Chester Martin
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The Austin Math Tutor's Home Page
Reasonable Rates, Flexible Scheduling
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Study guides for various courses in mathematics.
Helpful Links at ACC, UT, St Ed's
The Austin Math Tutor works with the following courses from local schools.
The Austin Math Tutor
The Austin Math Tutor's Home Page Reasonable Rates, Flexible Scheduling Questions Comments Appointments How can I help you? Study guides for various courses in mathematics. The Austin Math Tutor works with the following courses from local schools.
Thoughts on Mathematics and Philosophy.

Then, my noble friend, geometry will draw the soul towards truth, and create
the spirit of philosophy, and raise up that which is not unhappily allowed to fall
down.
                                                                 Plato

The primary question was not what do we know, but how do we know it.
                                                                 Aristotle

Today, it is not only that our kings do not know mathematics, but our
philosophers do not know mathematics.
                                                                 Julius Robert Oppenheimer

Every good mathematician is at least half a philosopher, and every good
philosopher is at least half a mathematician.
                                                                 Gottlob Frege

A marvelous neutrality have these things Mathematical, and also a strange
participation between things supernatural, immortal, intellectual, simple, and
indivisible and things natural, mortal, sensible, compounded, and divisible.
                                                                 John Dee

Six is a number perfect in itself, and not because God created the world in six
days; rather the contrary is true. God created the world in six days because this
number is perfect, and it would remain perfect, even if the work of the six days
did not exist.
                                                                 Saint Augustine of Hippo

All our surest statements about the nature of the world are mathematical
statements, yet we do not know what mathematics "is" . . . and so we find that
we have adapted a religion strikingly similar to many traditional faiths. Change
"mathematics" to "God" and little else might seem to change. The problem of
human contact with some spiritual realm, of timelessness, of our inability to
capture all with language and symbol - all have their counterparts in the quest
for the nature of Platonic mathematics.
                                                                 John D. Barrow

Geometry existed before the creation.
                                                                 Plato

I think that modern physics has definitely decided in favor of Plato. In fact the
smallest units of matter are not physical objects in the ordinary sense; they are
forms, ideas which can be expressed unambiguously only in mathematical
language.
                                                                 Werner Heisenberg

Geometry is the only science that it hath pleased God hitherto to bestow on
mankind.
                                                                 Thomas Hobbes

Of all things, good sense is the most fairly distributed: everyone thinks he is so
well supplied with it that even those who are the hardest to satisfy in every
other respect never desire more of it than they already have.
                                                                 Rene Descartes

Perfect numbers like perfect men are very rare.
                                                                 Rene Descartes

We cannot take anything for granted, beyond the first mathematical formula.  
Question everything else.
                                                                 Maria Mitchell

He who can properly define and divide is to be considered a god.
                                                                 Plato

Mathematics is the handwriting on the human consciousness of the very Spirit
of Life itself.
                                                                 Claude Bragdon

The infinite! No other question has ever moved so profoundly the spirit of man.
                                                                 David Hilbert

God ever geometrizes.
                                                                 Plato

God exists since mathematics is consistent, and the devil exists since we cannot
prove the consistency.
                                                                 Morris Kline

[Mathematics] is an independent world created out of pure intelligence.
                                                                 William Wordsworth

What is best in mathematics deserves not merely to be learned as a task but to
be assimilated as a part of daily thought, and brought again and again before
the mind with ever-renewed encouragement.
                                                                Bertrand Russell

To create a good philosophy you should renounce metaphysics but be a good
mathematician.
                                                                Bertrand Russell

It can be shown that a mathematical web of some kind can be woven about
any universe containing several objects. The fact that our universe lends itself
to mathematical treatment is not a fact of any great philosophical significance.
                                                                Bertrand Russell

From the time of Kepler to that of Newton, and from Newton to Hartley, not
only all things in external nature, but the subtlest mysteries of life and
organization, and even of the intellect and moral being, were conjured within
the magic circle of mathematical formulae.
                                                                Samuel Taylor Coleridge

The surest sign that intelligent life exists elsewhere in the universe is that it has
never tried to contact us.
                                                                Bill Watterson