A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street. Mathematical Problems (1900)
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. Mathematical Problems (1900)
History teaches the continuity of the development of science. We know that every age has its own problems, which the following age either solves or casts aside as profitless and replaces by new ones. Mathematical Problems (1900)
To new concepts correspond, necessarily, new signs. These we choose in such a way that they remind us of the phenomena which were the occasion for the formation of the new concepts. Mathematical Problems (1900)