Innsbruck, Austria

Doctor of Philosophy, PhD

6 Semester

180 ECTS

6 Semester

180 ECTS

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change. It has no generally accepted definition.

Who has studied the works of such men as Euler, Lagrange, Cauchy, Riemann, Sophus Lie, and Weierstrass, can doubt that a great mathematician is a great artist? The faculties possessed by such men, varying greatly in kind and degree with the individual, are analogous with those requisite for constructive art. Not every mathematician possesses in a specially high degree that critical faculty which finds its employment in the perfection of form, in conformity with the ideal of logical completeness; but every great mathematician possesses the rarer faculty of constructive imagination.

E. W. Hobson, Presidential Address British Association for the Advancement of Science (1910) Nature Vol. 84 p. 290 as quoted by Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914) p. 184.

“It’s magic,” the chief cook concluded, in awe.

“No, not magic,” the ship’s doctor replied. “It’s much more. It’s mathematics.”

“No, not magic,” the ship’s doctor replied. “It’s much more. It’s mathematics.”

David Brin, Glory Season (1993), chapter 24

If you are interested in the ultimate character of the physical world, or the complete world, and at the present time our only way to understand that is through the mathematical type of reasoning... the great depth of character of the universality of the laws, the relationships of things... I don't know any other way to do it, we don't know any other way to describe it accurately... or to see the interrelationships without it... don't misunderstand me, there are many, many aspects of the world that mathematics is unnecessary for... but we were talking about physics... to not know mathematics is a severe limitation in understanding the world.

Richard Feynman, "The Rules of the Game," The Pleasure of Finding Things Out (1999)