“The study of networks, in the form of mathematical graph theory, is one of the fundamental pillars of discrete mathematics.” (p. 2) #Newman #networks #GraphTheory #mathematics
„A contribution to mathematics and/or science does not consist of a picture, but rather of a picture combined with a description. Without words and formulas, a picture can, at best, be praised for artistic quality. Without an interest in pictures and other aspects of ‚reality,‘ pictures can play no role whatsoever.“ (p. 26) #Mandelbrot #mathematics #picture
„A mathematical theory (or simply a theory) contains rules which allow us to assert that certain assemblies of signs are terms or relations of the theory, and other rules which allow us to assert that certain assemblies are theorems of the theory.“ (p. 16) #Bourbaki #theory #relation #theorem
„Mathematicians have always been convinced that what they prove is ‚true‘. It is clear that such a conviction can be only of a sentimental or metaphysical order, and cannot be justified, or even ascribed a meaning which is not tautological, within the domain of mathematics. The history of the concept of truth in mathematics therefore belongs to the history of philosophy and not of mathematics; but the evolution of this concept has had an undeniable influence on the development of mathematics, and for this reason we cannot pass over it in silence.“ (p. 306f.) #Bourbaki #mathematics #truth
„The originality of the Greeks consists precisely in a conscious effort of arranging mathematical proofs in a sequence so that the passage from one step to the next leaves nothing in doubt and compels universal assent. Of course, the Greek mathematicians, just like their present-day successors, made use of ‚heuristic‘ rather than rigorous arguments in the course of their researches“. (p. 297) #Bourbaki #Greek #mathematics #proof #passage