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)

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Main Mathematics / Maths Physics Pages

Philosophy / Metaphysics of Mathematics

Philosophy / Metaphysics of Mathematics - I fully agree with you about the significance and educational value of methodology as well as history and philosophy of science. So many people today - and even professional scientists - seem to me like somebody who has seen thousands of trees but has never seen a forest. A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is - in my opinion - the mark of distinction between a mere artisan or specialist and a real seeker after truth. (Albert Einstein)
On the Mystical Foundations of Mathematics - Pythagoras, .. was intellectually one of the most important men that ever lived, both when he was wise, and when he was unwise. Mathematics, in the sense of demonstrative deductive argument, begins with him, and in him is intimately connected with a peculiar form of mysticism. The influence of mathematics on philosophy, partly owing to him, has, ever since his time, been both profound and unfortunate. (Bertrand Russell)
Mathematics and Music - The astronomer Galileo Galilei observed in 1623 that the entire universe "is written in the language of mathematics", and indeed it is remarkable the extent to which science and society are governed by mathematical ideas. It is perhaps even more surprising that music, with all its passion and emotion, is also based upon mathematical relationships. Such musical notions as octaves, chords, scales, and keys can all be demystified and understood logically using simple mathematics.
Famous Mathematics Quotes - As I work on these maths physics pages I collect mathematics / mathematical physics quotes that I think are important and add them to this page.

On Censorship and the Evolution of Science / Truth

Covert Censorship by the Physics Preprint Archive - This page on censorship in Physics is here to show people that there are serious problems in getting new knowledge published in Journals (particularly if it contradicts current paradigm of 'particles' and 'fields', where it is just assumed that particle / wave duality is insolvable, waves are just 'probability waves', etc.). The particular example I have used relates to problems that Nobel Physics Laureate Brian Josephson had in getting articles published. But the problem is endemic and applies equally to philosophy.
Censorship at the Physics Forums http://www.physicsforums.com/ - This is a copy of a post that I replied to at http://www.physicsforums.com/. I don't think my reply was that bad given the criticism the Wave Structure of Matter received. However, when I went back to add a further comment, I found that I was BANNED for life from the physicsforums - the reason given was "crackpot" - and the post was deleted. I wrote to them asking for an explanation and have received no reply (funny about that!). And since then I have posted twice using new accounts. Each time my posts have been deleted and I have been banned. I wonder what people think of this form of censorship at the biggest physics forum on the internet? If you are like me and think this is wrong - please post at their forum and tell them so.

Mathematical Treatment of the Wave Structure of Matter

Mathematical Physicist Dr Milo Wolff on the Wave Structure of Matter (WSM) in Space
I think all scientists would agree that to be certain that the Spherical Wave Structure of Matter is true, we must demonstrate that its Principles correctly deduce what we observe from observation and experiment of the interconnected motion of matter in Space.
And here it is appropriate that I acknowledge the wonderful mind and pioneering work of Mathematical Physicist Dr Milo Wolff on the Wave Structure of Matter (1986 - 2007). His early work of applying the spherical scalar wave equations to mathematical physics led him to deduce the fundamentals of both Einstein's Special Relativity (mass increase) and Quantum Theory (de Broglie wavelength) in one set of wave equations, thus both theoretically and metaphysically uniting these two theories (metaphysics of Space and wave Motion - not Space and Time). His work over the past 19 years has led to further deductions of the fundamental laws of Nature from first principles (i.e. a priori, rather than their current a posteriori empirical / inductive foundation which is always uncertain).

Wolff: Wave Structure of Matter - Summary of the Logic and Mathematics of the Wave Structure of Matter.

Wolff: Richard Feynman's QED - From Feynman's Advanced and Retarded Spherical Vector Electromagnetic Waves (Mathematical) to Spherical Scalar Quantum Waves (real waves).

Wolff: Binary Universe - The Binary Nature of Reality (Waves form from two balanced forces, Spherical In-Waves and Out-Waves). Relates this to digital computing.

Wolff: PhD Mathematical Physics / Biography - Milo Wolff - Astronomer, Electrical Engineer, retired Professor of Mathematical Physics, first formalised the Wave Structure of Matter in 1986.

Video Interviews of Dr Milo Wolff on Physics and the Wave Structure of Matter - The following interview between Philosopher Geoff Haselhurst and Physicist Milo Wolff on the Wave Structure of Matter was filmed in 2000 on the grounds of Berkeley University in California. Milo Wolff is a fine theoretical physicist and one day he will no doubt receive a Nobel Prize for his pioneering work on the Wave Structure of Matter. I think you will find these video interviews to be interesting (at times amusing) and very informative about the problems of modern physics and how they can be solved by the Wave Structure of Matter.

Physics Book: Milo Wolff: 'Exploring the Physics of the Unknown Universe' - Buy Milo Wolff's Physics Book on the Wave Structure of Matter from Amazon.

Milo Wolff's Physics Website on the Wave Structure of Matter - My name is Milo Wolff and I am a physicist, astronomer, and explorer of the wondrous cosmology of the universe. I have worked for MIT, Aerospace Corporation, the United Nations, as well as taught at various universities in the USA and Asia. Join the exciting and fascinating exploration of matter, the natural laws, and the universe. You may become a famous pioneer and, at the least, you will have fun! (Milo Wolff)

http://www-conf.slac.stanford.edu/Einstein/Talks/Wolff.pdf - What is the Electron? Introduction: In his later years, Einstein was asked his thoughts about the huge numbers of short-lived heavy particles, kaons, pions, quarks, mesons, etc. found using high-energy accelerators and enormous amounts of time and money. These physicists thought they were finding important basic matter. They wanted to know what Einstein thought of their work. Einstein was a careful thinker and not given to theatrics so he was very serious when he replied, "I would just like to know what an electron is."
This article will show, just as Einstein speculated, that the electron is indeed the leading player in the universe and is intimately involved with light, matter, the laws of Nature, and our lives. The path to the answer, is simple: Reject the discrete material electron and replace it with a wave-structured electron as proposed by Schroedinger and Clifford - using a scalar-wave equation. The math and the proofs are straight-forward because scalar waves are the only possible choice. Only two principles underlie all results. Despite this simplicity the WSM explains the origin of the natural laws, new applications in micro-physics and chips, understanding light energy exchange and lasers, plus the answers to most current paradoxes of physics. It is breathtaking to find so many results together – simply by answering Einstein’s question "What is the Electron". (Milo Wolff, Geoff Haselhurst)

http://quantummatter.com/articles_html/body_point.html - The Wave Center forms the 'Point Particle' Effect. The dual particle/wave nature of the electron has long been a paradox in physics. It is now seen that the electron consists entirely of a structure of spherical waves whose behavior creates their particle-like appearance. The correctness of this structure is supported by the physical laws which originate from this wave structure, including quantum theory, special relativity, electric force, gravity, and magnetism. (Milo Wolff)

http://www.signaldisplay.com/Unified_Field_Theory.pdf - The Derivation of a Unified Field Theory From a Model of Spherical Quantum Waves.
Abstract: It is shown that if space is modeled as an elastic medium that propagates spherical, scalar quantum-waves, then the ratio of the square of the wave velocity to c² reveals the same results as the familiar time dilation formula that is produced from the Schwarzchild G44 component. The Schwarzchild radius derived from the scalar-wave model is shown to be equal to the radius of the observable universe, implying that there are no gravitational singularities present within the observable universe. The spherical wave model also produces a formula that calculates the mass of a vector particle associated with each of the four forces and its associated range. (Michael Harney)

http://redshift.vif.com/JournalFiles/V13NO2PDF/V13N2HAR.pdf - The Cosmological-Redshift Explained by the Intersection of Hubble Spheres (Observable Universe). The cosmological redshift is described by the intersection of two Hubble spheres, where a Hubble sphere is defined as a range over which spherical, quantum-waves interact, specifically Ru = 1.9 × 1026 m. (Michael Harney)

Deducing Heisenberg's Uncertainty Principle - Three short deductions of Heisenberg's Uncertainty Principle from Wave theorists, Mike Harney, Milo Wolff, and Chris Hawkings. The significant point is that by removing the 'particle' conception of matter and replacing this with the Spherical Standing Wave Structure of Matter we can deduce the Uncertainty Principle due to the spatially extended wave nature of matter. The confusion and paradox of Quantum Theory clearly results from the incorrect discrete 'particle' conception of matter. i.e. There is no discrete particle thus it is impossible to locate the exact position of something that does not exist (the continuous motion of a 'particle'!). In reality there is a discrete re-positioning of the wave center with each spherical in and out wave which gives the appearance of a continuously moving 'particle'.

http://www.ontostat.com/anglais/revisited_physics_gb.htm - In this section on Physics, I would like to feed the debate on a certain number of points, perhaps definitely established for physicists, but which seem to me still fragile. Tackling with general questions, the first pages (3.1 to 3.5) prepare the reader to this idea, matter is made of waves. From the sixth (3.6) which present an undulatory model of particle, we really enter into the subject.
The following pages display the basis of the Wave Structure of Matter (WSM) Theory that I treat from the particle model I have conceived. Other authors after Louis de Broglie, Milo Wolff, Gabriel LaFrenière, Geoff Haselhurst, Chris Hawkings, Serge Cabala, have developed this theory, broadly similar, but with differences in details. Nevertheless, the main difference goes beyond this physical theory, it shows through the whole of ideas and facts displayed on this site and is what leads the reader to this amazing finding: a unique thing as simple as a wave, is likely to explain the entire Universe, as well as the masse, the behaviour and the functioning of the objects it contains. (Denys Lepinard)

Chris Hawkings - Could Matter and Matter Waves be Derivable? - 'The similarity in behaviour between matter and radiation suggests that matter may have an electromagnetic (wave) origin. It is shown that two light-speed waves with opposite directions of propagation yield a formalism which is identical to that describing the properties of matter. For spherical waves, particle localisation is also obtained and phase waves are generated, the properties of which match identically with matter wave properties.' Note: We do not agree with Chris in his use of vector electromagnetic waves (mathematical constructs which have no spherical solutions). We must instead work with scalar waves / real waves in Space.

Wave Structure of Matter Theorists Websites - Links to websites of people working on the Wave Structure of Matter. Physicist Dr Milo Wolff, Denys Lepinard, Mike Harney, Mike Weber, Ray Tomes (Harmonics), Serge Cabala, Gabriel LaFreniere.