Science should be expressed in precise language, which facilitates clear thinking. One obvious clue that many of the quasi-sciences are subpar is their quasi-scientists giving flowery and/or terribly imprecise definitions of what science is, and what a scientific theory is, in their discipline. Therefore, in the interest of promoting all true science, I have devised the following argument for a general definition of a scientific theory.

All mathematicians agree that mathematics is anything that enables the creation of mathematical theorems, once precise definitions are given. Logically then, a scientific theory may be defined as any endeavor that mimics the greatest possible science according to David Hilbert's philosophy of physics. Thus, for those that think like mathematicians, a scientific theory only requires sophisticated logical reasoning, a logically consistent set of definitions and precisely stated fundamental axioms, and must generate a plethora of coherent, precisely stated physical concepts and ideas.

Mathematics is the science of discovering precise definitions and new theorems that reveal exquisite structures. A mathematician is a person that sees beauty in mathematics.

Last time, I asked: "What does mathematics mean to you?" And some people answered: "The manipulation of numbers, the manipulation of structures." And if I had asked what music means to you, would you have answered: "The manipulation of notes?" — S. Lang, The Beauty of Doing Mathematics, Springer-Verlag, 1985.

To Goethe again we owe the profound saying: "the mathematician is only complete in so far as he feels within himself the beauty of the true." — O. Spengler, in J. Newman, The World of Mathematics, Simon & Schuster, 1956.

Born of man's primitive urge to seek order in his world, mathematics is an ever-evolving language for the study of structure and pattern. Grounded in and renewed by physical reality, mathematics rises through sheer intellectual curiosity to levels of abstraction and generality where unexpected, beautiful, and often extremely useful connections and patterns emerge. Mathematics is the natural home of both abstract thought and the laws of nature. It is at once pure logic and creative art. — Lawrence University catalog, Cited in Essays in Humanistic Mathematics, Alvin White, ed, MAA, 1993.

The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics. — G. H. Hardy (1877 - 1947), A Mathematician's Apology, Cambridge University Press, 1994.

Mathematics in this sense is a form of poetry, which has the same relation to the prose of practical mathematics as poetry has to prose in any other language. The element of poetry, the delight of exploring the medium for its own sake, is an essential ingredient in the creative process. — J.Bronowski, Science and Human Values, Pelican, 1964.

The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful. — J.H.Poincare (1854-1912), (cited in H.E.Huntley, The Divine Proportion, Dover, 1970).

Mathematics, as much as music or any other art, is one of the means by which we rise to a complete self-consciousness. The significance of Mathematics resides precisely in the fact that it is an art; by informing us of the nature of our own minds it informs us of much that depends on our minds. — J.W.N.Sullivan (1886-1937), Aspects of Science, 1925.

I can hardly tell with what pleasure I have read the letters of those very distinguished men Leibniz and Tschirnhaus. Leibniz's method for obtaining convergent series is certainly very elegant... — I.Newton, Letter to H.Oldenburg, the Secretary of the Royal Society, October 24, 1676, in A Source Book in Mathematics, D. J. Struik, ed, Princeton University Press, 1990.

Good mathematicians have a sense of what important mathematics is:

Richard Hamming wrote:The purpose of computing is insight, not numbers.

If you don't work on important problems, it's not likely that you'll do important work.

It is better to do the right problem the wrong way than the wrong problem the right way.

A theorem is a proposition that can be deduced from the premises or assumptions of a system.

Here are my thoughts on the quintessence of the scientific method as I shared them with Carlos Cerna at http://www.educatetruth.com.

Ellen G. White wrote:We need to guard continually against the sophistry in regard to geology and other branches of science falsely so-called, which have not one semblance of truth. The theories of great men need to be carefully sifted of the slightest trace of infidel suggestions. One tiny seed sown by teachers in our schools, if received by the students, will raise a harvest of unbelief. The Lord has given all the brilliancy of intellect that man possesses, and it should be devoted to his service. RH, March 1, 1898.

Carlos,

Thanks for researching this question and for finding this powerful Spirit of prophecy quote. That's exactly what true believing scientists should be doing. As I see it, the Lord's recommended approach to science is virtually indistinguishable from the science practiced by the universal mathematical genius David Hilbert, the man who taught Albert Einstein how to derive the equations of general relativity.

In the book, David Hilbert and the Axiomatization of Physics (1898-1918): From Grundlagen der Geometrie to Grundlagen der Physik, author Leo Corry mentions why Hilbert's published papers in physics greatly annoyed physicists. It was the only useful thought that I found in the whole book but reading the book was worth this one laugh. What struck me as being so funny? Physicists were angered by reading Hilbert's scientific papers because Hilbert took the time to identify all his postulates and would then prove that his postulates were logically independent.

If Neo-Darwinian professors would practice that kind of scientific sifting and logical presentation of their assumptions, then true scientific postulates could be easily recognized and separated from the false.

Eugene Shubert
http://www.everythingimportant.org/physics/Hilbert.htm

Neo-Darwinists and Fundamentalists agree that the difference between the evolutionist and creationist worldview is the difference between the perceptions of mainstream scientists versus the fundamentalists' understanding of Scripture. They do not speak for me. The perceived disagreement between science and revelation is senseless in my point of view.

I believe that the correct explanation for the evolutionist-creationist controversy is the ridiculous amounts of arrogance and ignorance on both sides of the dispute.

Richard Dawkins has said:

The particular variety of truth that concerns me is scientific truth. And that is what I mostly want to talk about today. So what is this thing called science? … My own definition is the study of what is true about the real world. — Richard Dawkins, University of Valencia, March 31, 2009.

Dawkins should be ashamed of uttering that extraordinarily empty definition. What is true?

An email from a fundamentalist organization stated:

Can Genesis be trusted when it says God created the world in 6 days?

What does belief in evolution say about the character of God?

Is the earth really millions or billions of years old?

Who has the last word on interpreting what God said and did—scientists or Scripture?

In 2009, the world is celebrating the life and work of Charles Darwin, the man who popularized the notion of evolution. Are you prepared to combat this false doctrine and those who would compromise the Word of God?

Join Dr. John MacArthur, Dr. Henry Morris, and other dynamic speakers at Demand the Evidence, a worldview conference hosted by the Institute for Creation Research.

The only problem with creationism is the many willfully ignorant anti-science creationists. There is no question that creationists would be humbled if they submitted to the Lord's instructions, understood the definition of science and agreed to play the game of science according to the rules but they refuse to be humble. Note the arrogance of the fundamentalists' claim that their understanding of Scripture is beyond all doubt. They assert that they are not interpreting the Bible.

Consider the following ideas:

The fundamental cause of trouble in the world today is that the stupid are cocksure while the intelligent are full of doubt. — Bertrand Russell, "Christian Ethics" from Marriage and Morals (1950), quoted from James A Haught, ed, 2000 Years of Disbelief.

The opinions that are held with passion are always those for which no good ground exists; indeed, the passion is the measure of the holder's lack of rational conviction. — Bertrand Russell, Unpopular Essays "On the Value of Skepticism" (1950), quoted from James A Haught, ed, 2000 Years of Disbelief.

The most savage controversies are those about matters as to which there is no good evidence either way. Persecution is used in theology, not in arithmetic. — Bertrand Russell, Unpopular Essays, "An Outline of Intellectual Rubbish" (1950), quoted from James A Haught, ed, 2000 Years of Disbelief.

Heretical views arise when the truth is uncertain, and it is only when the truth is uncertain that censorship is invoked. — Bertrand Russell, "The Value Of Free Thought," thanks to Laird Wilcox, ed, "The Degeneration of Belief."

Dogma demands authority, rather than intelligent thought, as the source of opinion; it requires persecution of heretics and hostility to unbelievers; it asks of its disciples that they should inhibit natural kindness in favor of systematic hatred. — Bertrand Russell, thanks to Laird Wilcox, ed, "The Degeneration of Belief."

Most of the greatest evils that man has inflicted upon man have come through people feeling quite certain about something which, in fact, was false. — Bertrand Russell, Unpopular Essays, "Ideas That Have Harmed Mankind" (1950), p. 149, quoted from James A Haught, ed, 2000 Years of Disbelief.

If a man is offered a fact which goes against his instincts, he will scrutinize it closely, and unless the evidence is overwhelming, he will refuse to believe it. If, on the other hand, he is offered something which affords a reason for acting in accordance to his instincts, he will accept it even on the slightest evidence. The origin of myths is explained in this way. — Bertrand Russell.

My hypothesis

The quintessential quarrel in the evolution-creation debate is a senseless conflict between two warring groups of extremists. Both sides make exaggerated claims, argue unprovable ideas and venerate superficial kinds of evidence.

Bertrand Russell's characterization of controversy is nicely illustrated by noting how typical non-theorems in mathematics get resolved and by contrasting the civility of real scientists with those who occupy positions of power in the heartless "bone-pointing" quasi-science of the mainstream biomedical establishment.

Paul R. Halmos wrote:As my own focus on measure theory began to waver, I published a couple of comments on other people's measure theory. One was on Liapounov's theorem (to the effect that the ranges of well-behaved vector-valued measures are closed convex sets). Kai Rander Buch published a paper on closedness, and that paper made me angry: it struck me as wordy and pretentious and unnecessarily complicated. Surely one can do better than that, I said; I thought about the question, saw a way of doing much better, and dashed off a note to the Bulletin of the AMS. My proof was a lot slicker than Kai Rander Buch's and a lot shorter, but his was right, and, to my mortification, mine turned out to be wrong. Both Jessen and Dieudonne wrote and told me that my Lemma 5, the crucial lemma, was false. A pity; it was such a nice lemma. It says that the span of two compact topologies is compact (span, supremum, generated topology) — a statement for which it's not only easy to find counterexamples but it's hard to find any non-trivial instances where it is true. Being caught stumbling in public was all the motivation I needed to sit down and think matter through more deeply and more effectively. My second note came out a year after the first (1948), and it was twice as long (six pages), but it was elegant and correct, and has been quoted quite a bit since then. It is all superseded by now; in 1966 Lindenstrauss came out the slickest proof to end all proofs (J. of Math. and Mech.).

In 1949 I published another little note precipitated by an emotional reaction. The irritant in that case was a paper by Shin-Ichi Izumi proving a non-theorem. The subject is ergodic theory; the statement is that under certain rather restrictive conditions on a measure-preserving transformation T it can be concluded that the series such as {\sum}^\infty_{n=1}\frac{1}{n}f(T^n x) converge almost everywhere. Izumi's proof is rather complicated and, so far as I could tell, absolutely right. There is trouble however; the conditions are so restrictive that the only transformation that satisfies them is the identity transformation acting on a space consisting of exactly one point. — Paul R. Halmos, I Want To Be A Mathematician, pp. 156-157.

That's about as controversial as it gets in the real world of modern-day mathematics. Now compare that controversy to the differences of opinion in biology. I have in mind the devastating effects of thimerosal on infants and young children, and the axiom that AIDS is caused by a virus.

The following video suggests that AIDS dissidents are challenging the drug dogmatists on the basis of the scientific method and that the dogmatists refuse to resolve the dispute on the basis of real science.



Here is a brief excerpt from the transcript of another video, The Other Side of AIDS, which appears to confirm the charge that the drug dogmatists can't answer the AIDS dissidents on the basis of experiment and the testing of hypotheses — the definition of science. Conversely, it's absolutely clear that the dogmatists are taking an unscientific course of action. They are retaliating by uttering cowardly denunciations and threats.

Kary Mullis is a molecular biologist and Nobel laureate. Mark Wainberg is a Professor in the Departments of Microbiology and Immunology, Pediatrics, and Medicine at McGill University. Peter Duesberg is a professor of Molecular and Cell Biology at the University of California, Berkeley.

KARY MULLIS: “I mean I understand there are a lot of people if you ask them about HIV causing AIDS as being a fact, they’ll say, of course, it’s indisputable. And the very fact that they will say it’s indisputable might lead you to question their ability to understand scientific method. People that think any scientific fact is indisputable don’t understand about scientific facts.”

MARK WAINBERG: “As far as I’m concerned, and I hope this view is adequately represented, those who attempt to dispel the notion that HIV is the cause of AID are perpetrators of death. And I would very much for one like to see the Constitution of the United States and similar countries have some means in place that we can charge people who are responsible for endangering public health with charges of endangerment and bring them up on trial. I think that people like Peter Duesberg belong in jail.”

PETER DUESBERG: “We don’t say Toyotas and Mercedes shouldn’t be sold here because we want to sell General Motors. But when it comes to science, we act in America like the Pope acts in Rome. There is only one truth and only one direction to march in.”

RODNEY RICHARDS: “One of the distinguishing features in modern science is skepticism, the spirit to challenge other people’s work, the spirit to challenge your own work. And I fear that this spirit is disappearing in particular in the case of HIV and AIDS. Anybody that speaks up against or challenges some of the entrenched paradigms or principles is not only not welcome, but they are strongly criticized to the point of being called names, bigots, homophobes, baby killers, flat earthers, holocaust deniers. Certainly this would indicate to me that the spirit of skepticism, the spirit of challenge, the spirit of scientific debate in this field is virtually completely gone.”

MARK WAINBERG: “Someone who would perpetrate the notion that HIV is not the cause of AIDS is perhaps motivated by sentiments of pure evil, that such a person may perhaps really want millions of people in Africa and elsewhere to become infected by this virus and go on to die of it. And, who knows, maybe there’s a hidden agenda behind the thoughts of a madman. Maybe all psychopaths everywhere have ways of getting their views across that are sometimes camouflaged in subterfuge. But I suggest to you that Peter Duesberg is probably the closest thing we have in this world to a scientific psychopath.”

ROBIN SCOVILL: “There are a lot of other scientists that raise the challenges that he raises.”

MARK WAINBERG: “And now the interview is finished. Thanks.” — Transcript, The Other Side of AIDS.

See http://everythingimportant.org/AZT for the larger context.

JohnB wrote:

Eugene Shubert wrote:The real problem is that mainstream creationists completely misunderstand the definition of science.

Are you sure about that Eugene? Or is this just another over-generalization?

I'm sure and the only thing that I've ever over-generalized is the Lorentz transformation. Consider how persons in the Intelligent Design community respond to criticisms that ID isn't science:

On 12 February 2010, the blog uncommondescent.com quoted this criticism of the ID movement in their article, Darwinian Desperation: Petition to Re-Classify “Non-Science” Books:

“Science can be defined as the process of using empirical evidence to make predictions and test hypotheses in the effort to increase our understanding of the world around us. ID seeks to answer many of the same questions about life on Earth that science does. However, the two differ drastically in that ID invokes supernatural explanations to explain natural processes, while science explains natural processes using empirical data. As the study of ID does not involve the use of empirical evidence to make predictions and test hypotheses, it cannot be considered a science under any circumstances.”

Here was their rebuttal:

“Someone needs to tell these guys that there simply is no widely accepted, widely agreed upon definition of what science is, so invoking a particular one to justify their animus against ID isn’t all that helpful.”

As is plainly self-evident, that response is no defense unless the majority of noteworthy discoverers of the laws of nature disagree significantly on the definition of science.

Sadly, the Intelligent Design movement is in denial. There is a significant agreement on the definition of science among world-class scientists. It is absolutely shameful for informed Christians to not know this. There is nothing Christian or logical in refusing to accept An Irrefutable Definition of Science.

DonaldM wrote:So, science is defined by majority rule?

Yes. In fact, all common words are defined by majority rule. And I believe that dictionary.com’s definition of science nicely encapsulates the scientific definition (as defined by the noteworthy discoverers of the laws of nature).

DonaldM wrote:You might note that many of the “noteworthy discoverers” of the laws of nature saw science as extension of their Christian theology. Newton and Boyle come to mind here.

I also see the laws of nature as an extension of my Christian theology. And I understand how atheistic scientists, with their theology, interpret the laws of nature. I simply see no major disagreement among preeminent scientists on the definition of science.

DonaldM wrote:The larger issue for these guys is that even if they came up with some definition of what science is supposed to be, they still can’t make the case for the exclusion for ID because whatever that definition might be will also exclude some things that are considered quite scientific by nearly everyone.

I believe that I’m consistent in my definition of science and I don’t see any original science in Intelligent Design writings. And I’m not alone. Dr. David Berlinski is “a published critic of intelligent design.” Likewise, his judgment seems to be that Intelligent Design isn’t science:

An outspoken critic of evolution, Berlinski is a Senior Fellow of the Discovery Institute’s Center for Science and Culture, a Seattle-based think-tank that is hub of the intelligent design movement. Berlinski shares the movement’s disbelief in the evidence for evolution, but does not openly avow intelligent design and describes his relationship with the idea as: “warm but distant. It’s the same attitude that I display in public toward my ex-wives.”

“Creationism is, as far as I can tell, an empty doctrine,” empty at least of positive evidence for the nature and presence of a Creator-although he finds some of its negative arguments against Darwinism “very good.”

DonaldM wrote:The larger issue for these guys is that even if they came up with some definition of what science is supposed to be, they still can’t make the case for the exclusion for ID because whatever that definition might be will also exclude some things that are considered quite scientific by nearly everyone. The uniformity principle comes to mind here.

The issue for them is their religious zeal for pure conjecture and their profound ignorance of the highest levels of science. The issue before us is that it's misleading to presuppose that the Intelligent Design movement is right, just because evolutionary biologists are wrong. My assertions are unassailable. Believing scientists should exercise greater care to correctly distinguish between respectable science and outdated hypotheses. Many scientists have discarded the uniformity principle of evolution in favor of the theory of punctuated equilibrium. If you're referring to geology, neo-catastrophism is becoming very fashionable among geologists. Wikipedia, in their article on catastrophism, states, "Neocatastrophism is the explanation of sudden extinctions in the palaeontological record by high magnitude, low frequency events, as opposed to the more prevalent geomorphological thought which emphasizes low magnitude, high frequency events." There are favorable opinions there, such as "scientifically based catastrophism has gained wide acceptance with regard to certain events in the distant past."

There is no conflict between science and true religion but there is disharmony between science and Intelligent Design.

For all practical purposes, a proof is any completely convincing argument. And the problem with Intelligent Design is that most scientists are simply not persuaded that the highly ordered physical reality we live in and obviously exists is the work of an Intelligent Designer. It could very well be, and I believe it’s likely, that most scientists are being unreasonable in denying the existence of the Designer but it is the nature of science to be extraordinarily skeptical.

I don’t want to see the standards of science lowered so that the whims of the Intelligent Design movement would be satisfied. According to Dr. Michael Behe, astrology is a scientific theory. I refuse to be taken there. I believe that the standard of what is called science must be raised higher than it is now.

I think that the gods of evolution are revered too admiringly and submissively and that they should be laughed at instead. I got a good laugh out of Richard Dawkins' PhD thesis: "The ontogeny of a pecking preference in domestic chicks". That's right. Richard Dawkins received his PhD in ethology (the study of animal behavior, a sub-topic of zoology). And, of course, that makes him eminently qualified to pretend being a scientist and to criticize empirical facts and logically derived conclusions that were never a part of his professional training.

Richard Dawkins wrote:Newly hatched chicks peck at small objects such as spots of dirt on a wall, presumably a food-seeking response. Understandably they prefer solid to flat objects, and this carries over to photographs. But by what cues do they recognize a photographed object as solid? Humans use surface shading cues. Because the sun shines from above not below, upper surfaces tend to be lighter than lower surfaces, with a gradient between. Telescopic photographs of moon craters can look like hills depending on the direction from which the light falls. Predators use shading cues of solidity in hunting, which is why so many camouflaged animals employ countershading: the dorsal surface is pigmented darker than the ventral, thereby cancelling the expected solid appearance. The upside-down catfish (Synodontis nigriventis) is the exception that proves the rule (for once, the expression is spot on). This fish habitually swims upside down and, fascinatingly, it is reverse countershaded. The ventral surface has the dark pigmentation; the dorsal surface is light coloured like the ventral surface of a normal fish.

Back to the chicks: I used grain-sized photographs of top-lit hemispheres mounted at beak height on the wall of the cage, and compared them with the same photographs inverted so that the light appeared to come from below. Chicks strongly preferred to peck at correctly oriented photographs over inverted ones. Apparently, then, chicks used the same surface shading cues of solidity as we do: they seem to 'know' that sunlight shines from above. Now for the deprivation experiments. Day-olds hatched in total darkness, who had never seen anything before, gave their first (sighted) pecks indiscriminately to inverted and correctly oriented photographs equally. Did this mean they normally learn the surface shading cues of solidity — learn, in effect, that the sun is overhead? Not necessarily. It could be that the naive day-olds, having never before seen so much as a chink of light, were too startled or dazzled to discriminate. So I did the definitive experiment. I reared and tested chicks in a special cage in which light came from below. They would be accustomed to light, and not startled or dazzled when they came to be tested. If learning is important, these chicks should if anything learn that solid objects are lighter on the underside, and hence prefer inverted photographs when tested. In fact, the chicks behaved like normal chicks. They overwhelmingly preferred the uninverted photograph, the one illuminated from above, the one that looked solid to human eyes. In Lorenzian terms, this showed that the adaptive information is innate: my chicks were telling me that they are born with the 'advance knowledge' that the sun shines from overhead. No doubt there are loop-holes in the logic, but I still think the experiment is a nice teaching aid: a neat demonstration of the kind of logic we employ when distinguishing the innateness of behaviour itself from the innateness of the adaptive information whereby behaviour fits its environment as a key fits a lock. [1].

Everything today revolves around either true axioms or incredible deceptions. For example, Richard Dawkins, an ethologist, thinks he’s qualified to speak authoritatively about real science but he’s really not even a bonafide biologist.

The mathematical physicist John Barrow—who is a believer—made a similar point directly to Richard Dawkins. When Dawkins challenged Barrow in Cambridge about the mathematical precision found in nature Barrow responded: “You have a problem with these ideas, Richard, because you are not really a scientist. You are a biologist.” Barrow views biology as little more than a branch of natural history, and thinks biologists lack an intuitive understanding of complexity. Their study of the higgledy-piggledy paths of life on this planet give them limited appreciation for the rich laws of physics that enable those paths. [2].

I like this John Barrow character. He wrote, "A universe simple enough to be understood is too simple to produce a mind capable of understanding it." [3].

It is NOT a mathematical problem.

It most certainly is a mathematical problem. And here are a few reasons why I make everything a mathematical problem:

"With me everything turns into mathematics." -- Descartes

"It is easier to square a circle than to get round a mathematician." -- de Morgan

"Physicists defer only to mathematicians, and mathematicians defer only to God."

"The mathematician has reached the highest rung on the ladder of human thought." -- Havelock Ellis

"Mathematics is the life of the gods." -- Novalis (Friedrich von Hardenberg)

"Biologists think they are biochemists,
Biochemists think they are physical chemists,
Physical chemists think they are physicists,
Physicists think they are gods,
And God thinks he is a Mathematician."

"Small minds discuss persons.
Average minds discuss events.
Great minds discuss ideas.
Really great minds discuss mathematics."

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

"Mathematics is written for mathematicians." -- Copernicus

"The life of a mathematician is dominated by an insatiable curiosity, a desire bordering on passion to solve the problems he is studying." -- Jean Dieudonne

"All mathematicians share ... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics." -- Martin Gardner

"Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different." -- Johann Wolfgang von Goethe

"How happy the lot of the mathematician. He is judged solely by his peers, and the standard is so high that no colleague or rival can ever win a reputation he does not deserve." -- W.H. Auden

"The reason that every major university maintains a department of mathematics is that it is cheaper to do this than to institutionalize all those people."

It's interesting that the truest science has the greatest number of believers and that the most superficial science has the greatest number of unbelievers.

"We found the highest percentage of belief among NAS mathematicians (14.3% in God, 15.0% in immortality). Biological scientists had the lowest rate of belief (5.5% in God, 7.1% in immortality), with physicists and astronomers slightly higher (7.5% in God, 7.5% in immortality)." http://www.colorado.edu/philosophy/vste ... t/3-32.txt

This thesis seems to have an abundance of scientific support. See Lowering brain activity increases unbelief in God.

"You don’t need proof when you have a credible theory. All you need is a theory that enough people will believe." --Michael “Hockey Stick” Mann.

“Proof is for mathematical theorems and alcoholic beverages. It’s not for science.” --Michael “Hockey Stick” Mann.

The Funnel of Smoke wrote: Its the application of reason to empirical data that makes science what it is....
Does logic always have to be expressed mathematically?

Obviously, deeply mathematical reasoning trumps the arm-waving and screeches of poo-flinging chimpanzees. Indisputably therefore, inventive ideas and extraordinarily sophisticated reasoning should always be considered more important and more scientific than merely checking trivial things with off-the-shelf devices. As Richard Feynman once said, speaking of quantum electrodynamics,“If I could explain it to the average person, it wouldn't have been worth the Nobel prize.”

Your assertion that Hilbert wasn't doing physics when tutoring Einstein on how to derive general relativity and that general relativity wasn't science until the first empirical test of general relativity was completed is patently absurd.