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The infinite in mathematics is always unruly unless it is properly treated.
It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.
Mathematics is no more computation than typing is literature.
I love mathematics...principally because it is beautiful; because man has breathed his spirit of play into it, and because it has given him his greatest game the encompassing of the infinite.
In most sciences one generation tears down what another has built and what one has established another undoes. In mathematics alone each generations adds a new story to the old structure.
The only way to learn mathematics is to do mathematics.
Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.
It is impossible to overstate the imporance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps... Every new discovery in mathematics, results from an attempt to solve some problem.
The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver.
For me it remains an open question whether [this work] pertains to the realm of mathematics or to that of art.
By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I had made, I ended up in the domain of mathematics. Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.
It will be another million years, at least, before we understand the primes.
Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent to a pair of ears. Mathematics can only be "seen" with the "eyes of the mind". It is as if we had no sense of hearing, so that only someone able to sight read music would be able to appreciate its patterns and harmonies.
Mathematics is one of the deepest and most powerful expressions of pure human reason, and, at the same time, the most fundamental resource for description and analysis of the experiential world.
Somebody came up to me after a talk I had given, and say, "You make mathematics seem like fun." I was inspired to reply, "If it isn't fun, why do it?"
I will live a hope-filled life every day. I will handle my problems as opportunities in a different, more effective manner, based on the power of advanced mathematics; "You + God = Enough
No human investigation can be called real science if it cannot be demonstrated mathematically.
I don't believe in mathematics.
As long as algebra is taught in school, there will be prayer in school.
Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.
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