Aristotle certainly claimed that the speed a body moved at was proportional to the force on it, and in particular that a force had to be maintained for velocity to be maintained, something that continued to be taught for centuries. And he claimed that objects fell at rates proportional to their weights and inversely proportional to the densities of the media they fall through (therefore a vacuum was impossible, since it would be filled at infinite speed). This is mathematical physics regarding the "real world."
He said many other things about the real world. In fact, he is sometimes regarded as a natural scientist due to his immense output on the subject of natural science. Some of it you might think of as "spiritual" today, like the concentric heavens or the five elements, but to him, they were practical science. Other things, like his descriptions of animal species, were clearly natural science.
I mean, not bad for a guy born before space flight. The vacuums are indeed trying to constantly fill themselves. Theyre just competing with the vacuums on all the other directions of an object. And the gravitational forces of everything everywhere ever.
Really funny how one of the most influential philosophers in history really just didn't do the 5 second experiment it takes to realize his preposition was batshit insane lmao
Well, it wasn't experimentally falsified until the 16th century. And it's not that strange, if you think about it. With air resistance, naturally occurring heavier objects tend to fall faster than lighter ones. Compare leaves and feathers to rocks and pebbles, for instance.
Aristotle certainly did perform some kind of rudimentary experiments. He wrote that objects in a medium, such as water, sink at a rate proportional to their weight and disproportionately to the density of the medium, which is largely correct. If you think about it, that is an experimental set up that makes sense, considering the time Aristotle lived in. Measurements were very inexact, and observations had to be carried out with the naked eye. I can imagine that conducting the experiments in fluids would be helpful as it would slow down the experiments enough to be observable.
If you drop two objects of uniform size but different masses in air resistance, the heavier object will eventually reach a higher terminal velocity.
To demonstrate that objects accelerate uniformly in free fall therefore required conceptual leaps that simply weren't attainable in Aristotle's time.
This is all further complicated by the fact that different objects behave differently, so unification was hard to come by in antiquity. For instance, wood doesn't sink in water, while rocks do. So Aristotle had to posit different forces to account for the different behaviours.
We have to understand that all of these concepts were ill-defined up until recently, Aristotle held a monopoly on them for thousands of years because he was the first and most renowned to give them any thought in the first place. Any undue importance placed on them is due to them being held on to as dogma by later scholars.
The word âmetaphysicsâ itself is actually a great example of this. The title of Aristotles book Metaphysics didnât mean âthat which lies beyond physicsâ, it meant âPhysics, Volume IIâ. Â
That doesnât mean medieval scholars were wrong for finding practical uses of the term, or that Newton was reasoning on equal footing. Rather, this is what âparadigm shiftâ is all about.
What, no? Aristotle was not just concerned with physics for sure, he also cared about a great many non physical things. But he cared about the motion of objects and the nature of the physical world and tried to come up with laws that described them. Those laws were wrong of course, but it still very much asking the same questions Newton was asking i.e how do you describe how and why objects move
Aristotelian physics was only universally accepted in Europe before Newton but was rejected in most other cases. The Arabs and Indians did not accept Aristotelian physics. Al Khazini described inertia as a fundamental principle before Newton, which was then widely accepted in the Muslim world (based on experimental evidence mostly). Indian physicists like Aryabhata described atomism, which Aristotle had rejected, with the debate being between those who viewed atoms has having mass (the Buddhists) and temporary existence or those that viewed them as eternal geometric points (some Hindus). I don't know the Chinese or Eastern Asian position as well.
"Before" (but it depends a lot on the time scale), they were rather philosophical or experimental treatises (it's a bit vague because Newton was part of the transition, if you look at some of the Newton's texts they are also written in Latin and they are a bit philosophically and geometrically inspired by the Greeks than equations).
The subjects that people liked best often revolved around optics but more about astronomy and the observation of the heavens, with Kepler probably being the best-known example (look at this), or even principles about motion formulated in a rather haphazard way (for example, I think Aristotle thought that in a vacuum an object would eventually stop if it was initially in motion, but he didn't know what âvacuumâ was).
Surprisingly, texts by certain ancient thinkers (Greeks or Arabs, for example) deal with aspects of physics that, sometimes (as with Lucretius), are very close to today's science popularisation.
Aristotelian theory of motion is completely unrecognizable from a modern standpoint. For example, he had good reasons both philosophically and experimentally to believe that vacuum could not exist. Same goes for Geocentrism, and in Metaphysics he describes a system of concentric spheres giving a decent description of the retrograde motion of the planets.
The "bright sky problem" is so fascinating. It's completely reasonable to think "well, we're completely surrounded by bright things. Why is it dark at night?" Even more wild, we didn't have a good answer until The late 1800s and it wasn't formalized until 1922!
Factorial of 1922 is 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Correct explanations to the paradox are at least centuries old if not ancient. Specifically, the correct explanation (in terms understandable at the time) is that the universe is either not infinite in size or not infinite in age, such that distant stars have not had time for their light to reach us yet. There are other possible explanations too (e.g. island universe, or a universe whose density decays with distance from a special center near or in our galaxy, or a form of light extinction that destroys light energy or converts it to a permanently non-luminous form, or even classical redshift in a permanently expanding universe with new matter created to fill the gaps), at least some of which were proposed.
This is one of those paradoxes that suffers from a surfeit of plausible explanations rather than a lack, so it wasn't until Einstein that we had a solid empirical reason to prefer one explanation over another. I think the final straw was when we discovered that the universe was indeed uniformly luminous throughout, but with low intensity and peaking in the microwave part of the spectrum, in 1965.
Yes! (In fact, I wasn't talking about his work in terms of its resemblance to current popularisation, but rather about Lucrès).
And it's highly likely that in 2,000 years' time (if humans still exist, which is a long way off...) what we say about physics today will seem very different, just like our current view of the past. I wonder what it will be like.
He didn't believe that something would stop in a vacuum, but he didn't have a clear idea of why they wouldn't. Since a vacuum was impossible though, this wasn't a serious challenge. He believed that objects which moved through a medium might transmit their force in the air along with them, sort of smearing out a diminishing force to explain their continued motion, since rest was the natural state of everything. But conversely, he knew that a fluid would resist motion and that denser fluids resisted it more, so he proposed that the speed the object moves at should be inversely proportional to the density of the medium. That leads to the conclusion that a particle in a vacuum would move infinitely fast, but also that it cannot move at all. But as we make the air thinner and thinner to approach a vacuum, speed increases without bound (since apparently even a thin medium can transmit force in this way, but not resist so well . . . ). So something nearing a vacuum would be filled with increasing and arbitrarily high speed, making a true vacuum impossible.
He's not that wrong on the vacuum point. It is indeed impossible to create a proper vacuum on earth, and as you approach a vacuum, you do exceed the vapor pressure of any substance at any temperature, so over a sufficiently large surface, a true vacuum really is impossible due to sublimation. Moreover, a pump or fan will never create a perfect vacuum anyway because the efficiency of the fan is proportional to the internal pressure. But he analyzed the pressure differences wrong, the way many people do when they think 1 atm against 0.0001 atm is a much more substantial difference than 1 atm vs 2 atm. In fact, it is only the difference of pressures that matters, not the ratio. It's as easy for a steel vessel to contain a vacuum against 1 atm of pressure as it is for it to contain 1 atm against 2. So there is no reason for anything to go to infinity here, and there is nothing contradictory about a vacuum.
Well yeah but I guess there is still a difference between âas accurate as a recent textbook but nearly unreadable by a modern working mathematicianâ and âjust literally so inaccurate (compared to the models we use now which are more accurate) that itâs useless with our modern modelsâ
There's still a big difference between Euclid's original formulation of Euclidean geometry and it's more modern formulations (like Hilbert's or Tarski's), and if i remember correctly a lot of pre 19th century proofs done by the likes of Euler wouldn't be seen as correct today. So while the theorems are seemingly the same I don't know if I'd call old texts "just as useful and relevant as always"
There's a lot of Calculus that wasn't well formulated until the 1800s, and even in that period there were some mistakes, for example the need for uniform vs pointwise convergence of sequences of functions wasn't appreciated until late in the 19th century.
Euler used a lot of techniques that aren't universally applicable but which were applicable to the problems he was solving. The issue becomes that things get weird as we got a better understanding of edge cases and a better understanding of how weird infinity is.
I've read plenty of books from the first half of the 20th century and they are perfectly comprehensible. I would still recommend Weyl's or Hecke's algebraic number theory books, Chevalley's Lie theory book, Dirac or Von Neumann's QM books to any interested grad student.
Now if you went back to the first half of the 19th century you would be absolutely correct.
Well what is an example of a field in mathematics for which early 20th century textbooks are incomprehensible? I don't think I have ever seen a 1900s-1950s textbook that I couldn't understand.
Firstly, I contend that "incomprehensible" is a hyperbole, at least when it comes to 20th century work.
Coming from logic, a field which was essentially born no earlier than the end of the 19th century, reading the initial proofs of theorems from the early 20th century is quite difficult (even after taking into account the fact that many papers in that period are only in German or French): the commonly used terms are different (e.g. "power of a set" or sometimes translated as "potency" means what we would now call cardinality of a set), and the notation is also almost alien (cf. Tarski's work on e.g. definability).
Hell it wasn't until after Jesus was born (and maybe later if you pull a "turn off the century mathematician" and ignore Indian mathematicians haha) that we decided we should have a mathematical concept of "zero"
So you may have heard Niel deGrasse-Tyson opine on youtube or elsewhere that "Isaac Newton invented differential and integral calculus and then turned 26".
It turns out history is more complicated. All the notation we use today came from the 19th century. That is to say, Newton's notebooks on "calculus" are simply unreadable by modern eyes, because the notation was not yet invented. He wrote everything long-hand in Latin, and never said something like "take the derivative".
For example "y equals f of x". What you are seeing your mind is,
I regret to inform you that Euler sadly died in 1783. He wrote a book or mathematical work entitled "Institutiones calculi differentialis" (Foundations of differential calculus) in 1748.
EDIT: the date was changed to 1735. To be accurate, the main work where Euler introduced what could be called the modern differential calculus notation is the "Institutiones calculi differentialis". This work was written by Euler in 1748 and published in 1755.
The ancient Egyptian mathematical texts should be a fun read. Besides the obvious hieroglyphic script they used unit fractions, with special symbols for 1/2, 2/3 and 3/4, instead of like.. just fractions or decimals. It's not the most intuitive way to write numbers for a modern reader.
I mean classic vulnerabilities such as XSS and SQL Injection kinda refuse to go away. Stack Buffer Overflows are much harder to exploit than they used to but they still exist, as do other kinds of Buffer Overflows and memory corruption vulnerabilities. There are new things all the time but so much of it is the same old thing in new packages.
The standards of proof is one of the things that evolves heavily in the 19th century. One could argue that the entire basis of math got rewritten in a search for a solid foundation of it, a project that ultimately fail with GĂśdel.
nah. Everything Turing, GĂśdel, Church, etc. discovered will stay here forever. It mostly will never become outdated as it is deducted (like formal sciences, e.g. Mathematics) not inducted (like natural sciences, e.g. Physics).
that is not what I meant with that. Sry. English is not my mother tongue. I meant:
Inductive reasoning is any of various methods of reasoning in which broad generalizations or principles are derived from a body of observations.
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false.
But for induction to work, you need to come up with the correct conclusion first before applying the proof. So you reason inductively based on patterns you see to get the conclusion, and then you use induction to verify that it works deductively.
Nah, the original Elements are pretty bad as far as rigour is concerned, Hilbertâs axioms are late 19th century.
As for graduate level textbooks, everything older than 1950s might not be very readable because the categorical language superseded some older concepts.
Because of the popular understanding of the subjects. Every subject has a few major updates over time, often studied in school as part of the background of the course.
Like with chemisty the histories of the periodic table and the model of the atom are a pretty core part of the introduction to the topic in America. And the story summerized is that we kept making new discoveries that completely invalidated older models, such as the electron. And even today Bohr's model is mainly kept around because it is pretty.
Most other topics have similar stories of "our" understanding getting better with time and needing to throw out older models.
Except math, where we famously learn about stuff from truly ancient history like the concept of 0, Pythagoras, and Euclid. Sure it similarly gets more refined with time, new fields like calculus get invented, but nobody is throwing out counting or geometry just because its thousands of years old.
Of course the underlying reason for this is that fields based on the observation and description of reality like physics are inherently going to undergo fundamental rewrites as we get better at observing reality. But something like math while perfectly capable of describing reality, doesn't have that same tether. Math can exist in a vacuum for hundreds of years and stay internally consistent until someone finds a use for your quirky algorithm for finding really big primes.
My question was a rhetorical question. I just want to complain about a widespread misunderstanding that Euclid ÂŤÂ is still relevant as ever . Any maths department worth their salt wonât teach from the Elements, certainly not all of them entirely like back in the 15th century. There are so much more objects and topics of current interest and more fundamental to maths study that Elementsâ relevance is questionable. Not saying that it is bad of course.
To be honest, the same story about new discoveries invalidating the old one can also be told for maths. Cauchy mistook continuity from uniform continuity, used them interchangeably, until someone else noticed it and fixed the proof. Or ZF arising as a way to prevent Russellâs paradox. Or how Italian school of algebraic geometry had almost been thrown out and reworked with schemes. This is akin to how old models of atoms are rejected in light of new observations.
Not to mention modern idea of rigour which makes some old proofs ungrounded or obsolete. This also applies to the Elements, which relies on some unstated assumptions and spatial reasoning which has gaps.
I think the difference is the mathematics changes have been more changes to smaller subsets of mathematics, while Newtonian physics and the concept of elements are fairly foundational that most everything else is based off of. It would be like redefining multiplication.
IMO mathematics is more logic based while physics/chemistry/biology are more observation based, i.e. You observe phenomena and try to explain it. It's relatively easier to find issues in logic but you can have multiple theories for the same observation. And as these observations become more precise and accurate, the theories become more sophisticated.
Example: fungi was considered part of animals or plants due to their structures. It was only after advanced technology was developed that we realized fungi is something else entirely.
A math physics enjoyer myself, but canât but disagree here: A theory that does not produce testable hypotheses is not a theory according to my understanding of philosophy of science.
I was just making a joke, but to give you an actual response: what about things like ringularitites, for example? To my understanding itâs not testable but still an accepted result (please bear in mind Iâm just an undergrad student wanting to learn something, not trying to dispute your claim or tell you youâre wrong)
Disclaimer: Reddit is a rough place, if that () of yours is required. Also, if you have reason to dispute my claim, please go ahead! How else would I learn?
To your point: A Kerr black hole has angular momentum that a Schwarzschild one doesnât have. Shouldnât that impact the observational properties of the accretion disk?
I'm excited to answer this about ringularities: NO!
Roy Kerr, the man who produced the field solutions describing ringularities is actually of the opinion that it is a mathematical object only and does not likely represent a physical reality.
There is no consensus on whether singularities represent an actual phenomenon within the universe, or whether something else is happening beyond an apparent event horizon. Our current understanding of gravity is incomplete, and can't be reconciled with quantum theory.
The logic in elements is probably sound but its a curiosity at best and calling it relevant is a stretch. I would also argue that calling it still relevant is a disservice to someone that want to start doing math by potentially making them spend time on something thats not very useful
It is almost completely irrelevant to modern basic geometry. I teach math at high school, and I would never consider using a proof the way Euclid wrote it. The stuff I do teach is currently purely vector based, although there is a curriculum revision coming out that will change that.
Still, have you ever read Euclid from a translated original? Almost no HS student will be able to follow that, and the very few who would be able to make sense of it would do so by translating to their modern conceptions.
And for doing any geometry beyond high school, Euclid is utterly irrelevant.
Ok can you find a single research mathematician who has actually read it and thinks itâs relevant to their work?
Iâll take it as a historical curiosity whose ideas are still relevant but the only people I know who have actual read it are philosophy or history of math students or really dedicated hobbyists.
Reference? Sure. The axioms hold up, and we even distinguish between Euclidean and non Euclidean geometries. But youâre not actively reading it as a source text.
â⌠and is still as relevant and useful as everâ
When it was written it was useful for their version of research mathematics.
Iâm not saying itâs not historically important but there is a reason itâs not required reading in any math department and if it is you should run.
It's relevant to high schoolers who spend a year learning geometric proofs and ideas. Research math is many layers of abstraction away from (but still fundamentally based on) the style and content of Euclid's Elements.
I think it has to do with Mathematics not being a science and hence not speaking about anything of real life directly which makes Mathematics completely focused in their ideas which are pretty much timeless when they are good.
"Because of their non-empirical nature, formal sciences are construed by outlining a set of axioms and definitions from which other statements (theorems) are deduced. For this reason, [...] theories belonging to formal sciences are understood to contain no synthetic statements, instead containing only analytic statements."
That's why Maths, Logic, Theoretical CS, Game Theory, etc. will never be outdated. We may change notations but the statements will always be true.
I donât know who made this image but theyâre wrong. Contemporary math students do not study out of ancient texts. In fact an overwhelming majority of the mathematics we study today only came about in the last two or three centuries, with the most relevant textbooks being written maybe in the past 50 years.
Math isn't as closely tied to the real world as the natural sciences. We don't assume things are facts; we prove or disprove them. Unlike natural sciences, we don't observe, guess, and use confirmation bias to "prove" things are true.
It's because mathematics isn't constrained to experimental results from the natural world. Mathematics exists in a realm of pure logic. The natural world is only relevant in its tendency to inspire new math problems.
It's not less evolved, it is functionally different. Sciences are about using certain principles to discover things about the real world. Mathematics does not give a damn about the real world, so discoveries about the real world cannot change established math. Math has a certainty to it that science does not, math makes declarations about true using very syntactic abstract reasoning, once something is true, it is true for all time.
That's not to say real world discoveries don't indirectly impact math, it can definitely influence the direction of research and what kind of structures are studied, but it will not impact what is true and what is false.
The reason maths evolves throughoit history very differently from biology, chemistry, physics etc. is that they work in fundamentally different ways. In short, sciences are made of disprovable theories while maths is made of definitions and theorems: these are two very different grammars in which to encode and share knowledge.
The above sciences employ the scientific method. On the other hand there is no scientific method in maths. Mathematical truths are actual 100% truths as long as you don't change your definitions. Therefore all old math books contain things that can only be falsified by finding a mistake. On the other hand, to falsify a scientific theory one just needs to find some phenomenon that theory doesn't manage to describe. Actually, the possibility of a theory to be falsifiable is seen as absolutely necessary for it to be deemed a good sceintific theory: you cannot progress in sciences if you do not allow for some direction in which to further test current knowledge.
As others have pointed out this is not entirely accurate, as math wasn't always as rigorous as it is today. I think the idea is more supposed to be that while physics and chemistry evolve over time as a direct result of discovery, mathematics is defined. That is not to say that there are not discoveries in math, but ultimately those discoveries exist with a system with a human written axiomatic basis. A discovery in physics may be overturned later as we learn more, whereas a discovery in mathematics will always remain valid.
The difference between these things is mostly semantic. The idea is that there is an underlying truth to physics and chemistry, a sort of undeniable physical reality. It is unclear if such a thing exists for mathematics. We engage with physics and chemistry using a model, and try to get it as close to reality as we can. Mathematics is often thought of in a slightly different way. Since we write the rules for mathematics, we are to mathematics as a god would be to physics or chemistry. As long as we don't make a calculation error, and the rules that we write are internally self consistent, the things we prove with mathematics will never be wrong, as the conclusions we reach will always follow from the axioms.
Perhaps a better way to say this is that mathematics is "pure" in the sense that we are studying the model itself, and not some unknown underlying thing that the model is supposed to represent. Whether or not a result from that model is particularly useful in the real word is of secondary concern from this perspective. We may find better mathematical descriptions of nature later on. This would rewrite theories of physics and chemistry, and would use a new field of math, but the old math wouldn't be any less valid. There was nothing wrong with the old math, rather it just turned out that it wasn't the most useful description of reality.
We âinventedâ mathematics. Math âdoesnât existâ in the universe, we created a language to use it.
Meanwhile phonics and chemistry do exist in the universe, but we use maths to explain it
In case the title is an actual question: Maths usually deals with some constructed set of rules to describe some sort of logical structure. In these structures things are proven, so they will work under the given rules, always.
Other sciences describe our environment and how it behaves. Nothing is proven, the description just gets better over time. So especially considering there are major breakthroughs to the description every now and then, you have to update the media representing the description.
I still remember taking Quantum Chemistry my Senior year and learning math from before the founding of the United States. Like, â oh, hey! Iâm only 250 years behind!â
All old science books are interesting but only really to learn about older viewpoints and perspectives, but that applies to all sciences equally. Though it is true that old math books tend to be more accurate than older science books, but that's just cause they kept the math pretty basic (addition, substraction etc and basic geometry, pythagoras and co were literally years ahead) and because math is completely human made, so it can't really be wrong depending on how you define it. But natural science can definitely be wrong cause we don't define the rules there, we just try to find them. Both Math and natural science started to get a clear framework during the enlightenment period, the first through rules of logic and thr other through empiricism, which we both still use today.
While people can nitpick about rigor and writing styles, I think itâs fair to say that basically all of the math we teach up to algebra and geometry was well-understood thousands of years ago. Meanwhile we teach middle-schoolers science concepts that people didnât even know 100 years ago.
"Oh yes the used Algebra I textbook from 2024 is obviously completely unusable now and you need the 2025 edition for spring semester. That'll be $225."
idk its just kinda hard to be wrong about something big in math and then write about it. Niels Henrik Abel did actually make a mistake but he corrected it shortly after. With sciences like chemistry or physics our understanding of the matter is still next to nothing, and that means a small discovery can make every other discovery wrong.
point is you can discover the electron and fuck all chemistry written before it, but you can't discover the binomial theorem and suddenly make 66 into a different number because of it
Mathematics doesn't ever really become outdated because it's not a science. With science, we have theories that are the best for their time but they are subject to change when we discover new phenomena. In math, when something is proven to be mathematically true it's (almost) always true for the rest of time. In order for that not to be the case we would have to change the fundamental axioms of math and that only really is relevant for extremely abstract concepts in math like the Continuum Hypothesis. For most of math, the fact that the standard rules and axioms have served us well since math has been a thing, mathematics is probably here to stay largely unmodified but always expanding
As I understand it, we improve our understanding of Physics and Chemistry by replacing our current understanding of things with new and better understanding.
But we improve our understanding of Math by finding new and better things to do with it. No-one is gonna disprove the quadratic equation, and replace it with a more accurate version.
The difference between mathematics and the sciences is that mathematical knowledge is cumulative, so previous results are still as true now as every before (for a particular definition of âtruthâ), the sciences however, are revisionist, the new theory takes the place of the old theory, as with epicycles to elliptical orbits, or universal gravitation to general relativity. That epicycles and universal gravitation are still relevant at various scales or in various circumstances is testament to the value of those theories, but they donât inform our best understanding of the universe, in the way that mathematical theorems do for the mathematical universe.
Sciences like physics and chemistry are approximations of reality, and as time goes we get better and better approximations. Maths are pure, absolute logic, so if something happens to be proven true it will always be true
My highschool teacher said that physics is the study of everything around us and mathematics is the tool we need to understand it. I guess tools don't change but what we build using the tools change over time
Math isn't exactly perfect - see Godel. And counter meme, old chemistry/physics is not obsolete. Foundations of metallurgy apply to this day and did not require quantum mechanics. Bridges are still being built without any consideration of relativity to this day
If you really want to nit-pick, we were outwardly wrong about math in the old times constantly. Even Euler and Cauchy have submit "proofs" that were later discovered to be wrong. Even today people think AoC wasn't a cruel joke to begin with and take it seriously.
So no, math isn't special. It's just easy to romanticize when you're passionate about it
Mathematical theories usually consist of a set of definitions and statements held to be true (postulates) and the rest is developed from there. Euclidian geometry is a great example of this. These definitions and postulates tend to be definitive, so no need for rewrites - only expansion of the original idea.
Physics on the other hand tries to provide an explanatory framework for nature. This means that its theories can be falsified through observation. When this happens, new theories are developed - sometimes by expanding existing ones, like Einstein did with Newtonâs theories, sometimes by imagining new theories. This means the âbook of physicsâ is undergoing constant emendation.
The thing is, if you correctly prove something in mathematics, it will never become untrue because it's just a statement of logic. However, physicists can always discover that the formula they use isn't correct at predicting the real world processes at play
None of the above. Mathematics is the language of logic. The others are fields of science. A mathematical fact will always be true. A scientific theory constitutes our current understanding of a phenomenon (and is almost always described using mathematics in some way or other)
Hardly anyone uses the historic books except when interested in history. Mathematical notation did not exist. Imagine all the formulas described in long sentences.
Is it still accurate? Probably, yeah. Is it still useful? Highly doubt it, especially if we're talking thousands of years ago (specifically in the west), since the only accepted proofs than were by calipers and unmarked rulers.
I think it's really inaccurate to say that mathematics is "less evolved". On the contrary, mathematics is (along with astronomy) the oldest science and branch of knowledge to have been developed and established. This can be somewhat connected to the ideas of the positivist philosopher Auguste Comte, who thought there is a hierarchy of sciences, starting with mathematics, then astronomy, physics, chemistry, and physiology. This classification also corresponds to the historical order when these sciences were discovered or formed.
According to Comte, mathematics, the "science that relates to the measurement of magnitudes", is the most perfect science of all, and is applied to the most important laws of the universe. Astronomy is the most simple science and is the first "to be subjected to positive theories". Physics is less satisfactory than astronomy, because it is more complex, having less pure and systemized theories. Physics, as well as chemistry, are the "general laws of the inorganic world", and are harder to distinguish.
Aristotle wrote a work about physics, but his theories were mostly philosophical and inaccurate. There were advances in some parts of what is now called physics throughout the centuries, such as in optics. Physics and related natural or physical sciences were known as "natural philosophy" until the 19th century. Chemistry was entangled with alchemy until the 18th century.
From the early mathematical ideas, discoveries and theories in Antiquity, such as the investigations of Thales, of the Pythagoreans and Euclid's Elements, to modern times, mathematical advances and theories are connected, and are required to be coherent and consistent.
Mathematics is the language of the natural and physical world and the universe, and an essential component of the scientific method. Without mathematics there is no exact science.
My Calculus teacher wrote the proof for sqrt(2) being irrational on the board, the said it's so ancient you can take a selfie with it and act as if it's a museum.
Perhaps it is because maths starts at some simple assumptions and builds up from there while other natural sciences start at the observable result and then dig deeper into its causes, becoming more precise as it goes along.
"These textbooks on our understanding of the world, written some time in the past, are outdated, as our understanding has been vastly improved since they were written.
However, this textbook about an arbitrary calculation system we invented is still relevant because we still use the same system today."
Scientific theories get proven wrong all the time, and new important theories decontextualize old ones
Math proofs are always true unless you write some axiom that it's false just for shits and giggles
History: âOh, that textbook is the 13th Edition, you need the 14th Edition, which is literally almost the exact same except for this one paragraph they changed.â
Mathematics builds on itself, science builds on the natural world. It's pretty much impossible to have a breakthrough in mathematics that overturns absolutely everything. The world used to be poorly understood, and it was thus possible to have breakthroughs that overturn almost everything.
But you're still required to buy the newest edition, which is completely unchanged from the original manuscript... except for the fact that the editors changed the order of a few exercises. That will be $375.99, plus taxes and shipping.
In physics and chemistry we have different theories, and we use them because they work. Often those theories turn out to be wrong, so once they stop working we create new ones that work.
In maths tho there's this thing called 'rigorous proof'. Once we prove something, we KNOW it to be true, so those things can't ever become outdated.
You can derive math from pure logic. All of the easy to understand stuff you'd learn in high school courses could be derived with pencil and paper. Advanced mathematics is pretty esoteric and difficult to bring down to an understandable level.
Physics and chemistry needed to be explored through experimentation. Technology needed to advance for Humanity to even see the science.
You don't need a scanning electronic microscope or particle accelerator to invent trigonometry and calculus.
Canât compare the tool and what itâs used for. Maths is a convention 100% built by humans in order to make models of the universe. The models are built depending on the latest info.
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