Mathematical analysis is as extensive as nature itself; it defines all perceptible relations, measures times, spaces, forces, temperatures:;; this difficult science is formed slowly, but it preserves every principle which it has once acquired; it grows and strengthens itself incessantly in the midst of the many variations and errors of the human mind. It's chief attribute is clearness; it has no marks to express confused notations. It brings together phenomena the most diverse, and discovers the hidden analogies which unite them.
- Joseph Fourier
source: Joseph Fourier (2007). “The Analytical Theory of Heat”, p.7, Cosimo, Inc.
topic: Confused, Errors, Space, Clearness, Mathematical Analysis
The proof given by Wright, that non-adaptive differentiation will occur in small populations owing to "drift," or the chance fixation of some new mutation or recombination, is one of the most important results of mathematical analysis applied to the facts of neo-mendelism. It gives accident as well as adaptation a place in evolution, and at one stroke explains many facts which puzzled earlier selectionists, notably the much greater degree of divergence shown by island than mainland forms, by forms in isolated lakes than in continuous river-systems.
- Julian Huxley
source: Robert Fritz (1986). “The Path of Least Resistance: Principles for Creating what You Want to Create”, Stillpoint Pub
topic: Rivers, Lakes, Islands, Mathematical Analysis, Divergence
I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary -- being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived.
- George Boole
source: George Boole (1872). “A Treatise on Differential Equations”, p.5
topic: Order, Ideas, Doubt, Mathematical Analysis
Whether game theory leads to clear-cut solutions, to vague solutions, or to impasses, it does achieve one thing. In bringing techniques of logical and mathematical analysis gives men an opportunity to bring conflicts up from the level of fights, where the intellect is beclouded by passions, to the level of games, where the intellect has a chance to operate.
- Anatol Rapoport
source: "The Use and Misuse of Game Theory". Scientific American, (p. 114), December 1962.
topic: Passion, Fighting, Cutting, Mathematical Analysis, Vague
The great body of physical science, a great deal of the essential fact of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of one of the new great complex worldwide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write.
- H. G. Wells
topic: Writing, Thinking, Average, Mathematical Analysis, Physical Science
So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? Far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality.
- Henri Poincare
source: "Statistical Mechanics of Disordered Systems: A Mathematical Perspective". Book by Anton Bovier, p. 3, 2006.
topic: Eye, Reality, Games, Mathematical Analysis, Objective Reality
Now, in the development of our knowledge of the workings of Nature out of the tremendously complex assemblage of phenomena presented to the scientific inquirer, mathematics plays in some respects a very limited, in others a very important part. As regards the limitations, it is merely necessary to refer to the sciences connected with living matter, and to the ologies generally, to see that the facts and their connections are too indistinctly known to render mathematical analysis practicable, to say nothing of the complexity.
- Oliver Heaviside
topic: Knowledge, Play, Important, Inquirers, Mathematical Analysis