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Mathematical reasoning may be regarded rather schematically
by Alan Turing

Mathematical reasoning may be regarded rather schematically
as the exercise of a combination of two facilities,
which we may call intuition and ingenuity.
- Alan Turing

We are not interested in the fact that the brain has
the consistency of cold porridge.
- Alan Turing

No, I'm not interested in developing a powerful brain.
All I'm after is just a mediocre brain,
something like the President of the American Telephone and Telegraph Company.
- Alan Turing

We can only see a short distance ahead,
but we can see plenty there that needs to be done.
- Alan Turing

 

Science is a differential equation.
Religion is a boundary condition.
- Alan Turing

A computer would deserve to be called intelligent if
it could deceive a human into believing that it was human.
- Alan Turing

Machines take me by surprise with great frequency.
- Alan Turing

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I believe that at the end of the century the use of
words and general educated opinion will have altered
so much that one will be able to speak of machines
thinking without expecting to be contradicted.
- Alan Turing

Cyberspace.
A consensual hallucination experienced daily by billions of legitimate operators,
in every nation, by children being taught mathematical concepts.
- William Gibson

Mathematical discoveries, like springtime violets in the woods,
have their season which no man can hasten or retard.
- Janos Bolyai

Here at Wisconsin we didn't get an undergraduate course
in mathematical logic until the '60s.
- Stephen Cole Kleene

To emphasize only the beautiful seems to me to be like
a mathematical system that only concerns itself with positive numbers.
- Paul Klee

The great appeal of the doctrine that the mind is a
blank slate is the simple mathematical fact that zero equals zero.
- Steven Pinker

Archimedes will be remembered when Aeschylus is forgotten,
because languages die and mathematical ideas do not.
- G. H. Hardy

I had become interested in economics,
an interest that was transformed into a lifetime dedication
when I met with the mathematical theory of general economic equilibrium.
- Gerard Debreu

The social sciences, I thought, needed the same kind
of rigor and the same mathematical underpinnings that
had made the "hard" sciences so brilliantly successful.
- Herbert Simon

It seems that jazz is more cerebral and more mathematical in a sense.
- Rita Coolidge

A sane mind should not be guilty of a logical fallacy,
yet there are very fine minds incapable of following
mathematical demonstrations.
- Henri Poincare

Never had any mathematical conversations with anybody,
because there was nobody else in my field.
- Alonzo Church

I did what I could to inflate the rumor I was on my way to stardom.
What I was on my way to, by any mathematical standards known to man,
was oblivion, by way of obscurity.
- Tallulah Bankhead

I tried reading Hilbert.
Only his papers published in mathematical periodicals
were available at the time.
Anybody who has tried those knows they are very hard reading.
- Alonzo Church

It is with children that we have the best chance of
studying the development of logical knowledge,
mathematical knowledge, physical knowledge,
and so forth.
- Jean Piaget

Eccentric doesn't bother me.
'Eccentric' being a poetic interpretation of a mathematical
term meaning something that doesn't follow the lines -
that's okay.
- Crispin Glover

Music assists him in the use of harmonic and mathematical proportion.
- Marcus V. Pollio

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.
- Edmund Husserl

The definition of a good mathematical problem is the
mathematics it generates rather than the problem itself.
- Andrew Wiles

I think part of the appeal of mathematical logic is
that the formulas look mysterious -
You write backward Es!
- Hilary Putnam

A mathematical theory is not to be considered complete
until you have made it so clear that you can explain
it to the first man whom you meet on the street.
- David Hilbert

The time was not yet ripe for the growth of mathematical science among us,
and any development that might have taken place in
that direction was rudely stopped by the civil war.
- Simon Newcomb

And for mathematical science, he that doubts their
certainty hath need of a dose of hellebore.
- Joseph Glanvill

We have overcome the notion that mathematical truths
have an existence independent and apart from our own minds.
It is even strange to us that such a notion could ever have existed.
- James Newman

I hope no man takes what I said about the living and
dieing of men for mathematical demonstration.
- William Petty

The mathematical facts worthy of being studied are those which,
by their analogy with other facts, are capable of leading
us to the knowledge of a physical law.
- Henri Poincare

Ignorance and superstition ever bear a close and mathematical relation to each other.
- James F. Cooper

Mathematical discoveries, small or great are never
born of spontaneous generation.
- Henri Poincare

Much of what I make is geometric, and has a kind of
almost mathematical logic to the form.
- Anish Kapoor

As for everything else, so for a mathematical theory:
beauty can be perceived but not explained.
- Arthur Cayley

I would finally renounce my delusional hypotheses and
revert to thinking of myself as a human of more conventional
circumstances and return to mathematical research.
- John Forbes Nash, Jr.

Mathematical science is in my opinion an indivisible whole,
an organism whose vitality is conditioned upon the connection of its parts.
- David Hilbert

A pure mathematical series would be one in which each
term is derived from the preceding term by a rule.
- George Oppen

There has to be a mathematical explanation for how bad that tie is.
- Russell Crowe

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.
- Abraham Robinson

Mark all mathematical heads which be wholly and only bent on these sciences,
how solitary they be themselves, how unfit to live with others,
how unapt to serve the world.
- Roger Ascham

The analysis of variance is not a mathematical theorem,
but rather a convenient method of arranging the arithmetic.
- Ronald Fisher

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.
- Jean Piaget

The circumstances of human society are too complicated
to be submitted to the rigor of mathematical calculation.
- Marquis De Custine

Out of fifty mathematical papers presented in brief at such a meeting,
it is a rare mathematician indeed who really understands
what more than half a dozen are about.
- E. T. Bell

Statistics: the mathematical theory of ignorance.
- Morris Kline

In a few decades of reconstruction, even the mathematical natural sciences,
the ancient archetypes of theoretical perfection,
have changed habit completely!
- Edmund Husserl

I was very much on the mathematical side,
where you probably do your best work before you're forty-five.
Having passed that significant date,
I thought I would do something else.
- John Polkinghorne

I received my undergraduate degree in engineering in
1939 and a Master of Science degree in mathematical
physics in 1941 at Steven Institute of Technology.
- Frederick Reines

The laws of nature are but the mathematical thoughts of God.
- Euclid

The computer can't tell you the emotional story.
It can give you the exact mathematical design,
but what's missing is the eyebrows.
- Frank Zappa

One cannot really argue with a mathematical theorem.
- Stephen Hawking

Pure mathematics is on the whole distinctly more useful than applied.
For what is useful above all is technique,
and mathematical technique is taught mainly through pure mathematics.
- G. H. Hardy

I know this world is ruled by infinite intelligence.
Everything that surrounds us- everything that exists -
proves that there are infinite laws behind it.
There can be no denying this fact.
It is mathematical in its precision.
- Thomas A. Edison

How thoroughly it is ingrained in mathematical science
that every real advance goes hand in hand with the
invention of sharper tools and simpler methods which,
at the same time, assist in understanding earlier theories
and in casting aside some more complicated developments.
- David Hilbert

I regard it in fact as the great advantage of the mathematical
technique that it allows us to describe,
by means of algebraic equations, the general character
of a pattern even where we are ignorant of the numerical
values which will determine its particular manifestation.
- Friedrich August von Hayek

The universal medicine for the Soul is the Supreme
Reason and Absolute Justice;
for the mind,
mathematical and practical Truth; for the body,
the Quintessence, a combination of light and gold.
- Albert Pike

If indeed, as Hilbert asserted, mathematics is a meaningless
game played with meaningless marks on paper,
the only mathematical experience to which we can refer
is the making of marks on paper.
- E. T. Bell

My suggestion is that at each state the proper order
of operation of the mind requires an overall grasp
of what is generally known,
not only in formal logical, mathematical terms,
but also intuitively, in images, feelings,
poetic usage of language, etc.
- David Bohm

All science requires mathematics.
The knowledge of mathematical things is almost innate in us.
This is the easiest of sciences, a fact which is obvious
in that no one's brain rejects it;
for laymen and people who are utterly illiterate know how to count and reckon.
- Roger Bacon

The thing that got me started on the science that I've
been building now for about 20 years or so was the question of okay,
if mathematical equations can't make progress in understanding
complex phenomena in the natural world,
how might we make progress?
- Stephen Wolfram

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.
- David Hilbert

You kind of alluded to it in your introduction.
I mean, for the last 300 or so years,
the exact sciences have been dominated by what is really a good idea,
which is the idea that one can describe the natural
world using mathematical equations.
- Stephen Wolfram

If God creates a world of particles and waves,
dancing in obedience to mathematical and physical laws,
who are we to say that he cannot make use of those
laws to cover the surface of a small planet with living creatures?
- Martin Gardner

When I speak of the beauty of a game of chess,
then naturally this is subjective.
Beauty can be found in a very technical,
mathematical game for example.
That is the beauty of clarity.
- Vladimir Kramnik

The immediacy of mystic experience simply means that
we know God just as we know other objects.
God is not a mathematical entity or a system of concepts
mutually related to one another and having no reference to experience.
- Muhammad Iqbal

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.
- James C. Maxwell

Thus, the more succinctly a train of thought was expounded,
and the more comprehensive the unity of its basic idea,
the closer it would approximate to the prerequisites
of the mathematical way of thinking.
- Max Bill

I chose to deal with the science of cryptography.
Cryptography began in mathematics.
Codes were developed, even from Caesar's time,
based on number theory and mathematical principles.
I decided to use those principles and designed a work that is encoded.
- James Sanborn


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