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.