Topology and number theory are my faves.

 

Topology and number theory are my faves.
--
Barnard Physics Mechanics PHYS BC2001 (Autumn 2010)

 

Janna Levin

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Topology provides the synergetic means of ascertaining the values of any system of experiences. Topology is the science of fundamental pattern and structural relationships of event constellations.

 

Buckminster Fuller

 

Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory. As philosopher of science Karl Popper has emphasized, a good theory is characterized by the fact that it makes a number of predictions that could in principle be disproved or falsified by observation. Each time new experiments are observed to agree with the predictions the theory survives, and our confidence in it is increased; but if ever a new observation is found to disagree, we have to abandon or modify the theory.

 

Stephen Hawking

 

Circumst‘ntial evidence, Markham, is the utt‘rest tommyrot imag‘nable. Its theory is not unlike that of our present-day democracy. The democratic theory is that if you accumulate enough ignorance at the polls, you produce intelligence; and the theory of circumst‘ntial evidence is that if you accumulate a sufficient number of weak links, you produce a strong chain.

 

S. S. Van Dine

 

In these days the angel of topology and the devil of abstract algebra fight for the soul of every individual discipline of mathematics.

 

Hermann Weyl

 

Ten is the very nature of number. All Greeks and all barbarians alike count up to ten, and having reached ten revert again to the unity. And again, Pythagoras maintains, the power of the number 10 lies in the number 4, the tetrad. This is the reason: if one starts at the unit (1) and adds the successive number up to 4, one will make up the number 10 (1+2+3+4 = 10). And if one exceeds the tetrad, one will exceed 10 too.... So that the number by the unit resides in the number 10, but potentially in the number 4. And so the Pythagoreans used to invoke the Tetrad as their most binding oath: "By him that gave to our generation the Tetractys, which contains the fount and root of eternal nature..."

 

Pythagoras