it and phases when we were less involved, but we never stopped. It was a group of three people: Maryna Viazovska (a former MPIM student), Andrii Bondarenko,and myself. We did a lot of computations over the time, but somehow didn’t make the progress we wanted. Then, last year, Maryna had the brilliant idea of not constructing the functions we actually needed, but slightly different ones using the theory of modular forms. She discovered that there is a direct relation between these two different fields. She made the real breakthrough. At first, I was skeptic and thought this couldn’t be true. But then I realized quickly that this was going to be the answer. Still, it took us more than a year of hard work until the solution was complete in dimension eight. I helped Maryna on some minor details and with some of the computer calculations, but the solution in this case is rightfully hers.

What was the next step?
Several days after Maryna had submitted her paper on the sphere packing problem in dimension eight, she called me and asked if we could now join forces with Henry Cohn, Abhinav Kumar, and Stephen D. Miller, who were also working on this problem, to solve the problem in dimension 24, which is more challenging for technical reasons. Of course I was happy to do so. We then completed the paper in one week of very intense work. At peak moments our team exchanged about ten emails every hour. We were in quite a hurry, because now that the solution in dimension eight was out there, others could have done it for dimension 24 as well.

Is this only of theoretical interest or are there some aspects of the sphere packaging problem that are related to practical issues?
It is for example related to coding theory and combinatorics. Improvements made for the sphere packing problem also stimulate new developments in those fields.  An object closely related to the solution in the 24-dimensional case, the so-called binary Golay code, was used by the NASA in the Voyager program to check if messages sent through long distances arrive correctly despite the high background noise in space.

In the end, I think that the most important result of our work is different: it is not the solution of the sphere packing problem itself, but the newly discovered connection to modular forms. This could lead to completely new developments. That’s very exciting, and we are currently trying to better understand this connection.

Is the sphere packaging problem part of your PhD project, too?
No. In my PhD, I’m working on the topic of functional equations for polylogarithms. That was a bit stressful because when the intense phase of working on the sphere packaging problem started, I was about to submit my PhD thesis. Of course, then I thought, the PhD could wait. But now I’ve submitted it, finally, and I will defend it soon.

You’re originally from the Ukraine. How did you come to Bonn?
Maryna invited me as a guest to the Max Planck Institute when she was a PhD student here herself and I was still a bachelor student. Back then I also met Don Zagier for the first time, who’s now my advisor. I was really impressed by the atmosphere here and wanted to return. It’s actually hard to find words for how nice it is. There just happens so much in mathematics in Bonn. You have really great colleagues to talk to, there are a lot of talks and events, and researchers from all over the world come to the Hausdorff Center for guest programs. That’s very inspiring. The mood here in Bonn definitely contributed significantly to my work.

Prof. Kari Vilonen has received one of the prestigeous Humboldt Research Awards of 2014 for his important contributions to geometric representation theory. He will use the award for a research stay at the Max Planck Institute for Mathematics in Bonn. His host is MPIM researcher Geordie Williamson.

Kari Vilonen received his PhD in 1983 from Brown University. After postdoctoral positions at MIT and MSRI from 1983-1986, he was Assistant Professor at Harvard University from 1986-1989. From 1989-2000 he held a faculty position at Brandeis University and was visiting professor at MPIM in 1998 and Harvard University in 1999. Since 2000 he is on the faculty at Northwestern University and since 2010 at Helsinki University. Kari Vilonen was awarded a Guggenheim Fellowship in 1997 and an AMS Centennial Fellowship in 1991. He was editor of Annals of Mathematics from 2003-2009 and is member of the Finnish Academy of Science and Letters.

The Humboldt research award is granted "in recognition of a researcher's entire achievements to date to academics whose fundamental discoveries, new theories, or insights have had a significant impact on their own discipline and who are expected to continue producing cutting-edge achievements in the future." Award winners are invited to spend a period of up to one year cooperating on a long-term research project with specialist colleagues at a research institution in Germany. The award is valued at 60,000 EUR.

Im Alter von nur 25 Jahren und 3 Monaten hat Moritz Rodenhausen seine Dissertation „Centralisers of polynomially growing automorphisms of free groups“ abgeschlossen. Dafür wurde ihm auf der Jahreshauptversammlung der Max-Planck-Gesellschaft im Juni dieses Jahres der Dieter-Rampacher-Preis 2013 für den jüngsten Doktoranden der gesamten Max-Planck-Gesellschaft verliehen. Der Preis ist mit 2400 Euro dotiert und wurde vom Präsidenten der MPG, Prof. Dr. Martin Stratmann, überreicht. Die Doktorarbeit wurde von Prof. Dr. Carl-Friedrich Bödigheimer von der Universität Bonn betreut und abschließend mit „sehr gut“ bewertet.

Der Dieter-Rampacher-Preis: Um einen Anreiz für eine frühzeitige Promotion zu geben, zeichnet die Max-Planck-Gesellschaft alljährlich ihren jüngsten Doktoranden - meist im Alter zwischen 25 und 27 Jahren - für seinen hervorragenden Promotionsabschluss mit dem Dieter-Rampacher-Preis aus. Der Preis wurde 1985 von Hermann Rampacher, Förderndes Mitglied der Max-Planck-Gesellschaft, gestiftet; er dient dem Andenken an seinen 1945 im Alter von zwanzig Jahren gefallenen Bruder Dieter Rampacher, Student der Physik an der TH Stuttgart. Seit 2011 hat Carsten A. Rampacher, der Sohn des Stifters und ebenfalls Förderndes Mitglied der Max-Planck-Gesellschaft, die Finanzierung des Preises übernommen.

(Photo credit: Denise Vernillo/MPG)

Werner Nahm, externes wissenschafliches Mitglied des Max-Planck-Instituts für Mathematik, wird die Max-Planck-Medaille 2013, die höchste Auszeichnung für theoretische Physik der Deutschen Physikalischen Gesellschaft, verliehen. Werner Nahm hat auf dem Gebiet der Quantenfeldtheorie herausragende Leistungen vollbracht. Grundlegend waren seine Arbeiten zur Klassifikation der Super-Lie-Algebra, die Klassifikation der magnetischen Monopol-Lösungen in Yang-Mills-Theorien, und die in diesem Zusammenhang aufgestellten, nach ihm benannten „Nahm-Gleichungen“. Nahm hat Pionierarbeit bei der Entwicklung der so genannten „heterotischen Stringtheorie“ geleistet. Diese Theorie bildet heute die Basis für die Mehrzahl der gegenwärtig diskutierten phänomenologischen Anwendungen der Superstringtheorie. Die Auszeichnung besteht aus einer Goldmedaille, die im März 2013 während der DPG-Jahrestagung in Dresden überreicht wird.

Werner Nahm wurde 1972 in Bonn promoviert. Von dort wechselte er ans CERN, arbeitete am Max-Planck-Institut für Mathematik in Bonn und ging 1986 als Associate Professor an die University of California (UC Davis). 1989 wurde er auf einen Lehrstuhl nach Bonn berufen, folgte aber 2002 einem Ruf als „Senior Professor“ an das Dublin Institute for Advanced Studies. Nahm zeichnet sich durch ein breites wissenschaftliches Interesse aus, das von der Mitarbeit im Arbeitskreis Energie der DPG bis zur Linguistik und Altertumswissenschaft reicht.

The renowned mathematician Curtis McMullen from Harvard University is one of the recipients of the Humbold Research Award 2011. He will use the award to spend the Fall of 2011 as sabbatical at the Max Planck Institute for Mathematics in Bonn.

The award is given to researchers whose fundamental discoveries, new theories, or insights have had a significant impact on their own discipline and beyond and who are expected to continue producing cutting-edge academic achievements in future. It consitst of a cash prize of 60,000 euro. In addition, award winners are invited to conduct a research project of their own choosing in Germany in close collaboration with a specialist colleague.

Curtis McMullen is Professor for Mathematics at Harvard University. He works in the field of Riemann surfaces, complex dynamics, and hyperbolic geometry. His research has already earned him a number of prizes, among others the Fields Medal of 1998.

Director emeritus Prof. Yuri Manin received the János Bolyai International Award for Mathematics from the Hungarian Academy of Sciences on December 1, 2010. The prize was established in 1902 and is awarded every five years for the best mathematical monograph of the last 15 years. It consists of a cash award of US$ 25,000 and a medal.

The past recipients of the prize include such renowned scientists as Henri Poincaré or David Hilbert. Prof. Manin was awarded the prize for his “breakthrough results and methods” published 1999 in the book Frobenius manifolds, quantum cohomology, and moduli spaces. The monograph draws from several different fields of mathematics such as algebra, geometry or topology, to answer questions originating from theoretical physics.

For more information see: Hungarian Academy of Sciences