To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers.
--
Diary entry (March 1906), # 759, The Diaries of Paul Klee, 1898-1918Paul Klee
If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.
George Dantzig
In a mathematical sense, space is manifoldness, or combination of numbers. Physical space is known as the 3-dimension system. There is the 4-dimension system, there is the 10-dimension system.
Charles Proteus Steinmetz
Pythagoras, as everyone knows, said that "all things are numbers." This statement, interpreted in a modern way, is logical nonsense, but what he meant was not exactly nonsense. He discovered the importance of numbers in music and the connection which he established between music and arithmetic survives in the mathematical terms "harmonic mean" and "harmonic progression." He thought of numbers as shapes, as they appear on dice or playing cards. We still speak of squares or cubes of numbers, which are terms that we owe to him. He also spoke of oblong numbers, triangular numbers, pyramidal numbers, and so on. These were the numbers of pebbles (or as we would more naturally say, shot) required to make the shapes in question.
Pythagoras
One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?
Stephen Hawking
The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers.
Bill Gates
Klee, Paul
Klein, A.M.
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