Moscow, Russia

Geometric Group Theory, Geometric Topology, Hyperbolic Geometry, Discrete Subgroups of Lie Groups, Arithmetic Groups, Reflection Groups, Coxeter Polytopes

Language: English Studies in English
University website: mipt.ru/english/
4 years
Discrete
Discrete in science is the opposite of continuous: something that is separate; distinct; individual. Discrete may refer to:
Theory
A theory is a contemplative and rational type of abstract or generalizing thinking, or the results of such thinking. Depending on the context, the results might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.
Theory
Philosophical theories or ideas, as points of view, instruments of criticism, may help us to gather up what might otherwise pass unregarded by us. “Philosophy is the microscope of thought.” The theory or idea or system which requires of us the sacrifice of any part of this experience, in consideration of some interest into which we cannot enter, or some abstract theory we have not identified with ourselves, or what is only conventional, has no real claim upon us.
Walter Pater (1873), The Renaissance, Conclusion
Theory
Their ideas seemed to him fruitful when he was reading or was himself seeking arguments to refute other theories, especially those of the materialists; but as soon as he began to read or sought for himself a solution of problems, the same thing always happened. As long as he followed the fixed definition of obscure words such as spirit, will, freedom, essence, purposely letting himself go into the snare of words the philosophers set for him, he seemed to comprehend something. But he had only to forget the artificial train of reasoning, and to turn from life itself to what had satisfied him while thinking in accordance with the fixed definitions, and all this artificial edifice fell to pieces at once like a house of cards, and it became clear that the edifice had been built up out of those transposed words, apart from anything in life.
Leo Tolstoy, Anna Karenina (1873-1877), Tr. C. Garnett (New York: 2003), Part 8, Chapter 9, p. 728
Theory
The final test of a theory is its capacity to solve the problems which originated it.
George Dantzig (1963) Linear Programming and Extensions, Princeton University Press, p. vii.
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