In recent years, mathematical algorithms have helped art historians and art conservators putting together the thousands of fragments into which an unfortunate WWII bombing destroyed world famous frescos by Mantegna, decide that certain paintings by masters were "roll mates" (their canvases were cut from the same bolt), virtually remove artifacts in preparation for a restoration campaign, get more insight into paintings hidden underneath a visible one.

The presentation reviews these applications, and gives a glimpse into the mathematical aspects that make this possible.

The 19th century saw the emergence of mathematical logic which to some extent became part of the spectrum of mathematical disciplines, and a new interest in the foundations of mathematics driven not only by philosophers, but also by the mathematicians themselves. Weierstrass was ambivalent about these developments. There is no doubt that his new approach to analysis contributed significantly to the concept of number and thus to the philosophy of arithmetic, but he was rather sceptical about the new foundational set theory of his student Georg Cantor (1845–1918). Nevertheless, Weierstrass is mentioned in the context of the foundational crises in mathematics. Heinrich Scholz (1884–1956), the theologian, philosopher and founder of the Department for Mathematical Logic and Foundational Research in Münster, associated Weierstrass with the first foundational crisis in Greek mathematics which led to the concept of irrational numbers and to the development of the infinitesimal calculus in modern times. According to Helmut Hasse and Heinrich Scholz, it was the “ingenious Weierstrass”, who showed that the foundations of the calculus were logically untenable. Weierstrass was also associated with the modern foundational crisis that arose from the problems to prove the consistency of arithmetic in modern axiomatics and triggered by the paradoxes of logic and set theory. This was confirmed by David Hilbert (1862–1943), the Göttingen mathematician and most important voice in foundational questions at the beginning of the 20th century. He held his famous lecture “Über das Unendliche” (“On Infinity”) at the Weierstrass Week in Münster in 1925.

The Weierstrass Lecture entitled Beyond Boundaries: Recent Advances in the Obstacle Problem was given by Prof. Dr. Alessio Figalli (ETH Zurich). In 2018, Figalli was awarded the Fields Medal, often referred to as the "Nobel Prize of Mathematics."

The historical lecture entitled Einstein and Pure Compass Geometry was given by Prof. Dr. Tilman Sauer (Johannes Gutenberg University Mainz).

Further information can be found here.

Impressions of the Weierstrass Lecture can be found here.

The Weierstrass Lecture 2023, entitled Critical Phenomena Through the Lens of the Ising Model, was given by Fields Medal winner Prof. Dr. Hugo Duminil-Copin (Geneva, Bures-sur-Yvette). The historical lecture Karl Weierstrass as innovative math teacher was given by Prof. Dr. Annette Vogt (MPI for the History of Science, Berlin).

Further information can be found here.

The Weierstrass Lecture 2022 entitled Analytical Geometry was given by Fields Medal winner Prof. Dr. Peter Scholze (Bonn). The historical lecture In Higher Spheres was given by Prof. Dr. Klaus Volkert (Wuppertal).

Further information can be found here.

The Weierstrass Lecture 2019, entitled From elliptic integrals to Diophantine equation, was given by Fields Medal winner Prof. Dr. Akshay Venkatesh (Princeton). The historical lecture was given by Prof. Dr. Gregor Nickel (Siegen).

Further information can be found here.

The 2018 Weierstrass Lecture entitled Results and open problems related to Ramsey's theorem was given by Fields Medallist Sir William Timothy Gowers (Cambridge). The historical lecture C. G. J. Jacobi (1804-1851) zwischen Profession und Assimilation. Ein jüdischstämmiger Mathematiker in der preußischen Wissenschaftskultur was given by Prof. Dr. Helmut Pulte (Ruhr-Universität Bochum).

Further information can be found here.

The 2017 Weierstrass Lecture entitled Taming infinities was given by Fields Medallist Prof. Dr. Martin Hairer (University of Warwick, UK), while the historical lecture Felix Hausdorff als Philosoph und Literat was given by Prof. Dr. Walter Purkert (Universität Bonn).

Further information can be found here.

The 2016 Weierstrass Lecture by Prof. Dr. Manjul Bhargava (Princeton University, USA) unfortunately had to be cancelled at short notice.

The 2015 Weierstrass Lecture will be given by Professor Dr. Wendelin Werner, winner of the Fields Medal. Wendelin Werner (born 1968) works in the field of probability theory. In particular, he is interested in self-avoiding wandering and the theory of percolation. He studied at the Ècole normale supérieure in Paris and obtained his doctorate in 1993 at the Pierre and Marie Curie University under Jean-Francois Le Gall. From 1991 to 1997 he was Chargé des Recherches at the CNRS and from 1993 to 1995 a post-doctoral candidate at the University of Cambridge. In 1997 he became a professor at the University of Paris South. He has been a professor at ETH Zurich since 2013.
From the 1990s onwards, Werner played a leading role in the rigorous substantiation of universal properties of Brownian motion and two-dimensional systems at the critical point, which had previously been a central field of research in statistical physics. He collaborated with Oded Schramm and Gregory F. Lawler, among others, as well as with the Fields Medal winner Stanislaw Smirnov. In 2001/2002, for example, he was able to derive the universal exponents for the overlap probability of plane Brownian random paths with Lawler and Schramm. They also proved a conjecture by Benoit Mandelbrot about the fractal dimension of Brownian fronts in two dimensions, namely that this is 4/3.
Wendelin Werner has been honoured many times: in 1998 he received the Rollo Davidson Prize, in 1999 the Paul Doistau-Émile Blutet Prize of the Academie des Sciences, in 2000 the Prize of the European Mathematical Society, in 2001 the Fermat Prize, in 2003 the Jacques Herbrand Prize of the Academie des Sciences, in 2005 the Loève Prize, in 2006 the George Pólya Prize and in 2006 the Fields Medal.

The 2015 historical lecture will be given by Professor Dr. Peter Ullrich, Universität Koblenz-Landau.

The Weierstrass Lecture 2014 "Points and Lines" will be given by Professor Ben Joseph Green. Ben Green (born 1977) specialises in the fields of combinatorics and number theory. He studied at Trinity College, Cambridge, and received his doctorate in 2002 on "Topics in arithmetic combinatorics" under William Timothy Gowers (winner of the Fields Medal). He was then a visiting researcher at the Alfréd Rényi Institute in Budapest and then from 2003 to 2004 at the University of British Columbia in Vancouver. In 2005 he was appointed Professor of Pure Mathematics at the University of Bristol, a post he held until 2006. During this time he was also a Clay Research Fellow and Visiting Professor at MIT - Massachusetts Institute of Technology. From September 2006 to July 2013 he was Herchel Smith Professor of Pure Mathematics at the University of Cambridge. Since August 2013, he has been Waynflete Professor of Pure Mathematics at the University of Oxford.

Green has proved deep combinatorial results that have far-reaching applications in number theory. Most famous are his proof of Cameron and Erdos' conjecture (2004) and his joint work with Terence Tao "The primes contain arbitrarily long arithmetic progressions", which shows that there are arbitrarily long arithmetic progressions of prime numbers.

Ben Green has received many honours: in 2004 he received the Clay Research Award, in 2005 the London Mathematical Society Whitehead Prize, in 2005 the Salem Prize, in 2006 the Ostrowski Prize (together with Terence Tao), in 2007 the SASTRA Ramanujan Prize, in 2008 the European Mathematical Society Prize. He has been a Fellow of the Royal Society since 2010 and a Fellow of the American Mathematical Society since 2012.

The 2014 historical lecture "Heldenverehrung, Rivalität, Epigonentum: Weierstraß und die Berliner Vormacht" will be given by Dr. rer. nat. Ulf Hashagen, Head of the Research Institute for the History of Technology and Science at Deutsches Museum, Munich.

The Weierstrass Lecture 2013 "Rigidity properties of diagonalizable flows on homogeneous spaces" will be given by Professor Elon Lindenstrauss on 14 June 2013 in the Auditorium maximum.

Elon Lindenstrauss (born 1970 in Jerusalem) specialises in the field of ergodic theory and its application to other areas, especially number theory. He completed his doctorate in 1999 under Benjamin Weiss at the Hebrew University of Jerusalem on entropy properties of dynamical systems. He then spent two years at the Institute for Advanced Study in Princeton, was subsequently appointed Szegö Assistant Professor at Stanford and was subsequently a Long Term Prize Fellow at the Clay Mathematics Institute in Cambridge, Massachusetts. He has been a professor at Princeton University since 2004. In 2009, he was also appointed professor at the Hebrew University of Jerusalem.
In 2006, together with A. Katok and M. Einsiedler, Lindenstrauss proved that J. Littlewood's conjecture about simultaneous Diophantine approximation of two real numbers cannot hold only for a set of pairs outside a set of Hausdorff dimension zero. Furthermore, Lindenstrauss (partly together with J. Bourgain) proved the "Quantum Unique Ergodicity Conjec-ture" (by P. Sarnak and Z. Rudnick 1991) for arithmetic hyperbolic surfaces. Recently, together with M. Einsiedler, P. Michel and A. Venkatesh, he studied distributions of periodic torus orbits on certain arithmetic spaces, which led to a generalisation of theorems by H. Minkowski and Y. Linnik.
Elon Lindenstrauss has been honoured many times: in 2003 he received the Salem Prize (together with Kannan Soundararajan), in 2004 the European Ma-thematical Society Prize, in 2005 the Michael Bruno Memorial Award, in 2009 the Erdös Prize, in 2009 the Fermat Prize and in 2010 the Fields Medal.

The 2013 historical lecture “Jewish émigré mathematicians and Germany after World War II” will be given by Professor Dr Volker Remmert, Bergische Universität Wuppertal.

The Weierstrass Lecture 2012 "Reciprocity Laws and Density Theorems" will be held by Professor Richard Taylor on 11 May 2012 in the Auditorium maximum.

Professor Richard Taylor (*19.5.1962) studied at Cambridge and received his doctorate in 1988 from Princeton University, USA, under Andrew Wiles. From 1995 to 1996 he was appointed to the Savilian Chair of Geometry at Oxford University. From 1996 to 2011 he was a professor at Harvard University and since 1 January 2012 he has been at the Institute for Advanced Study in Princeton. In 1994-1995, together with Andrew Wiles, he developed a fundamental and new method in number theory, now called the Taylor-Wiles method, which they both used to complete the proof of Fermat's Last Theorem. In 1998, together with Michael Harris, he proved the local Langlands conjecture for local p-adic solids. In 2001, together with Christophe Breuil, Brian Conrad and Fred Diamond, Taylor proved the Taniyama-Shimura conjecture. In 2009, in collaboration with Laurent Clozel, Michael Harris and Nicholas Shepherd-Barron, he proved the Sato-Tate conjecture. This makes him one of the leading number theorists of the present day. Richard Taylor was honoured with the Ostrowski Prize in 2001 and received the Fermat Prize. In 2002 he gave a plenary lecture at the International Congress of Mathematicians (ICM) in Beijing and in 1994 he was an invited speaker at the ICM in Zurich. In 2007 he received the Shaw Prize and the Clay Research Award. In 2008, he gave a plenary lecture at the European Congress of Mathematicians in Amsterdam.

The 2012 historical lecture "Claude Chevalley, Weierstrass's style, and the transformation of mathematics between the World Wars" will be given by Professor Dr Norbert Schappacher, University of Strasbourg, France.

The Weierstrass Lecture 2011 "Diophantische Approximation" will be given by Professor Dr. Gerd Faltings on 6 May 2011 in the Auditorium maximum.

Faltings studied mathematics and physics at the University of Münster (1972-1978) and received his doctorate there in 1978. He then went to Harvard University for a year and habilitated in Münster in 1981. In 1982, he moved to the University of Wuppertal and, at the age of 27, became Germany's youngest full professor of mathematics. In 1983, Faltings caused a stir in the mathematical world with a paper on so-called algebraic curves. In this work, entitled "Finiteness theorems for Abelian varieties over number fields", he proved that only a finite number of points with rational coordinates can lie on certain algebraic curves, a conjecture made by the British mathematician Louis Mordell in 1922. In this work, he proved two further central conjectures of number theory (the Tate conjecture in the number field case and the Shafarevich conjecture), which imply Mordell's conjecture. In his proof, he also developed new methods in Arakelov geometry. In 1986, he was awarded the Fields Medal - the highest honour in mathematics alongside the Abel Prize - for this breakthrough in arithmetic geometry. Faltings then went to the USA for an extended period to research and teach at Princeton University. He returned to Germany in 1994 and has been Director of the Max Planck Institute for Mathematics in Bonn ever since. His main areas of research are Diophantine equations, moduli spaces and p-adic Galois representations. He has made outstanding contributions to all these areas. Faltings also contributed significantly to the solution of Fermat's conjecture by the British mathematician Andrew Wiles.

The 2011 historical lecture "Die prägenden Jahre im Leben von Karl Weierstraß" will be given by Professor Dr. Jürgen Elstrodt, Universität Münster.