Cracow, Poland

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.

By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases... mental power... Probably nothing in the modern world would have more astonished a Greek mathematician than to learn that, under the influence of compulsory education, the whole population of Western Europe, from the highest to the lowest, could perform the operation of division for the largest numbers. This fact would have seemed to him a sheer impossibility.

Alfred North Whitehead, An Introduction to Mathematics (1911) Ch. 5, p. 59.

The final truth about a phenomenon resides in the mathematical description of it; so long as there is no imperfection in this, our knowledge of the phenomenon is complete. We go beyond the mathematical formula at our own risk; we may find a model or a picture which helps us understand it, but we have no right to expect this, and our failure to find such a model or picture need not indicate that either our reasoning or our knowledge is at fault. The making of models or pictures to explain mathematical formulas and the phenomena they describe is not a step towards, but a step away from reality; it is like making a graven image of a spirit.

Sir James Jeans, The Mysterious Universe (1930)

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.

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Exchange programmes

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30-059 Krakow

Centre for International Students

Regular studies

P: +48 12 617 50 92

P: +48 12 617 46 15

F: +48 12 617 52 39

E: international.students@agh.edu.pl

Exchange programmes

P: +48 12 617 52 37

P: +48 12 617 52 38

F: +48 12 617 52 39

E: exchange@agh.edu.pl