Press releases

Artificial intelligence and computer science are driving developments in many areas of society – including in scientific research. This has prompted the Max Planck Society and the Alexander von Humboldt Foundation to honour outstanding achievements in the use of algorithms in mathematics, microscopy and climate research in 2024: The Max Planck-Humboldt Research Award, endowed with 1.5 million euros, goes to Geordie Williamson, who was Advanced Researcher at the Max Planck Institute for Mathematics from 2011-2016, and is now Professor at the University of Sydney. Williamson uses artificial intelligence (AI) for his fundamental work in mathematics.

Scientists today use artificial intelligence in many areas, especially in the natural sciences, for tasks such as analysing data or images. In theoretical mathematics, on the other hand, AI has barely been used thus far. Now Geordie Williamson is aiming to change that. In his previous work he has already used artificial neural networks, which can guide mathematical intuition by drawing attention to previously unrecognised relationships in a large number of mathematical objects. Artificial intelligence can also help to generate examples or counterexamples that prove or disprove mathematical assumptions. Although artificial neural networks can recognise patterns in large data sets very efficiently and effectively, they know nothing about mathematics. It therefore remains the task of mathematicians to filter out the sensible proposals from AI, to interpret them and, in the case of new assumptions about mathematical relationships, to prove or disprove them. Geordie Williamson wants to optimise the possibilities of using AI in theoretical mathematics in the collaboration made possible by the Max Planck-Humboldt Research Award. To this end, he will work closely with researchers from the University of Bonn and the Max Planck Institute for Mathematics in Bonn, where he will also spend two periods of several months each.

Connecting the countable with geometry

Geordie Williamson's previous research work was characterised, among other things, by the fact that he brought together different fields such as combinatorics and geometry. In simple terms, combinatorics can be understood as the branch of mathematics that is dedicated to everything that can be counted; it includes subjects such as graph theory and discrete mathematics. Geometry is about objects in spaces, i.e. straight lines, surfaces, and solids, just like in school maths. Both sub-areas come together in a simple example when the intersection points of a curve and a surface are to be counted. Geordie Williamson has now opened up ways of solving combinatorics problems with geometric tools, for which purpose he first had to develop a kind of common mathematical language for the two fields so that combinatorial problems could be worked on in geometry, but geometry could also be translated into combinatorics. With this approach, Geordie Williamson has proved or disproved various assumptions that mathematicians have been working on intensively, but to no avail, for a long time.

For example, Williamson in collaboration with Ben Elias from the University of Oregon provided a general proof of an important conjecture in mathematics relating to Kazhdan-Lusztig polynomials. The work of David Kazhdan and George Lusztig provided precise recipes for building up certain mathematical objects out of constituent pieces. Imagine a recipe that contains a list of ingredients and instructions on what to do with them, but the recipe does not specify the quantities. Kazhdan and Lusztig hypothesised that there are polynomials in mathematics for such cases, from which the quantities for the recipe can be determined. Polynomials are formulae that are familiar to us in their simple form from the binomial formulae we study in school. Geordie Williamson has proven this assumption, for which evidence had previously been sought in vain for a long time. His methods, borrowed from geometry, also make it much easier to solve the polynomials that provide the unknown data and to analyse them in greater depth.

Solving knot theory problems with the help of AI

As part of the collaboration with researchers from the University of Bonn and the Max Planck Institute for Mathematics, all possible as a result of the award, Williamson will tackle various mathematical problems with the help of artificial intelligence. Amongst the problems that they will tackle is a problem in knot theory. In simple terms, this can be explained by the fact that it is often impossible to recognise whether knotted structures, such as in a string, are actually knotted. What this means is: does the knot remain intact when you pull on the ends of the cord or does it unravel? One aim of the project is to identify these cases in a simple way so that these uninteresting cases can be quickly filtered out and the researchers can focus on the real knots. AI is set to provide support here and assistance in gaining new mathematical insights. Geordie Williamson studied at the University of Sydney and received his doctorate from the University of Freiburg in 2008. He then conducted research at Oxford University until 2011 and headed a research group at the Max Planck Institute for Mathematics until 2016. After other shorter stints at the Hausdorff Centre for Mathematics in Bonn and at the Institute for Advanced Study, Princeton he was appointed Professor at the University of Sydney in 2017. He serves as the founding Director of the Sydney Mathematical Research Institute. Geordie Williamson is a Fellow of the British Royal Society and the Australian Academy of Science.

About the award

The Max Planck Society and the Alexander von Humboldt Foundation present the Max Planck-Humboldt Research Award, along with 1.5 million euros in prize money, to a researcher from abroad. 80,000 euros in personal prize money is also awarded. The focus here is on personalities whose work is characterised by outstanding potential for the future. The prize is intended to attract particularly innovative scientists working abroad to spend a fixed period of time at a German higher education institution or research facility. The Federal Ministry of Education and Research provides the funding for the award. The focus of the award alternates each year between natural and engineering sciences, life sciences, humanities and social sciences.

Emeritus director of institute passed away at age 85

Bonn, January 8, 2023. The Max Planck Institute for Mathematics in Bonn mourns the death of Professor Yuri Ivanovich Manin. The eminent mathematician passed away on Saturday, January 7, at the age of 85. Yuri Manin was a scientific member and director of the Max Planck Institute for Mathematics from 1992 to 2005, after which he remained an extremely active emeritus director. His work largely influenced the development of modern mathematics. With Yuri Manin, mathematics has lost one of his truly great personalities. He was a wonderful human being and a renowned researcher whose contributions have shaped the entire field. Our institute will always remain his institute, too.

Yuri Ivanovich Manin was born on February 16, 1937 in Simferopol, Crimea, in the Soviet Union. He studied physics and mathematics at Lomonosov Moscow State University where he graduated in 1958. In 1960 he received his doctorate and in 1963 his habilitation from the Steklov Institute of Mathematics in Moscow, where he was Principal Researcher until 1992. After a year on the faculty of MIT in 1992-1993, he became a director at the Max Planck Institute for Mathematics in 1993.

Yuri Manin's many important contributions to mathematics cover a wide spectrum of topics in algebraic geometry, number theory, and mathematical physics. He is an author of over 300 research papers and 11 books. For his manifold achievements he received a number of awards and prizes, among others, the Lenin Prize 1967, the Brouwer Medal 1987, the Frederic Esser Nemmers Prize 1994, the Rolf Schock Prize in Mathematics 1999, the King Faisal International Prize in Mathematics 2002, the Georg Cantor Medal 2002, the Order pour le Mérite for Science and Art, Germany, 2007, the Great Cross of Merit with Star, Germany, 2008, the János Bolyai International Mathematical Prize 2010. He was a member of nine Academies of Sciences and an Honorary Member of the London Mathematical Society. He held honorary degrees at the Sorbonne, and the Universities in Oslo and Warwick.

The Fields Medal is considered the Nobel Prize of mathematics. This year the International Mathematical Union chose to award it to Maryna Viazovska, who wrote her doctoral thesis at the Max Planck Institute for Mathematics with Don Zagier and received her PhD from the University of Bonn in 2013. The Ukranian mathematician is second woman to ever receive this prize.

Maryna Viazovska is awarded the Fields Medal 2022 "for the proof that the E8 lattice provides the densest packing of identical spheres in 8 dimensions, and further contributions to related extremal problems and interpolation problems in Fourier analysis." In doing so, she resolved a question that had stumped mathematicians for more than four centuries: how to pack spheres – such as oranges stacked in a pyramid – as close together as possible. It was in 1611 that Johannes Kepler posited, without proof, that the best solution for packing spheres in a three-dimensional space was in the shape of a pyramid. That hypothesis was finally proved in 1998. With the third dimension resolved, it was time for mathematicians to move on to other dimensions. “Formulating the problem in the same way complicates matters because each dimension is different, and the optimal solution depends very much on the dimension,” says Viazovska. Why did she focus on 8 and 24 dimensions? “Because these are special dimensions, and the solutions are particularly elegant.” The way spheres are packed in these particular dimensions is remarkably symmetrical, and uses the E8 and Leech lattices, respectively. More than a decade ago Henry Cohn and Noam Elkies found that these lattice patterns were close to perfection – to one billionth of a percent – but were unable develop a proof. Viazovska’s brilliant work provided the missing ingredient, demonstrating that these lattices are the densest possible packing patterns in their respective dimensions.

But Viazovska wanted to prove it, suspecting that an auxiliary function existed that could provide the right answer and match the density of the E8 and Leech lattices. In her quest for the right function, she drew on other areas of mathematics – a fact that, according to experts, makes her proof particularly elegant and original. Fueled by creativity and intuition, Viazovska turned to the focus of her dissertation: modular forms, a type of mathematical function with a high level of symmetry. After two years of work, she came up with the right function for 8 dimensions.

Maryna Viazovska was born in Kiev in Ukraine in 1984. She obtained her Bachelor degree in Mathematics in 2005 from Kiev National University and a Master's degree in 2007 from the University of Kaiserslautern. She was a doctoral student of Don Zagier in the MPIM graduate school from 2008-2012, working on modular forms. In 2013 she received her PhD from the University of Bonn. After a postdoctoral position at the Humboldt University in Berlin she joined the faculty of the École Polytechnique Fédérale Lausanne, where she became full professor in 2018.

Video portrait of Maryna Viazovska

Official announcement of the Fields Medals 2022 by the International Mathematical Union

Photo credit:
Matteo Fieni

A number of mathematicians who have held positions, were long-term visitors, or PhD students at the Max Planck Institute for Mathematics are invited to present their work at the next International Congress of Mathematicians (ICM), which will take place on August 1-9, 2018 in Rio de Janeiro. Most notably, the newly appointed MPIM director Peter Scholze and Geordie Williamson, who has been Advanced Researcher at MPIM from 2011-2016, are both invited plenary speakers. Further invited speakers with ties to MPIM include:

• Yves André (09/1985-01/1986: 11/1986-07/1987; 09/1989-12/1990)
• Arthur Bartels (PhD 1999 with Peter Teichner)

• Alexander Belavin (02-03/2012; 02-03/2014)
• Men Chen (academic year 2011/12)
• Vyacheslav Futorny (academic year 2011/12)
• Christof Geiss (academic years 2010/11, 2017/18)
• June Huh (08-11/2013)
• Adrian Iovita (06/2015)
• Jochen Koenigsmann (02-06/2007; 11/2007-02/2008)
• Ulrich Kohlenbach (03-06/2007)
• Wojciech Kucharz (fall 2015/16)
• Martin Möller (Advanced Researcher 2007-2009, recurring visitor since 2010)
• Andrei Okounkov (07/2002)
• Rahul Pandharipande (07/2002)
• Georgios Pappas (07-08/1999; 06/2007)
• Dipendra Prasad (09-10/2007)
• Feliks Przytycki (07-08/1996)
• Sujatha Ramdorai (2003)
• Alan Reid (06/2010, 06/2015)
• Tadashi Tokieda (Hirzebruch lecture 2018)
• Bernardo Uribe (multiple visits 2003, 2004, 2006, 2008, 2015, 2016, 2018)
• Maryna Viazovska (PhD 2009-2012 with Don Zagier, 08-09/2016)
• Anna Wienhard (PhD 2004 with Werner Ballmann)

The International Congress of Mathematicians is the largest and the most important conference in mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize, the Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Being invited to talk at the ICM is considered to be one of the highest honors for a mathematician.

Pavel Mnev, an Advanced Researcher at the Max Planck Institute for Mathematics from 2014-2016, has been awarded the 2016 André Lichnerowicz Prize in Poisson Geometry. The biennial award is given for outstanding work by young mathematicians in Poisson Geometry.

Pavel Mnev received his Ph.D. in 2008 from the Steklov Mathematical Institute of the Russian Academy of Sciences in St. Petersburg under the direction of the mathematical physicist Ludwig Faddeev. Mnev held a postdoctoral position at the University of Zurich, before coming to the Max Planck Institute for Mathematics in Bonn in 2014. This fall, he has moved to a faculty position at the University of Notre Dame. His research interests are in mathematical physics, in particular in the interactions of quantum field theory with topology, homological/homotopical algebra, and supergeometry.

The André Lichnerowicz Prize in Poisson Geometry was established in 2008. It is awarded for notable contributions to Poisson geometry, every two years at the "International Conference on Poisson Geometry in Mathematics and Physics", to researchers who completed their doctorates at most eight years before the year of the Conference. The prize is named in memory of André Lichnerowicz (1915-1998) whose work was fundamental in establishing Poisson Geometry as a branch of mathematics.

At a press conference on June 1, 2015 in Hong Kong, the Shaw Prize Foundation announced that this year's Shaw Prize in Mathematical Sciences is awarded in equal shares to Gerd Faltings and Henryk Iwaniec for their introduction and development of fundamental tools in number theory, allowing them as well as others to resolve some longstanding classical problems. The prize consists of a monetary award of one million US dollars.

From the prize justification of the Shaw Foundation: A polynomial equation of degree n in one variable with coefficients which are rational numbers has just n complex numbers as solutions. Such an equation has a symmetry group, its Galois group, that describes how these complex solutions are related to each other.

A polynomial equation in two variables with rational coefficients has infinitely many complex solutions, forming an algebraic curve. In most cases (that is, when the curve has genus 2 or more) only finitely many of these solutions are pairs of rational numbers. This well-known conjecture of Mordell had defied resolution for sixty years before Faltings proved it. His unexpected proof provided fundamental new tools in Arakelov and arithmetic geometry, as well as a proof of another fundamental finiteness theorem — the Shaferavich and Tate Conjecture — concerning polynomial equations in many variables. Later, developing a quite different method of Vojta, Faltings established a far-reaching higher dimensional finiteness theorem for rational solutions to systems of equations on Abelian Varieties (the Lang Conjectures). In order to study rational solutions of polynomial equations by geometry, one needs arithmetic versions of the tools of complex geometry. One such tool is Hodge theory. Faltings’ foundational contributions to Hodge theory over the p-adic numbers, as well as his introduction of other related novel and powerful techniques, are at the core of some of the recent advances connecting Galois groups (from polynomial equations in one or more variables) and the modern theory of automorphic forms (a vast generalization of the theory of periodic functions). The recent striking work of Peter Scholze concerning Galois representations is a good example of the power of these techniques.

Prof. Dr. Gerd Faltings, born in 1954, studied mathematics and physics at the University of Münster where he received his Diploma and Ph.D. in 1978. After visiting Harvard University from 1978-1979, he was Assistant at the University of Münster from 1979-1982, completing his Habilitation in 1981. Following Professorships at the University of Wuppertal from 1982-1984 and Princeton University from 1985-1994, he became director of the Max Planck Institute for Mathematics in Bonn in 1995. He has already received numerous awards for his work: the Fields Medal in 1986, a Guggenheim Fellowship in 1988, the Gottfried Wilhelm Leibniz Prize in 1996, the Karl Georg Christian von Staudt Prize in 2008, the Heinz Gumin Prize in 2010, and the King Faisal International Prize for Science in 2014.

The Shaw Prize honors individuals who have achieved significant breakthroughs in academic and scientific research or applications and whose work has resulted in a positive and profound impact on mankind. The prize is awarded annually in the three fields: Astronomy, Life Science and Medicine, and Mathematical Sciences,. This is the twelfth year that the Prize has been awarded and the presentation ceremony is scheduled for Thursday, 24 September 2015.

(Photo credit: MFO / Gert-Martin Greuel)

Die Max-Planck-Gesellschaft hat Stefan Willems vom Bonner Max-Planck-Institut für Mathematik mit dem Azubipreis 2014 ausgezeichnet. Stefan Willems hat seine dreijährige Ausbildung zum Fachinformatiker Fachrichtung Systemintegration im Sommer 2013 abgeschlossen und ist derzeit weiter in der IT-Abteilung des MPIM beschäftigt.

Die seit 2007 existierende Auszeichnung, die mit 750 Euro dotiert ist,  ist eine Anerkennung für herausragende berufliche und schulische Leistungen und besonderes soziales Engagement während der Ausbildung; es wird außerdem ein Augenmerk auf die persönliche Entwicklung gelegt. Bis zu 20 dieser Preise vergibt das Auswahlgremium, dem vier Ausbilderinnen und Ausbilder und je ein Mitglied des Gesamtbetriebsrats sowie der Gesamt-Jugend- und Auszubildendenvertretung angehören.

Gerd Faltings, Director at the Max Planck Institute for Mathematics in Bonn and Professor at the University of Bonn, was awarded the 2014 King Faisal International Prize for Science for his groundbreaking contributions to algebraic geometry and number theory. This was announced by the president of the King Faisal Foundation, Prince Khaled Al-Faisal, on 14 January 2014.

The King Faisal International Prize is awarded to “scientists and scholars whose research results in significant advances in specific areas that benefit humanity.” It consists of a certificate, hand-written in Arabic calligraphy summarizing the laureate’s work, a commemorative 24 carat gold medal, uniquely cast for each prize, and a cash award of 750,000 Saudi riyal (150,000 Euro).

Prof. Gerd Faltings is the second director of the Max Planck Institute for Mathematics to receive the prize, after Prof. Yuri Manin in 2002.

The prize committee stated that Prof. Faltings “work combines ingenuity, vision and technical power. He has introduced stunning new tools and techniques which are now constantly used in modern mathematics. His deep insights into the p-adic cohomology of algebraic varieties have been crucial to modern developments in number theory. His work on moduli spaces of abelian varieties has had great influence on arithmetic algebraic geometry. He has introduced new geometric ideas and techniques in the theory of Diophantine approximation, leading to his proof of Lang’s conjecture on rational points of abelian varieties and to a far-reaching generalization of the subspace theorem. Professor Faltings has also made important contributions to the theory of vector bundles on algebraic curves with his proof of the Verlinde formula.”

(Photo credit: MFO / Gert-Martin Greuel)

Founding director of institute passed away at age 84

Bonn, May 30, 2012. The Max Planck Institute for Mathematics in Bonn mourns the death of Professor Dr. Friedrich Hirzebruch. As it became known on Tuesday, the eminent mathematician and citizen of Bonn passed away on Sunday, May 27 at the age of 84. Professor Hirzebuch is the founding director of the Max Planck Institute for Mathematics, which he headed from 1980 to 1995. His work largely influenced the development of modern mathematics. Through his personal efforts and achievements he contributed in an essential way to the reconstruction of mathematics research in Germany after World War II.

Friedrich Hirzebruch was born on October 17, 1927 in Hamm, Westphalia. From 1945 to 1950 he studied mathematics in Munster and Zurich. After two years in Princeton from 1952 to 1954 he was appointed as full Professor at the University of Bonn. His research interests were in the fields of topology and geometry.

For his manifold achievements Friedrich Hirzebruch received a number of awards and prizes. Among others, the Grand Merit Cross with Star of the Federal Republic of Germany, the Wolf Prize for Mathematics, the Seki Takakazu Prize, the Lomonossov Gold Medal, the Albert Einstein Medal, and the Georg Cantor Medal of the Deutsche Mathematikervereinigung. He held honorary doctorates from over 14 universities. He was member of a number of Academies of Science and of the Order pour le mérite.

"With Friedrich Hirzebruch, mathematics has lost one of his truly great personalites. He was a wonderful human being and an eminent researcher whose contributions have shaped the entire field", said Peter Teichner, managing director of the Max Planck Institut for Mathematics in Bonn. "Our institute, which he founded, will always remain his institute, too."