A Quote by Barry Mazur
Sometimes a line of mathematical research extending through decades can be thought of as one long conversation in which many mathematicians take part. This is fortunately true at present.
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I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts... When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through the process of 'seeing'.
You know that I try to maintain a continuous conversation with you. I take comfort in the thought that the important thing is not for one person to write to Christ but for many people to love and emulate [you]. Fortunately, despite everything, this still occurs today.
As far as I know, only a small minority of mathematicians, even of those with Platonist views, accept the idea that there may be mathematical facts which are true but unknowable.
Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature, since it is independent of language.
The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.
If usually the "present age" is no very long time, still, at our pleasure, or in the service of some such unity of meaning as thehistory of civilization, or the study of geology, may suggest, we may conceive the present as extending over many centuries, or over a hundred thousand years.
I think of my own work as part of a decades-long conversation about books and reading with people I will mainly never meet.
The mathematical is that evident aspect of things within which we are always already moving and according to which we experience them as things at all, and as such things. The mathematical is this fundamental position we take toward things by which we take up things as already given to us, and as they must and should be given. Therefore, the mathematical is the fundamental presupposition of the knowledge of things.
The mathematical fraternity is a little like a self-perpetuating priesthood. The mathematicians of today teach the mathematicians of tomorrow and, in effect, decide whom to admit to the priesthood.
Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be solidly backed up. It's just that the reliability does not primarily come from mathematicians formally checking formal arguments; it comes from mathematicians thinking carefully and critically about mathematical ideas.
Mathematicians have been hiding and writing messages in the genetic code for a long time, but it's clear they were mathematicians and not biologists because, if you write long messages with the code that the mathematicians developed, it would more than likely lead to new proteins being synthesized with unknown functions.
It's such an overused phrase: 'to be part of the conversation.' But it's true. It is nice to be part of the conversation - just be sure they are talking about you in the right way.
The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty. He should take simplicity into consideration in a subordinate way to beauty ... It often happens that the requirements of simplicity and beauty are the same, but where they clash, the latter must take precedence.
[Before the time of Benjamin Peirce it never occurred to anyone that mathematical research] was one of the things for which a mathematical department existed. Today it is a commonplace in all the leading universities. Peirce stood alone-a mountain peak whose absolute height might be hard to measure, but which towered above all the surrounding country.
Playing football and rugby is the Samoan sport. It's part of the conversation at church. It's part of the conversation in their barbershops, in the grocery stores. It's what everyone is aware of and familiar with. They take a lot of pride in the beating you can take in the course of that sport.
An animal on a leash is not tamed by the owner. The owner is extending himself through the leash to that part of his personality which is pure dog, that part of him which just wants to eat, sleep, bark, hump chairs, wet the floor in joy, and drink out of a toilet bowl.
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