A Quote by Ivars Peterson
To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas.
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Few realize that the world of modern mathematics is rich with vivid images and provocative ideas.
The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.
It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.
One of the chief triumphs of modern mathematics consists in having discovered what mathematics really is.
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.
A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details.
Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity
If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
Now ... the basic principle of modern mathematics is to achieve a complete fusion [of] 'geometric' and 'analytic' ideas.
Modern Armenia survived only because it was the single province controlled, and protected, by the Russian Empire. The rest of the territory within its historical borders is almost wholly devoid of ethnic Armenians.
The power of equations lies in the philosophically difficult correspondence between mathematics, a collective creation of human minds, and an external physical reality. Equations model deep patterns in the outside world. By learning to value equations, and to read the stories they tell, we can uncover vital features of the world around us.
In the future, as in the past, the great ideas [of mathematics] must be simplifying ideas, the creator must always be one who clarifies, for himself, and for others, the most complicated issues of formulas and concepts.
Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand... So Greek mathematics is 'permanent', more permanent even than Greek literature.
Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.
The fact is there are few more popular subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune.
Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.
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