Topology Quotes (2 quotes)
No other theory known to science [other than superstring theory] uses such powerful mathematics at such a fundamental level.
because any unified field theory first must absorb the Riemannian geometry of Einsteins theory and the Lie groups coming from quantum field theory
The new mathematics, which is responsible for the merger of these two theories, is topology, and it is responsible for accomplishing the seemingly impossible task of abolishing the infinities of a quantum theory of gravity.
In 'Conclusion', Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (1995), 326.
The basic ideas and simplest facts of set-theoretic topology are needed in the most diverse areas of mathematics; the concepts of topological and metric spaces, of compactness, the properties of continuous functions and the like are often indispensable.
As co-author with H. Hopf, Topologie I (1935), 23. As quoted, translated and cited in Reinhold Remmert, Theory of Complex Functions (1991), 9-10. From the original German, Die Grundbegriffe und die einfachsten Tatsachen aus der mengentheoretischen Topologie braucht man in sehr verschiedenen Gebieten der Mathematik; die Begriffe des topologischen und des metrischen Raumes, der Kompaktheit, die Eigenschaften stetiger Abbildungen u. dgl. sind oft unentbehrlich.
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- 
