Problem-Solvers --- What AI Can Never Do

Prolog. AI is the most powerful tool of any kind to come along in many years. Almost all of us are frequent users. It's a time-saver, problem-solver, information resource, and grammar fixer. But it can't do everything. This is our problem for today: to explore its limitations. We build a wall around AI, which, if it gets out, we're in deep trouble. Be sure to read Section 2. Amazing.

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 Problem-Solvers --- What AI Can Never Do

G Donald Allen

Without creativity, we would see only the same old patterns.

1. Introduction. Every day brings new reports of astonishing advances in artificial intelligence and agentic systems. Truly, AI is the problem-solver we’ve always needed. The pace of achievement is genuinely remarkable. Yet students and young thinkers may gradually absorb the idea that AI can accomplish virtually anything, a notion that can feel intimidating, or even discouraging, to minds still awakening to the wonder and mystery of the world around them. What we examine here are several extraordinary achievements of human thought that may lie beyond the reach of AI, whether now or perhaps even in the future. These ideas were revolutionary in their time, emerging far beyond the expectations of even the greatest scholars of their age. To appreciate their significance, one must momentarily set aside modern knowledge and imagine a world in which none of these concepts yet existed. Even if you already know how these discoveries were made, try to suspend that knowledge and encounter them as humanity first did: as unimaginable leaps into the unknown. Additionally, we cite a fundamental flaw of AI, called the “Tyranny of Knowledge,” attributed to Philosopher J. Krishnamur, that too much knowledge may lead to stagnation and virtual imprisonment. Of course, the good professor was referring to us.

An argument we often hear is that a really smart AI engine could generate advanced conceptual ideas using some type of random generator, then check for efficacy at such a rapid pace that it would simply be thought of as a genius. However, to randomly “guess” some true stroke of genius may take quadrillions of guesses or orders of magnitude more. Even quantum computers don’t have the required speed. Thus, we argue against this Monte Carlo Universe, though AI plays dice, figuratively, with all data.

In a sense, AI is one highly complex voting machine based on Bayesian statistics, and it never sees anything for which there are no votes. So, for example, when Louis Pasteur was pursuing germ theory to explain disease, notables of the day would note that their AI engines gave it no credibility. This is the kernel of our argument, notwithstanding Agentic offerings. You can’t generate ideas out of thin air. As Sir Joshua Reynolds said, “Nothing can come from nothing.”  Humans can, though humans would be the first to agree that the vast majority of their new ideas amount to bunk. We have another talent, not often mentioned, and that is our ability to override apparent certainty. However, AI cannot, insofar as I know.

We begin our study by considering what anyone might regard as an off-the-wall question to AI, asking it to connect two almost disjoint theories, one in philosophy, the other in geology.

The other sections of this essay, each independent of the other, can be read as desired.

2.                An Example. You will see that what AI can do is assemble information that connects remarkably different fields of knowledge in ways few of us have even a notion of. But could it derive these fields independently? To test this hypothesis, we asked AI how it connects Kant’s theory of Transcendental Idealism with Plate Tectonics, something perhaps no one has pondered before.  Here’s its response, though edited.

Kant’s core breakthrough was that the mind is not a passive camera; it actively organizes the raw, chaotic data of reality into structured concepts using its own built-in software (like space, time, and cause-and-effect). If we look at plate tectonics through this lens, geology ceases to be just a study of rocks and becomes a masterclass in how human consciousness maps the unseeable. Kant distinguished between the noumenon (reality as it exists independently of us, which we can never truly perceive) and the phenomenon (reality as it appears to our senses). The interior of the Earth is a perfect physical analog for Kant's noumenon. No human eye has ever seen a tectonic plate subducting into the mantle, nor have we directly witnessed the churning convection cells thousands of kilometers beneath our feet. We have only ever scratched the outermost "skin" of the planet. The deep mantle is a hidden, chaotic world of extreme pressure and temperature, a geographic thing-in-itself. Plate tectonics is the ultimate triumph of Kant's Idealism: it is the human mind taking a world it can never physically touch, organizing it through space, time, and causality, and creating a coherent, predictable universe out of a subterranean abyss.

Speaking in Texan, “Did y’all know that?” This is just a portion of AI’s response. It also brought in details of seismology, causality, and Continental Drift into its discourse[1].

Has this example left us still a sense of hopelessness, that maybe humans can do something great, but only for those rare geniuses to find? This is not so. Recently, I wrote a brief essay titled “What is Micro-genius?” (Allen, 2025). It was intended for the many of us who can find truly imagined solutions to important problems, not perhaps on the genius scale, but revolutionary in their own way. Micro-geniuses are everywhere, in every profession. Possibly you are one. The essay contains several characteristics of the micro-genius (which are included here as Appendix A).

Moreover, does this connection given to us by AI still make competition or contribution seem futile? Maybe. However, this is not the problem before us. It is the deeper problem of whether AI could ever have conceived of Kant’s Transcendental Idealism or Plate Tectonics. This is a different problem altogether.

3.                Gravitation, Relativity, and Quantum theory. Every so often, a scientific theory does not merely update our textbooks; it destroys the baseline assumptions of what reality is. Universal Gravitation, Relativity, and Quantum Mechanics are the premier examples of these conceptual ruptures. When they were first proposed, they did not just challenge the science of their day; they violated contemporary common sense so deeply that they were widely regarded as absurd, unprovable, or borderline mystical. In each of these topics, whatever AI engine you used, it could not have leaped to the conceptual level required to go beyond its vast library resources.

3.1 Gravitation. Before Sir Isaac Newton, humanity operated under an Aristotelian view: the heavens were perfect and governed by divine geometry, while the Earth was mundane, governed by base mechanics. Newton’s formulation of gravity was history's first great unification. By stating that the exact same invisible force pulling an apple to the ground also loops the Moon around the Earth, he shattered the barrier between the celestial and terrestrial realms. He introduced the terrifying idea of action-at-a-distance: that two objects could instantly exert force on each other across millions of miles of empty, freezing vacuum.

It is significant to realize that before Newton, planets and stars were “just up there,” with nothing holding them up. So, phenomenological mechanisms were given to govern how they moved, through the two millennia' reason offered by Ptolemy’s epicycles. They worked until they didn’t. Errors crept in. Even the great Kepler based his laws only on data fitting. There was no physics whatsoever. That was astronomy at the time, together with its companion astrology, a truly mystical explanation still widely followed today.

To 17th-century thinkers, Newton’s gravity sounded like occult magic. The reigning scientific paradigm, led by René Descartes, held that objects could influence one another only through direct physical contact, such as billiard balls colliding.

Newton was asking the world to accept that an invisible, immaterial tether bound the cosmos together without any physical medium. Even Newton himself couldn't explain how it worked, famously writing "Hypotheses non fingo" (I frame no hypotheses). It took nearly a century for the scientific community to stop viewing gravity as a mystical concept and accept it as a physical fact. Afterward, it leaped off the pages and created a fully new world of explanations for the mechanism of the entire universe.

Unmentioned here is the small detail that Newton also needed to invent calculus to then prove Kepler’s laws and everything else. He also fully demonstrated the value of a mathematical model in explaining phenomena, a legacy that has grown exponentially ever since. Now, many claim mathematics is the language of the universe. With the emergence of various new systems of logic, it’s unclear if this praise will persist.

3.2 Relativity. By the late 19th century, physicists believed they had wrapped up the universe. Physics was a tidy house built on Newtonian mechanics, where space was a flat, permanent stage, and time was an absolute, cosmic clock ticking at the exact same rate for everyone.

The revolutionary Albert Einstein tore down the stage. He proved that space and time are not fixed backdrops, but fluid, interwoven entities (spacetime) that stretch, warp, and contract depending on speed and mass. As seen in the spacetime model above, gravity is not an invisible rope (as Newton thought); it is the geometric curvature of space itself.  A planet orbits the sun simply because it is rolling along a depression in the fabric of reality. Even still, imagining the universe as some non-Euclidean space defies the intuition of many truly intelligent persons. Sure, they learn the rules and the language, but do they fully comprehend?

Relativity violently insulted human intuition. It asserted that if you travel near the speed of light, time actually slows down for you relative to someone standing still. It claimed that gravity could bend light beams and that a massive enough star could collapse into a point of infinite density where time itself stops (a black hole). When Einstein published General Relativity in 1915, it was so mathematically dense and conceptually alienating that contemporary journalists famously claimed "only twelve men in the world understand it." It required an entirely new vocabulary of non-Euclidean geometry to even describe, upending centuries of philosophical and scientific consensus that treated time as an unyielding constant. At this point, the reader is possibly challenged. The next topic on quantum theory will take any remaining confusion to a new, fully incomprehensible level.

3.3 Quantum Theory. If Relativity warped the macro-cosmos, Quantum Mechanics completely fractured the micro-cosmos. Developed by a cohort of physicists including Max Planck, Albert Einstein, Niels Bohr, and Werner Heisenberg, it sought to explain the behavior of subatomic particles.

Quantum theory was revolutionary in that it replaced the clockwork, predictable universe with a matrix of pure probability. It revealed that at the foundational level of reality:

• Particles do not exist in a single, defined location until they are measured (Superposition).
• Light behaves simultaneously as a bullet and a ripple (Wave-Particle Duality).
• Observing a system fundamentally changes its outcome.

Quantum theory was so incomprehensible that even the geniuses who built it revolted against it. Einstein spent the latter half of his life trying to disprove it, famously dismissing quantum entanglement as "spooky action at a distance" and declaring that "God does not play dice with the universe."

It collapsed the bedrock of Western science: the principle of determinism. Under quantum mechanics, you can never simultaneously know where a particle is and where it is going (Heisenberg's Uncertainty Principle). It meant that at the subatomic level, reality dissolves into a haze of mathematical tendencies, a concept so deeply unsettling that the Nobel-winning physicist Richard Feynman later remarked: "If you think you understand quantum mechanics, you don't understand quantum mechanics." The equally great theoretical physicist John S. Bell famously stated regarding quantum physics: "I'm quite convinced that quantum theory is only a temporary expedient," meaning it lacks a clear and coherent account of physical reality.

Quantum theory is so counterintuitive that it seems to be fully inconceivable from any library containing knowledge predating its conception by humans. This is precisely the point of this essay. To see beyond what is, and even what can be extrapolated, may be impossible – except by humans. Of course, we have Kant’s Idealism (see §2); machines don’t.

4.                Scientific Laws --- The Architecture of Order. To step into the pre-modern world is to encounter a universe of profound volatility. Prior to the seventeenth century, human existence was oriented around a cosmic theater governed by the unpredictable whims of divine agency, demonic interference, or the shifting wheel of fortune. If a harvest failed, a plague struck, or a comet blazed across the night sky, it was interpreted as a localized act of volition, a personal response from a spiritual realm that demanded ritual, prayer, or sacrifice to appease. The birth of the scientific "Law" shattered this worldview entirely. By introducing the concept of a clockwork universe governed by immutable, mathematical rules, the early pioneers of the Scientific Revolution did not merely update contemporary textbooks; they engineered a conceptual rupture that was fundamentally beyond the comprehension of their era.

The revolutionary nature of a natural law lies in its assertion of absolute, non-negotiable uniformity. When figures like Johannes Kepler or Robert Hooke formulated their respective principles, they introduced the paradigm shift of a deterministic cosmos. A scientific law strips nature of its internal caprice, declaring that the physical universe operates under a strict code of conduct that remains identical yesterday, today, and forever, regardless of geography. Under this framework, the cosmos became an interconnected machine readable through the language of mathematics. For a population accustomed to a world of sudden, miraculous interventions and localized spiritual forces, the assertion that the entire universe was bound by a hidden, unchanging ledger of mathematical equations required an impossible leap of abstract imagination.

Consequently, this new conception of law was met with deep intellectual and theological resistance because it fundamentally threatened traditional views of divine sovereign power. To the early modern mind, a universe operating via autonomous, mechanical laws suggested an attempt to strip the Creator of His ongoing agency. If an unbreakable law dictated exactly how a planet must move or how heat must transfer, it implied a limitation on divine will. Thinkers like Galileo Galilei and René Descartes faced intense scrutiny precisely because their mechanical philosophies bordered on heresy to an establishment that believed the material world required constant, active spiritual maintenance to avoid dissolving into chaos.

Furthermore, the introduction of universal law completely inverted the relationship between humanity and the environment, fundamentally shifting human agency. In his 1620 treatise Novum Organum, Francis Bacon famously encapsulated this new reality by writing that "nature, to be commanded, must be obeyed" (Omodeo, 2021). The frontispiece of his broader work, “Instauratio Magna”, depicted a ship boldly sailing past the Pillars of Hercules—the classical boundary markers of the known world—under an inscription from the Book of Daniel: "Multi pertransibunt et augebitur scientia" ("Many shall pass to and fro and knowledge shall be increased"). This imagery boldly declared that humanity was entering an unmapped territory of empirical discovery (Harrison, 2012).

By decoding the underlying mathematical laws of the cosmos rather than passively reacting to environmental crises, humanity moved from a state of anxious appeasement to active engineering. This intellectual leap from a chaotic, spirit-filled world to a rigorous, law-bound reality served as the structural foundation for the Industrial and Technological Revolutions, permanently revealing and rewriting the baseline of human capability.

Now, let's connect all this to AI. Imagine we possessed today’s AI capabilities just before the year 1600. At that time, almost nothing was known about science as we understand it today. If we asked the AI, “How should I discover new facts about how the planets move?” it would simply regurgitate existing knowledge about epicycles, or perhaps mention Kepler’s laws and the ideas he was exploring. Yet it would have no basis for linking those ideas to Galileo’s pioneering work on falling bodies, because no established physics yet existed to describe planetary motion, let alone the mathematics required to do it. A question about the cause of disease would produce only a scholarly discourse on malaise. (This is discussed in the next section.) And if we inquired about a new material, such as a rust-free form of iron (stainless steel[2]),  AI would likely offer no answer at all, or offer teachings from the Bronze or Iron Ages. Also, the key ingredient, chromium, was totally unknown until 1797.  An AI trained solely on pre-1600 information would have no concept of these things and no capacity to invent them. This thought experiment shows that pattern matching or LLMs is not the solution to every question,

AI cannot see what will come only through imagination. Only humans can, and we can’t predict what it will be, or when it will happen.

Yet, all is not perfect for us. We invent new concepts, such as infinity and its trappings, that render marvels to much of modern science, but in themselves yield the worst of possibilities, those of incompleteness and undecidability (Gödel, 1934). In brief, there are true things we can never prove are true. Not only that, while mathematics has given the tool (functional analysis) that works miracles in science, it allows massively counterintuitive conclusions. It goes by a friendly name: the Axiom of Choice[3]. It is tempting to say we have our imperfect science proved by an imperfect tool. Alas, AI is not yet a player in this game.

5.                Medicine. Just as physics was redefined by relativity, the history of medicine features structural ruptures that shattered ancient paradigms. For millennia, human illness was attributed to the supernatural, an imbalance of the bodily fluids (humorism), or toxic air (“miasma”). The top four revolutionary concepts in medicine, Germ Theory, Antisepsis, Vaccination, and Selective Toxicity (Antibiotics), completely altered human life expectancy by exposing an invisible biological battlefield. When first conceived, each of these concepts violently insulted contemporary common sense and faced fierce resistance from the medical establishment. It is noted that AI has proven excellent at diagnosis and X-ray reading, both of which are technical and well-established subjects in medical schools. Remember, our goal was originally to determine if AI would be suitable for new and different situations. We take up the first two of these, though the patterns for all four are similar: a. Radical idea b.Rejection c. Evidence accumulates e, Acceptance.

5.1. Germ Theory. For centuries, the leading scientific explanation for epidemics was miasma theory, the belief that diseases such as cholera and the Black Plague were caused by noxious, foul air emanating from decaying organic matter.  It was revolutionary because it proposed that specific microscopic, living organisms (bacteria, viruses, and fungi) invade humans and reproduce, directly causing specific illnesses. It stripped disease of moral or atmospheric ambiguity, introducing a physical, identifiable agent that could be tracked, contained, and killed.

The idea that invisible, microscopic entities could topple healthy, full-grown human beings sounded like a fairy tale. This made it impossible, or at least beyond understanding.  When Louis Pasteur began proving that microorganisms caused fermentation and spoilage, and Robert Koch later isolated the bacteria causing anthrax and tuberculosis, the old guard fought back. Leading medical minds argued that microbes were the result of disease rather than its cause, believing they spontaneously generated within diseased tissue. Asking a nineteenth-century doctor to believe that an unseeable organism on a clean-looking hand could kill a patient required a massive leap of faith into a microscopic universe they could not perceive.

To explain why AI might miss this, consider that AI requires enormous volumes of structured data to identify correlations. In the nineteenth century, the data available to train any prospective AI would have been overwhelmingly biased toward miasma theory. As well, there is the AI blindspot where it can find correlations where there are none, such as with cholera, which occurs in low-lying marshlands. Finally, AI excels at correlations rather than understanding. So, the causation of miasma would come from this correlation. Humans make this mistake as well, and all too often.

5.2. Antisepsis. Before the mid-nineteenth century, hospitals were centers of horrific mortality. Surgeons proudly wore blood-and-pus-splattered surgical coats as badges of experience, and surgical instruments were rarely washed between patients.

Building directly on early germ theory, British surgeon Joseph Lister conceptualized antisepsis: the deliberate use of chemical barriers (like carbolic acid) to sterilize surgical instruments, wounds, and hands. It shifted surgery from a desperate, final gamble plagued by "hospital gangrene" to a controlled, sterile discipline.

It was beyond understanding because it was different. Antisepsis was universally mocked when it was first introduced. Ignaz Semmelweis, an early pioneer who demonstrated in the 1840s that childbed fever deaths plummeted if doctors simply washed their hands in chlorinated lime, was dismissed as mentally unstable by his peers. The medical establishment found the idea deeply offensive: it implied that prestigious, upper-class physicians were the active vehicles transferring death from corpses to living patients. Because the mechanisms of bacterial infection were not yet deeply integrated into hospital culture, the idea that invisible dirt on a polished instrument could cause a fatal systemic infection contradicted the sensory experience of the era.

To explain why AI could miss this, understand that machine learning algorithms are fundamentally conservative; they optimize their parameters based on a loss function that rewards matching the historical outcomes of their training sets. The AI blindspot would correlate a high mortality across all hospitals as statistically unavoidable. As well, there was a conceptual (bias) failure that hand washing had any effect.

In conclusion, the most recent example I know of is a similar situation, hardly more than 40 years ago, when another origin of disease was proposed. The prion is a misfolded protein that induces folding problems in normal variants of the same protein. Prions were discovered in 1982 by American neurologist and biochemist Dr. Stanley B. Prusiner at the University of California, San Francisco (UCSF). To summarize, Prusiner got the Louis Pasteur treatment from his colleagues. Finally, in 1997, he was awarded the Nobel Prize in medicine. AI would have missed this completely. Moreover, his paper might never have been published if it had been submitted to AI referees.

6.                Conclusion. As the physicist Erwin Schrödinger instructs us, "The task is not so much to see what no one has yet seen, but to think what nobody has yet thought, about that which everybody sees."  From just these few examples, we have tried to illustrate that with AI in the mix from time immemorial, many, if not most, of our breakthroughs would never have happened. We can generalize to note that our failures and faulty insights, followed by rare insights, have ultimately led us to more great discoveries than we would have had we used an AI engine all along. So, while millions use these tools every day, we cannot rely on them when what we need is new. It cannot become the essential decision maker when uncertainty and its diabolical cousin, information bias, are lurking about.

Students should graduate with some knowledge of what AI can and cannot do, what they can do with it, and why they would be valuable additions to their firm. Faculty should be aware of how they can remain valuable to students, not just by transferring knowledge but also by teaching the thought process behind it. AI may be a ready solutions manual, but it can’t do everything.

References

1.     Allen, G Donald, 2025, “What is Micro-genius”, https://donall.substack.com/p/what-is-micro-genius?r=b7yml, Online.

2.     Newton, I. (1999). The Principia: Mathematical principles of natural philosophy (I. B. Cohen & A. Whitman, Trans.). University of California Press. (Original work published 1687).

3.     Westfall, R. S. (1980). Never at rest: A biography of Isaac Newton. Cambridge University Press.

4.     Einstein, A. (1916). Relativity: The special and the general theory (R. W. Lawson, Trans.). Henry Holt and Company.

5.     Isaacson, W. (2007). Einstein: His life and universe. Simon & Schuster.

6.     Pais, A. (1982). 'Subtle is the Lord...': The science and the life of Albert Einstein. Oxford University Press.

7.     Bohr, N. (1934). Atomic theory and the description of nature. Cambridge University Press.

8.     Heisenberg, W. (1958). Physics and philosophy: The revolution in modern science. Harper & Brothers.

9.     Planck, M. (1920). The origin and development of the quantum theory (H. T. Clarke & L. Silberstein, Trans.). Clarendon Press.

10.  Kuhn, T. S. (2012). The structure of scientific revolutions (4th ed.). University of Chicago Press. (Original work published 1962).

11.  Harrison, P. (2012). Francis Bacon, natural philosophy, and the cultivation of the mind. Perspectives on Science, 20(2), 139–158. https://doi.org/10.1162/posc_a_00060

12.  Omodeo, P. D. (2021). Bacon’s Anthropocene. Epistemology & Philosophy of Science, 58(3), 149–170. https://doi.org/10.5840/eps202158350

13.  Ehrlich, P. (1960). The relations of chemistry to medicine and particularly with regard to the thesis of the "magic bullet". Pergamon Press. (Original work published 1906).

14.  Fleming, A. (1929). On the antibacterial action of cultures of a penicillium, with special reference to their use in the isolation of B. influenzae. British Journal of Experimental Pathology, 10(3), 226–236.

15.  Jenner, E. (1798). An inquiry into the causes and effects of the variolae vaccinae, a disease discovered in some of the western counties of England, particularly Gloucestershire, and known by the name of the cow pox. Sampson Low.

16.  Koch, R. (1882). Die aetiologie der tuberculose [The etiology of tuberculosis]. Berliner Klinische Wochenschrift, 19, 221–230.

17.  Lister, J. (1867). On the antiseptic principle in the practice of surgery. The Lancet, 90(2299), 351–353. https://doi.org/10.1016/S0140-6736(02)51827-4

18.  Pasteur, L. (1861). Animalcules infusoires vivant sans gaz oxygène libre et déterminant des fermentations [Infusorial animalcules living without free oxygen gas and causing fermentations]. Comptes Rendus de l'Académie des Sciences, 52, 344–347.

19.  Gödel, K, (1934) “On Undecidable Propositions of Formal Mathematical Systems” (mimeographed lecture notes; taken by S. Kleene and J. Rosser), reprinted with corrections in Davis 1965, 41–81, and Gödel 1986, 346–371.

20.  Semmelweis, I. (1983). The etiology, concept, and prophylaxis of childbed fever (K. C. Carter, Trans.). University of Wisconsin Press. (Original work published 1861).

 

Appendix A. General Traits of Micro-Genius.

The concept of a "micro-genius" highlights that intelligence is not a monolithic trait but can be highly fragmented and specialized. It's a useful term for describing those who demonstrate brilliance in ways that defy conventional notions of "all-around" smartness.

The 10% solution. I used to tell my numerical analysis students that when I showed a new and faster method to solve a problem,  they were particularly unimpressed. Why give us yet another method? This was their thinking. I said, suppose you could cut the cost of drilling a new oil well by just 10%? You’d save your firm millions. Just a little can make a huge difference; you’d be a micro-genius.

Here is a list of their general characteristics.

• Elegant simplicity. Solves a problem with minimal effort.
• Intense focus. They can concentrate for long periods on their specific domain, often to the exclusion of other activities.
• Pattern recognition. A micro-genius has an exceptional ability to identify and analyze patterns within their specialized area.
• Highly intrinsic motivation. Their drive to excel is often deeply personal and self-directed.
• Repurposing. Finding new ways to use old ideas is often spontaneous.
• Cleverness. Witty twists rather than world-shaking changes.

·       Creative Micro-Skills. A home cook who can balance flavors instinctively, turning random pantry items into a cohesive dish without a recipe.

·       Intuitive Social Cues. Someone who can defuse a tense conversation with a single well-timed joke or phrase, like a coworker, ambassador, or manager who senses an ill mood and redirects it with subtlety.

I believe it is safe to say that while AI is unparalleled in its pattern-finding abilities, it lacks these characteristics.

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[1] So, for any geologist reading, there is now a serious philosophical interpretation of plate tectonics with one of the deepest and revolutionary theories in philosophy.

[2] Remarkably, stainless steel was only invented in 1913, where it found a place right away for cutlery. Now, it’s a foundational metal for thousands of applications. BTW, I wrote my high school term paper on its use in the aircraft industry during WWII.

[3] By the way, Kurt Gödel used this tool to prove the existence of God. Interesting proof. Not difficult.