A Quote by Franz Karl Achard
Everyone now agrees that a physics lacking all connection with mathematics ... would only be an historical amusement, fitter for entertaining the idle than for occupying the mind of a philosopher.
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The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics.
He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics. The fact which interests us most is the life of the naturalist. The purest science is still biographical.
Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.
It seems that every practitioner of physics has had to wonder at some point why mathematics and physics have come to be so closely entwined. Opinions vary on the answer. ..Bertrand Russell acknowledged..'Physics is mathematical not because we know so much about the physical world, but because we know so little.' ..Mathematics may be indispensable to physics, but it obviously does not constitute physics.
One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics.
Never allow any unnecessary or vain thought to occupy your mind. This is more easily said than done. You cannot make your mind a blank all at once. So in the beginning try to prevent evil or idle thoughts by occupying your mind with the analysis of your own faults, or the contemplation of the Perfect Ones.
My father said he did have the mathematics of mind physics, or the physics of consciousness.
I do not think the division of the subject into two parts - into applied mathematics and experimental physics a good one, for natural philosophy without experiment is merely mathematical exercise, while experiment without mathematics will neither sufficiently discipline the mind or sufficiently extend our knowledge in a subject like physics.
Young people are fitter to invent than to judge; fitter for execution than for counsel; and more fit for new projects than for settled business.
There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depends heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood.
Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.
I would rather write for the instruction, or even the amusement of the poor than for the amusement of the rich.
As for me, I want to have fun while I'm working. Now not everyone thinks physics is fun, but I do. I think experimental physics is especially fun, because not only do you get to solve puzzles about the universe or on Earth, there are really cool toys in the lab.
The history of mathematics, lacking the guidance of philosophy, [is] blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, is empty.
I was trained as a philosopher never to put philosophers and their ideas into historical contexts, since historical context has nothing to do with the validity of the philosopher's positions. I agree that assessing validity and contextualizing historically are two entirely distinct matters and not to be confused with one another. And yet that firm distinction doesn't lead me to endorse the usual way in which history of philosophy is presented.
It seems to me that if one had kept silence up to now regarding religion, people would still be submerged in the most grotesque and dangerous superstition ... regarding government, we would still be groaning under the bonds of feudal government ... regarding morals, we would still be having to learn what is virtue and what is vice. To forbid all these discussions, the only ones worthy of occupying a good mind, is to perpetuate the reign of ignorance and barbarism.
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