To some extent I agree with the review from the point of view that mathematics is the language of science. You can not do science without mathematics, at least science as is understood by most scientists.

As you may know there are some exeptions (I quote from wikipedia) such as "Fictionalism" in mathematics (philosophy of mathematics). This was brought to fame in 1980 when Hartry Field published "Science Without Numbers", which rejected and in fact reversed Quine's "indispensability argument". Where Quine suggested that mathematics was indispensable for our best scientific theories, and therefore should be accepted as a body of truths talking about independently existing entities, Field suggested that mathematics was dispensable, and therefore should be considered as a body of falsehoods not talking about anything real. He did this by giving a complete axiomatization of Newtonian mechanics that didn't reference numbers or functions at all. He started with the "betweenness" of Hilbert's axioms to characterize space without coordinatizing it, and then added extra relations between points to do the work formerly done by vector fields. Hilbert's geometry is mathematical, because it talks about abstract points, but in Field's theory, these points are the concrete points of physical space, so no special mathematical objects at all are needed.

Having shown how to do science without using numbers, Field proceeded to rehabilitate mathematics as a kind of useful fiction. He showed that mathematical physics is a conservative extension of his non-mathematical physics (that is, every physical fact provable in mathematical physics is already provable from Field's system), so that mathematics is a reliable process whose physical applications are all true, even though its own statements are false. Thus, when doing mathematics, we can see ourselves as telling a sort of story, talking as if numbers existed. For Field, a statement like "2 + 2 = 4" is just as fictitious as "Sherlock Holmes lived at 221B Baker Street"—but both are true according to the relevant fictions.

By this account, there are no metaphysical or epistemological problems special to mathematics. The only worries left are the general worries about non-mathematical physics, and about fiction in general. Field's approach has been very influential, but is widely rejected. This is in part because of the requirement of strong fragments of second-order logic to carry out his reduction, and because the statement of conservativity seems to require quantification over abstract models or deductions.

Why don't you try to send your article to a more philosophically oriented journal? The British Journal for the Philosophy of Science, Philosophy of Science (APS), the philosophy sections of the Rev. Mex. Fis. among many others. In your position I wouldn't feel discouraged.

In conclusion, I believe that Physics is not necessarily a branch of mathematics...but without mathematics you cannot do physics.

To some extent I agree with the review from the point of view that mathematics is the language of science. You can not do science without mathematics, at least science as is understood by most scientists.

As you may know there are some exeptions (I quote from wikipedia) such as "Fictionalism" in mathematics (philosophy of mathematics). This was brought to fame in 1980 when Hartry Field published "Science Without Numbers", which rejected and in fact reversed Quine's "indispensability argument". Where Quine suggested that mathematics was indispensable for our best scientific theories, and therefore should be accepted as a body of truths talking about independently existing entities, Field suggested that mathematics was dispensable, and therefore should be considered as a body of falsehoods not talking about anything real. He did this by giving a complete axiomatization of Newtonian mechanics that didn't reference numbers or functions at all. He started with the "betweenness" of Hilbert's axioms to characterize space without coordinatizing it, and then added extra relations between points to do the work formerly done by vector fields. Hilbert's geometry is mathematical, because it talks about abstract points, but in Field's theory, these points are the concrete points of physical space, so no special mathematical objects at all are needed.

Having shown how to do science without using numbers, Field proceeded to rehabilitate mathematics as a kind of useful fiction. He showed that mathematical physics is a conservative extension of his non-mathematical physics (that is, every physical fact provable in mathematical physics is already provable from Field's system), so that mathematics is a reliable process whose physical applications are all true, even though its own statements are false. Thus, when doing mathematics, we can see ourselves as telling a sort of story, talking as if numbers existed. For Field, a statement like "2 + 2 = 4" is just as fictitious as "Sherlock Holmes lived at 221B Baker Street"—but both are true according to the relevant fictions.

By this account, there are no metaphysical or epistemological problems special to mathematics. The only worries left are the general worries about non-mathematical physics, and about fiction in general. Field's approach has been very influential, but is widely rejected. This is in part because of the requirement of strong fragments of second-order logic to carry out his reduction, and because the statement of conservativity seems to require quantification over abstract models or deductions.

Why don't you try to send your article to a more philosophically oriented journal? The British Journal for the Philosophy of Science, Philosophy of Science (APS), the philosophy sections of the Rev. Mex. Fis. among many others. In your position I wouldn't feel discouraged.

In conclusion, I believe that Physics is not necessarily a branch of mathematics...but without mathematics you cannot do physics.

I appreciate what you're saying. I was trying to be brief in my question, and probably should have included my more balanced position on mathematics that you can find in my paper. I think mathematics is an important tool, and essential for the confirmation of hypotheses. My objection is that with gravitation theory there are all sorts of mathematical formalisms based on force-based analogies that are physically incoherent. The mathematics used to predict the properties of gravitons, for example, ignores the fact that there is no evidence of a gravitational force, and no good reason to think there might be such a force. As I show in the paper, the only time gravitation is associated with force is when it's being resisted. But that simple empirical fact is ignored by those who focus on mathematics, and a conceptual objection can't even be raised in present-day physics journals, simply because mathematics is Queen, and physics has been rendered Common.

Thank you for the suggested journals. I looked at the British Phil of Sci and wasn't encouraged by the papers they've published, but there's no harm in trying. I've already run the cycle of all the cosmology journals with my other paper, and ended up with a rather obscure (but insightful!) general science journal in southern Europe.

James:

It appears that you are searching for the physical cause of gravitation. Puetz and I recently published our paper on it "Neomechanical gravitation theory" (Borchardt, G., and Puetz, S.J., 2012, Neomechanical gravitation theory ( http://www.worldsci.org/pdf/abstracts/abstracts_6529.pdf ), in Volk, G., Proceedings of the Natural Philosophy Alliance, 19th Conference of the NPA, 25-28 July: Albuquerque, NM, Natural Philosophy Alliance, Mt. Airy, MD, v. 9, p. 53-58.

As you found out, most physics journals are not interested in anything other than math. Almost any conceptual work based on materialism instead of immaterialism would contradict the math and would be unwelcome.

Glenn

www.scientificphilosophy.com

Indeed.

Two questions, Glenn. How can ether density vary if there are an infinity of particles in every region? And if one region is less dense than another doesn't that mean there is some EMPTY SPACE?

Glenn,

I wholeheartedly share you interest in discovering the mechanism that physically produces the kinetic effects of gravitation (even intermediate effects such as spacetime distortions) from localized potential mass energy density (resulting from gravitation's effects). I personally suspect some boundary interaction between mass-energy and some not fully detected energy directly corresponding to spacetime dimensional coordinates (perhaps indirectly indicated by the evidence for the existence of vacuum energy).

Your paper is interesting, but seems to require the existence of some form of aether particles of matter that has not been established. Did I miss the physical establishment of aether particles?

Thanks,

Jim

James #1:

Thanks for the question. What we know as "empty space" always contains matter that is less resistant to the things we consider matter. We explain this in detail in our latest book: Puetz, S.J., and Borchardt, Glenn, 2011, Universal cycle theory: Neomechanics of the hierarchically infinite universe: Denver, Outskirts Press ( www.universalcycletheory.com ), 626 p.

Our assumption is the same as Aristotle's: matter is infinitely subdividable. Baryonic matter is formed from aether-1 and aether-1 is formed from aether-2, ad infinitum. Empty space and solid matter are idealizations and cannot exist. All real things contain what we deem to be "empty space" and "solid matter." There is no end to the subdivision, which always results in particles containing "empty space" and "solid matter."

James #2:

Thanks for the question. Remember that the MM87 experiment was looking for a "fixed aether." Aether, instead, is entrained, just like our atmosphere. Their experiment was like trying to measure the jet stream in your basement. Aether measurements are a square root function of altitude (see Borchardt, G., 2007, The scientific worldview: Beyond Newton and Einstein: Lincoln, NE, iUniverse, p.202).

Even though Einstein recanted in 1920, any talk of aether has been considered grounds for banishment. There is plenty of evidence for aether, with physicists calling it by various names (Higgs, WIMPs, etc.). Einstein's "immaterial fields" satisfy the math for gravitation and magnetism, but they don't have any way to physically hold my kitchen knives onto my wall magnet.

BTW: You can download a couple of significant papers at the website:

Borchardt, G., 2007, Infinite universe theory: Proceedings of the Natural Philosophy Alliance (http://scientificphilosophy.com/Downloads/IUT.pdf), v. 4, no. 1, p. 20-23.

Borchardt, G., 2008, Resolution of SLT-order paradox ( http://scientificphilosophy.com/Downloads/SLTOrder.pdf ).

Borchardt, G., 2009, The physical meaning of E=mc2 (http://www.scientificphilosophy.com/Downloads/The%20Physical%20Meaning%20of%20E%20=%20mc2.pdf): Proceedings of the Natural Philosophy Alliance, v. 6, no. 1, p. 27-31.

Borchardt, G., 2011, Einstein's most important philosophical error, in Proceedings of the Natural Philosophy Alliance, 18th Conference of the NPA, 6-9 July, 2011 (http://www.worldsci.org/pdf/abstracts/abstracts_5991.pdf), College Park, MD, Natural Philosophy Alliance, Mt. Airy, MD, p. 64-68.

Also, there are over 200 blog entries that continue our analysis based on materialistic assumptions, many of which are just the opposite of those used by the mainstream:

Borchardt, G., 2004, The ten assumptions of science: Toward a new scientific worldview: Lincoln, NE, iUniverse, 125 p.

If either of you are employed in physics or cosmogony, I am sorry for the disturbance.

Glenn,

Thanks for explaining further - and pointing out that the negative results for the 1887 Michelson–Morley experiment applied only to unbound, stationary aether.

In answer to your closing, I'm merely a retired information system analyst who is skeptical of many well established precepts, especially the analyses inferring the existence of galactic dark matter. I'm not concerned with banishment - its an unavoidable consequence.

Higgs boson, WIMPS and gravitons, as well as aether, have specific properties that are dictated by their intended purpose - they are not equivalent by virtue of any envisioned relation they might have to gravitation. As a result, the experimental evidence for the existence of Higgs bosons, the perceived evidence for the existence of any exotic dark matter particles (resulting from observational discrepancies with gravitational a evaluations of large scale, compound objects), etc. cannot be simply transferred to support material aether.

"Einstein's "immaterial fields" satisfy the math for gravitation and magnetism, but they don't have any way to physically hold my kitchen knives onto my wall magnet."

I understand that magnetism is considered to be physically produced by a directional flow of energy - in the form of particle charge flows. Likewise, if some vacuum energy, perhaps also producing the quantum flux of virtual particles, whose density directly corresponds to the distortion of dimensional spacetime, exists in sufficient magnitudes it might, similarly, physically produce gravitation as an "immaterial field". We only detect the existence of energy by its effects on matter - in the absence of matter, in the vacuum, the principal effect observed is gravitational effects imparted to material objects...

As for the existence of some material aether, it seems to me that some compelling material evidence is necessary to establish it as a physical component of a gravitational mechanism. In the absence of such evidence, I prefer my own interpretation of vacuum energy...

Thanks for sharing your insight into publication in 'alternative' journals - I'm certainly not likely to produce any research report acceptable for publication in an established scientific journal.

James:

Glad to see that you have a questioning mind. You might want to check out my E=mc2 paper as well as the one on AE's philosophical error. I also have a bit on dark matter and dark energy on the blog. Once you figure out what energy is, we can discuss more.

In my humble opinion, I disagree. I think that mathematics are necessary when we measure things in order to apply or understandable in a way. mathematics are to quantify things. It is often said that when we put our minds to work thinking about physics, we are doing philosophy.

But the truth is, when are theories that are difficult to experience in order to find its validity, then there recently are doing philosophy, we do not know the truth of the thoughts that we are holding.

However, if we think based on physical concepts and theories that have scientific bases heavily tested and accepted by the scientific community, then we are doing science gentlemen, science that can be tested by anyone, experimentally or mathematical form. We are using concepts accepted, true. When one tries to solve a physical problem, do not start writing the equations. We started thinking that's what happens, what is the physics involved and what is the way to solve. Once done, it's when we started writing equations and find the unknowns.

Cristopher:

The key to what you wrote is the phrase "what happens." In other words, we want to know what is colliding with what according to Newton's Second Law (F=ma). The "physics" that claims that fields are "immaterial" is a physics about nothing. It is pure math and nothing else. There is no "there" there.

yes, i agree. My opinion is for clarify the question about if a topic are physics, mathematics of philosophy.

You say:

The "physics" that claims that fields are "inmaterial" is a physics about nothing. is pure mathematics and nothing else.

I say:

Why we need to make physics about something, i mean, things "materials"? I say that because we do physics about photons, a massless particle. In past years the physicists thought that neutrinos are massless too, but all that physicist keen doing all the physics no matter if we can materialize things.

The questions resides there. We do physics about fields, like electromagnetic, gravitational, the fields of particles, etc. And we accept the existence of these fields, but we can´t see those fields, they don´t have mass, practically for all the people in the world, those fields doesn´t exists. But, the physicists do something like that with the string or branes in the string theories. Most of the physicist assume that strings doesn´t exist because doesn´t exist an experiment to "messure" strings, and for that, physicists say string theories are philosophical theories, however, all the days appears papers and books of string theories without problems, but they can´t publish articles of conceptual things.

Ths scientific comunity need a definition of what is philosofical or not, or what is just mathmatics or physics.

Agree. But that will not happen because the current philosophy of physics is bankrupt. An evaluation of the philosophy, as in Borchardt (2004a,b), shows how bad it is. One cannot do physics or math without philosophy. It just has to be the right kind...

Borchardt, G., 2004a, Ten assumptions of science and the demise of 'cosmogony' (http://www.scientificphilosophy.com/Downloads/TTAOSATDOC.pdf): Proceedings of the Natural Philosophy Alliance, v. 1, no. 1, p. 3-6.

Borchardt, G., 2004b, The ten assumptions of science: Toward a new scientific worldview: Lincoln, NE, iUniverse, 125 p.

Glenn,

You stated earlier:

"There is plenty of evidence for aether, with physicists calling it by various names (Higgs, WIMPs, etc.)."

Other than this improperly 'hijacked' evidence, is there any other evidence for the existence of aether, since it's central to your Neomechanical gravitation theory?

I particularly object to the attribution of physical effects to imaginary 'proxy' elements, especially when their required properties cannot precisely specified. As a result, I cannot formally propose a 'Vacuum Energy' theory of gravitation... As I understand, there is currently much more evidence for the physical existence of virtual particles and vacuum energy than aether.

While, as I understand, general relativity does not define a mechanism that physically produces the described dimensional distortion of spacetime as a result of the presence of mass-energy, it does precisely describe the effects those dimensional distortions impart to material objects. That makes GR gravitation a testable and very useful predictive theory.

Check out p. 202 in TSW (2007). Fig. 8-2 demonstrates the aether entrainment in which the relative velocities measured in MM87- type experiments are a square root function of altitude. Folks have been taught to dismiss aether and to accept energy instead, which is even more nebulous (Borchardt, 2009, 2011). If one assumes infinity, as we do at PSI, there will always be a particle that is not measurable even though its physical actions are manifest, as in gravitation and magnetism. Have you gotten a chance to download and read my 2009 and 2011 papers?

Borchardt, G., 2007, The scientific worldview: Beyond Newton and Einstein: Lincoln, NE, iUniverse, 411 p.

Borchardt, G., 2009, The physical meaning of E=mc2 (http://www.scientificphilosophy.com/Downloads/The%20Physical%20Meaning%20of%20E%20=%20mc2.pdf): Proceedings of the Natural Philosophy Alliance, v. 6, no. 1, p. 27-31.

Borchardt, G., 2011, Einstein's most important philosophical error, in Proceedings of the Natural Philosophy Alliance, 18th Conference of the NPA, 6-9 July, 2011 (http://www.worldsci.org/pdf/abstracts/abstracts_5991.pdf), College Park, MD, Natural Philosophy Alliance, Mt. Airy, MD, p. 64-68.

Glenn,

TSW is not a household acronym at my house, and I'm not able to find a reference to it here. Sorry, I won't be investigating any philosophies requiring the existence of aether without at least some substantive evidence of its existence.

As for the vacuum energy I suggest, I don't even think there is yet sufficient evidence of its existence to warrant producing gravitational theories requiring it, only the circumstantial evidence for the existence of transient virtual particle manifestations that may suggest it. Please see

http://en.wikipedia.org/wiki/Virtual_particle#Manifestations

Sorry James,

I use too much shorthand. TSW is:

Borchardt, G., 2007, The scientific worldview: Beyond Newton and Einstein: Lincoln, NE, iUniverse, 411 p.

As I mentioned p. 202 shows "substantive evidence." You can see it in the Amazon "Inside the book" feature.

Maybe you should take a look at this paper by E. Wigner

http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

It will help you a lot.

A very interesting article that looks into the relation between mathematics and physics from a physicist and mathematician point of view is the one by Benjamin Plybon

The Relation between Mathematics and Physics:

http://www.academia.edu/1739599/The_Relation_between_Mathematics_and_Physics

No question: mathematics is an essential tool in physics. But it's only a tool. I give two examples in my paper on gravitation, showing how an absorption in the math can lead one to serious mistakes in physics:

Two principal mathematical analogies can be identified in the early development of relativistic gravitation theory and implicated in its diversion. One derives from Einstein’s heuristic insight associating gravitation with geometry, apparently due to an idea suggested by his friend Paul Ehrenfest (1909), who was himself inspired by Max Born’s investigation of relativistic rigidity (1909). Ehrenfest noted that the ratio of circumference to diameter of a rotating disk would have to deviate from pi with relativistic accelerations at the radius. In Einstein’s subsequent pursuit of a generalization of relativity the similarity between the inertial effect produced at the radius of the rotating disk and the gravitational pressure we experience at the earth’s surface suggested that gravitation might be explicable as a fundamentally geometric principle. Experimentation has confirmed the validity of that seminal geometric insight and the service of the mathematical analogy. But in the kinematical similarity between objects on a rotating disk and in gravitational orbit there is a distinct empirical difference: A test body in a box that is fixed at the edge of a rotating disk presses against the radial wall of the box, manifesting a centrifugal “force”, derivative of the actual force that is rotating the disk; in contrast, a test body in a box orbiting an astronomical body floats freely, following its geodesic in spacetime in parallel with the box, and gives no indication of the presence of a force or acceleration. There is thus a mathematical analogy due to the similar kinetics of the rotating disk and the orbiting body, but not a physical equivalence.

The development of the field equations of General Relativity was based on another mathematical analogy, formalizing the behavior of bodies being accelerated or pressured toward an attractive or determinant vortex as in a field of force, and a collapsing, concentrating sphere. The analogy holds in this case because gravity, like a field of force, produces a typically concentric form to the motion of affected bodies. But again, the mathematical analogy is not a physical equivalence. A neutral test body inside a charged box that is accelerating toward the vortex of a field of force presses against the wall of the box opposite the direction of force, and a charged body of different mass than the box accelerates at a different rate than the box, moving consequently toward one wall or its opposite. In contrast, a test body in a box falling or spiraling in a gravitational field floats freely, following its geodesic in spacetime in parallel with the box, and gives no indication of the presence of a force or acceleration.

In both cases -- in the similarities between the rotating disk or orbiting body and between the attractive or determinant field -- there is a discernible difference in the empirical behavior of test bodies being acted upon by a force and those moving in a gravitational field. In these pivotal models grounding relativistic gravitation theory, the mathematical analogies between gravitation and force are limited to descriptions of idealized curvilinear trajectories of idealized, dimensionless particles.

This upcoming discussion might be of some interest...

http://www.kavlifoundation.org/science-spotlights/kavli-origins-of-math

Thank you James for the reference.

Jon Richfield,

I had to laugh at first, but you do have a point. Is it the chicken or the egg? However, the posted question was prompted by a journal editor's rejection notice that stated:

"... That is because your manuscript seems to be a philosophical rather than physical [sic], and contains no mathematical explanations at all. Thus, this is a little bit away from the modern standards and traditions of research in the field of theoretical physics, where each new model or conception has a significant proportion of mathematical considerations besides the conceptual ideology or pure thought experiments. Our journal is focused on a mathematically based physical research in the field of gravitation, general relativity, and cosmology."

So the primary question is: can the study of physics be advanced without presenting sophisticated mathematical analyses?

I think it can certainly be argued that mankind's fascination with the universe began long before his development of abstract mathematical representations. As I recall, cave paintings depicting cosmological events and buildings specifically aligned to denote the seasonal solstices and other events indicate that humanity had developed some significant understanding of the cosmos prior to the development of math and likely even written language. Math may have been more properly a development of agriculture than physics...

One aspect of the question is whether the formal study of physics is now so dependent on mathematical representation that physicists cannot communicate effectively without it. Was the quote of the journal editor accurate: "... manuscript seems to be a philosophical rather than physical, and contains no mathematical explanations at all..." - [sic]?

Perhaps some crucial insights are being overlooked as a result...

This is how Paul Dirac view the relation between mathematics and physics:

"The physicist, in his study of natural phenomena, has two methods of making progress: (1) the method of experiment and observation, and (2) the method of mathematical reasoning. The former is just the collection of selected data; the latter enables one to infer results about experiments that have not been performed. There is no logical reason why the second method should be possible at all, but one has found in practice that it does work and meets with reasonable success. This must be ascribed to some mathematical quality in Nature, a quality which the casual observer of Nature would not suspect, but which nevertheless plays an important role in Nature's scheme."

"Pure mathematics and physics are becoming ever more closely connected, though their methods remain different. One may describe the situation by saying that the mathematician plays a game in which he himself invents the rules while the physicist plays a game in which the rules are provided by Nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen. It is difficult to predict what the result of all this will be. Possibly, the two subjects will ultimately unify, every branch of pure mathematics then having its physical application, its importance in physics being proportional to its interest in mathematics."

------------------------------------------------------------------------------------

The Relation between Mathematics and Physics, By Paul Adrien Maurice Dirac, Proceedings of the Royal Society (Edinburgh) Vol. 59, 1938-39, Part II pp. 122-129

Issam Sinjab,

Very interesting - especially to the extent that Dirac's award winning perspective some 75 years ago may have influenced the current state of affairs. Another portion of the same lecture discusses the replacement of a principle of simplicity in physics with the principle of mathematical beauty...

"We have followed through the main course of the development of the relation between mathematics and physics up to the present time, and have reached a stage where it becomes interesting to indulge in speculations about the future. There has always been an unsatisfactory feature in the relation, namely, the limitation in the extent to which mathematical theory applies to a description of the physical universe. The part to which it does not apply has suffered an increase with the arrival of quantum mechanics and a decrease with the arrival of the new cosmology, but has always remained.

"This feature is so unsatisfactory that I think it safe to predict it will disappear in the future, in spite of the startling changes in our ordinary ideas to which we should then be led. It would mean the existence of a scheme in which the whole of the description of the universe has its mathematical counterpart, and we must suppose that a person with a complete knowledge of mathematics could deduce, not only astronomical data, but also all the historical events that take place in the world, even the most trivial ones. Of course, it must be beyond human power actually to make these deductions, since life as we know it would be impossible if one could calculate future events, but the methods of making them would have to be well defined. The scheme could not be subject to the principle of simplicity since it would have to be extremely complicated, but it may well be subject to the principle of mathematical beauty."

Again, I think it's true that mathematics is an essential tool in physics. The question is, has it become so ingrained that it has replaced physical thinking. I gave two examples above where a reliance on mathematics has led physicists to identify fundamentally different phenomena, simply because they can be described in part by superficial mathematical analogies (an inertial rotation and an orbit, a collapsing field of force and a gravitational field). Mathematics is both helpful and problematic.

Arno,

Yes, I think the interplay of imagination, observation, experimentation, and mathematics are all important. So I think it follows that a legitimate paper on physics can focus on any one aspect, or several, or all, so long as it doesn't ignore a conflict with any other aspect. Therefore, if physics journals are refusing to consider papers which assert that mathematics is in conflict with observation (which means the mathematics is fine in-itself), they are practicing bad physics.

Along similar lines to this question, recently a panel forum was held by the Kavli Foundation to discuss the question:

"WHAT ARE THE ORIGINS OF MATH?"

"Four scientists debate ideas on whether math is an inherent part of our reality, or merely something our brains use to cope with and explain our environment."

The transcript is available at http://www.kavlifoundation.org/science-spotlights/kavli-origins-of-math.

It is strange to convince many scientists the statement, " any invention very original is only by intuition and not otherwise" The mathematical deductions follow only after that. Mathematics do not come first in our dreams. Also advanced scientific concepts rarely have straightforward expressions like ; E=mc^2 and F=mxdv/dt. But then there is a connection between physics and mathematics just as Keats said " truth is beauty and beauty is truth". Here the beauty is intuition and mathematics the truth. But unfortunately the beauty is appreciated by few people while the truth i.e mathematics the tool is taken for granted., and tools are rarely suspected. History has seen these ups and downs of great people. Never give up the intuition which has its roots from genuine study and research.