Quotable Mathematics

"In dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a s...

"A physical system is said to possess a symmetry if one can make a change in the system such that, after the change, the system is exac...

"Because the question for me was always whether that shape we see in our lives was there from the beginning or whether these random eve...

" Mathematics is an exploratory science that seeks to understand every kind of pattern - patterns that occur in nature, patterns invent...

"Because of its foundation in topology, catastrophe theory is qualitative, not quantitative. Just as geometry treated the properties of...

"Every object that we perceive appears in innumerable aspects. The concept of the object is the invariant of all these aspects. From th...

"The calculation of probabilities is of the utmost value, […] but in statistical inquiries there is need not so much of mat...

"The symbols organized by knowledge, or concepts, themselves belong to social nature as its ideological elements. Therefore, by operati...