Logical positivists have never taken psychology into account in their epistemology, but they affirm that logical beings and mathematical beings are nothing but linguistic structures.
I went to a liberal arts college, and as part of my background, I was majoring in mathematics and physics.
I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.
All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.
We have failed to protect science against speculative extensions of nature, continuing to assign physical and mathematical properties to hypothetical entities beyond what is observable in nature.
I was a mathematician by nature, and still am - I just knew I didn't want to be a mathematician. So I decided not to take any mathematics courses.
Over the centuries, monumental upheavals in science have emerged time and again from following the leads set out by mathematics.
The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.
In the past, there was active discrimination against women in science. That has now gone, and although there are residual effects, these are not enough to account for the small numbers of women, particularly in mathematics and physics.
As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.
The mathematics of quantum mechanics very accurately describes how our universe works.
To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers.
There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.
Certainly the best times were when I was alone with mathematics, free of ambition and pretense, and indifferent to the world.
If everybody who was in the Forbes 400 said they were going to create 10,000 jobs, by my mathematics, that would be 4 million jobs.
It's fine to work on any problem, so long as it generates interesting mathematics along the way - even if you don't solve it at the end of the day.
Without troublesome work, no one can have any concrete, full idea of what pure mathematical research is like or of the profusion of insights that can be obtained from it.
Newton was asked as a mathematician, not as a moralist. He replied 'Gentlemen, in applied mathematics, you must describe your unit.
As a purely mathematical fact, people who sleep less live more.
At the age of 12, I developed an intense interest in mathematics. On exposure to algebra, I was fascinated by simultaneous equations and read ahead of the class to the end of the book.
Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usef...
