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Beyond the natural numbers, addition, multiplication, and mathematical induction are intuitively clear.
But in spite of the obvious effectiveness of mathematics in physics, I have never heard of a good a prioriargument that the world must be organised to mathematical principles.
Those who condemn the supreme certainty of mathematics feed on confusion, and can never silence the contradictions of the sophistical sciences which lead to eternal quackery.
No price is too high to pay to try to make the financial system go on a little bit longer. But ultimately it can't be saved, because of the mathematics that are involved.
The temptation to use mathematics is irresistible for economists. It appears to convey the appropriate air of scientific authority and precision to economists' musings.
As an exercise of the reasoning faculties, pure mathematics is an admirable exercise, because it consists of reasoning alone and does not encumber the student with any exercise of judgment.
Library Science is the key to all science, just as mathematics is its language - and civilization will rise or fall, depending on how well librarians do their jobs.
It can be argued that the mathematics behind these images [of the orbit diagram for quadratic functions and the Mandelbrot set] is even prettier than the pictures themselves.
Mathematics may, be briefly defined as the science of quantities, and is one of the most important of disciplining studies which engage the practical student.
To create a language all of a piece which would be a women's language, that I find quite insane. There does not exist a mathematics which is only a women's mathematics, or a feminine science.
As you are entered with the class of Nat. philosophy, give to it the hours of lecture, but devote all your other time to Mathematics, avoiding company as the bane of all progress.
The desire to explore thus marks out the mathematician. This is one of the forces making for the growth of mathematics. The mathematician enjoys what he already knows; he is eager for more knowledge.
Very few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languanges of the world than to master all mathematics at present known.
If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics.
One must divide one's time between politics and equations. But our equations are much more important to me, because politics is for the present, while our equations are for eternity.
Maxwell's theory of electromagnetism is generally studied only by advanced students of physics, but Albert had mastered it by the time he was sixteen years old.