## Famous Quotes on Mathematics

Mathematical Physics Quotations

As I work on these maths physics pages I collect mathematics / mathematical
physics quotes that I think are important and add them below. Hope you find
them interesting!

If you know of any good mathematics quotations then Email
them to me please.

Thanks,

Geoff Haselhurst

### Albert Einstein Quotes on Mathematics / Mathematical Physics

As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality. (Albert Einstein)

The eternal mystery of the world is its comprehensibility. (Albert Einstein)

The skeptic will say: "It may well be true that this
system of equations is reasonable from a logical standpoint. But this does
not prove that it corresponds to nature." You are right, dear skeptic.
Experience alone can decide on truth. ... Pure logical thinking cannot yield
us any knowledge of the empirical world: all knowledge of reality starts
from experience and ends in it.

(Albert Einstein, 1954)

To be sure, it has been pointed out that the introduction
of a space-time continuum may be considered as contrary to nature in view
of the molecular structure of everything which happens on a small scale.
It is maintained that perhaps the success of the Heisenberg method points
to a purely algebraical method of description of nature, that is to the
elimination of continuous functions from physics. Then, however, we must
also give up, by principle, the space-time continuum. It is not unimaginable
that human ingenuity will some day find methods which will make it possible
to proceed along such a path. At the present time, however, such a program
looks like an attempt to breathe in empty space.

(Albert Einstein, Out of My Later Years)

Pure mathematics is, in its way, the poetry of logical ideas. (Albert Einstein)

One reason why mathematics enjoys special esteem, above all other sciences, is that its propositions are absolutely certain and indisputable, ... How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality. (Albert Einstein)

I don't believe in mathematics. (Albert Einstein, quoted by Carl Seelig, in 'Albert Einstein')

### Bertrand Russell Quotes on Mathematics / Mathematical Physics

Mathematics was associated with a more refined type of error. Mathematical knowledge appeared to be certain, exact, and applicable to the real world; moreover it was obtained by mere thinking, without the need of observation. Consequently, it was thought to supply an ideal, from which everyday empirical knowledge fell short. It was supposed on the basis of mathematics, that thought is superior to sense, intuition to observation. If the world of sense does not fit mathematics, so much the worse for the world of sense. ... This form of philosophy begins with Pythagoras. (Bertrand Russell)

Mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the actual world, but every possible world, must conform. (Bertrand Russell)

I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because like Spinoza's God, it won't love us in return. (Bertrand Russell, 1912)

Mathematics is, I believe, the chief source of the belief
in eternal and exact truth,

as well as a sensible intelligible world. (Bertrand Russell)

Mathematical knowledge is, in fact, merely verbal knowledge. "3" means "2+1", and "4" means "3+1". Hence it follows (though the proof is long) that "4" means the same as "2+2". Thus mathematical knowledge ceases to be mysterious. (Bertrand Russell, History of Western Philosophy)

Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover. (Bertrand Russell)

### Miscellaneous Quotes from philosophers of Science / Maths Physicists

Some things that satisfy the rules of algebra can be interesting to mathematicians even though they don't always represent a real situation. (Richard P. Feynman)

Thus we can get the correct answer for the probability of partial reflection by imagining (falsely) that all reflection comes from only the front and back surfaces. In this intuitively easy analysis, the 'front surface' and 'back surface' arrows are mathematical constructions that give us the right answer, whereas .... a more accurate representation of what is really going on: partial reflection is the scattering of light by electrons inside the glass. (Richard P. Feynman)

One does not, by knowing all the physical laws as we know
them today, immediately obtain an understanding of anything much.

I love only nature, and I hate mathematicians. (Richard Feynman 1918-1988)

Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality. (Nikola Tesla)

Our minds are finite, and yet even in those circumstances of finitude, we are surrounded by possibilities that are infinite, and the purpose of human life is to grasp as much as we can out of that infinitude. (Alfred North Whitehead)

I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce. ( Freeman John Dyson, Missed Opportunities)

Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its conclusions, except that in the higher formulas the identity fades out of sight. (Johann Wolfgang Von Goethe)

Heisenberg has discussed the coupled double harmonic oscillator, and has shown that the ordinary rules of quantization lead to two non-combining sets of states in one of which the electrons are in phase and out of phase. The energy of the system is successively transferred from one to the other – resonance! (Linus Pauling, 1977)

One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics. (Luitzen Brouwer)

... the progress of science has itself shown that there can be no pictorial representation of the workings of nature of a kind that would be intelligible to our limited minds. The study of physics has driven us to the positivist conception of physics. We can never understand what events are, but must limit ourselves to describing the pattern of events in mathematical terms: no other aim is possible .... the final harvest will always be a sheaf of mathematical formulae. These will never describe nature itself, but only our observations on nature. (Sir James Jeans, 1942)

Mathematics is the only good metaphysics. (William Thomson Baron Kelvin)

From these experiments it is seen that both matter and radiation possess a remarkable duality of character, as they sometimes exhibit the properties of waves, at other times those of particles. Now it is obvious that a thing cannot be a form of wave motion and composed of particles at the same time - the two concepts are too different. ... The solution of the difficulty is that the two mental pictures which experiment lead us to form - the one of the particles, the other of the waves - are both incomplete and have only the validity of analogies which are accurate only in limiting cases. ... Light and matter are both single entities, and the apparent duality arises in the limitations of our language.

It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme - the quantum theory - which seems entirely adequate for the treatment of atomic processes; for visualization, however, we must content ourselves with two incomplete analogies - the wave picture and the corpuscular picture." (Heisenberg, 1930)

If there is a God, he's a great mathematician. (Paul Dirac)

One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers. (Heinrich Hertz)

The laws of Nature are but the mathematical thoughts of God. (Euclid)

Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting. (Ernst Mach)

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. (E.P. Wigner)

I would like to make a confession which may seem immoral: I do not believe in Hilbert space anymore. (John von Neumann in a letter to G. Birkhoff)

When in the 18th century Euler discovered those formulas which today still delight the mathematical phantasy, he seriously stated that his pencil was more clever than himself. This impression that mathematical structures can include a kind of self-determination concerns me at this time. ... Mathematics and Philosophy attack the world's problems in different ways. Only by their complementary action do they give the right direction. (E. Kaehler)

Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions. (Eric Temple Bell, 1883-1960)

... it would be better for the true physics if there were no mathematicians on earth. (Bernoulli)

God forbid that Truth should be confined to Mathematical Demonstration! (Blake)

It is the merest truism, evident at once to unsophisticated observation, that mathematics is a human invention. (Bridgman, P. W. The Logic of Modern Physics)

The Way begets one; one begets two; two begets three; three begets the myriad creatures. (Lao Tse, Tao Te Ching)

The essence of mathematics is not to make simple things complicated, but to make complicated things simple. (S. Gudder)

The highest form of pure thought is in mathematics. (Plato)

The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. (Aristotle)

## Help Humanity

*"You must be the change you wish to see in the world."
(Mohandas Gandhi)*

*"When forced to summarize the general theory of relativity in one sentence:
Time and space and gravitation have no separate existence from matter. ... Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning. ... The particle can only appear as a limited region in space in which
the field strength or the energy density are particularly high. ...
The free, unhampered exchange of ideas and scientific conclusions is necessary for the sound development of science, as it is in all spheres
of cultural life. ... We must not conceal from ourselves that no improvement in the present depressing situation is possible without
a severe struggle; for the handful of those who are really determined to do something is minute in comparison with the mass of the lukewarm
and the misguided. ...
Humanity is going to need a substantially new way of thinking if it is to survive!" (Albert Einstein)*

Our world is in great trouble due to human behaviour founded on myths and customs that are causing the destruction of Nature and climate change. We can now deduce the most simple science theory of reality - the wave structure of matter in space. By understanding how we and everything around us are interconnected in Space we can then deduce solutions to the fundamental problems of human knowledge in physics, philosophy, metaphysics, theology, education, health, evolution and ecology, politics and society.

This is the profound new way of thinking that Einstein realised, that we exist as spatially extended structures of the universe - the discrete and separate body an illusion. This simply confirms the intuitions of the ancient philosophers and mystics.

Given the current censorship in physics / philosophy of science journals (based on the standard model of particle physics / big bang cosmology) the internet is the best hope for getting new knowledge known to the world. But that depends on you, the people who care about science and society, realise the importance of truth and reality.

## It is Easy to Help!

Just click on the Social Network links below, or copy a nice image or quote you like and share it. We have a wonderful collection of knowledge from the greatest minds in human history, so people will appreciate your contributions. In doing this you will help a new generation of scientists see that there is a simple sensible explanation of physical reality - the source of truth and wisdom, the only cure for the madness of man! Thanks! Geoff Haselhurst (Updated September, 2018)

A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. (**Max Planck**, 1920)

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*"In a time of universal deceit - telling the truth is a revolutionary act."(George Orwell)*

*"Hell is Truth Seen Too Late."(Thomas Hobbes)*

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