But its methods are not as simple as is popularly made out. It looks like supersymmetry and octonions are deeply linked, and and it all emerges naturally from the mathematics of uncertainty. rev 2020.11.24.38066, The best answers are voted up and rise to the top, Philosophy Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. You are conflating different ideas. If yes, we've got a confirmation and may be more confident in our hypothesis, otherwise we have falsified our hypothesis and have to modify it (and again, mathematics will tell us what assumptions will be compatible with our new knowledge from the experiment). In fact, "What is Counting ?" Perhaps it will get a different perspective here.\, @wingman: "Mathematics is not about being correct or wrong, it is about being consistent." History does not support this statement. As Fraenkel put it: "If the attack on the infinite (the finished infinite of set theory) will succeed ... only remnants of mathematics will remain." Even Animals are known to be capable of this. That is, determining the principles from the results, which is much harder than determining the results from the principles (mathematics). Mathematics is based on foundations, known as axioms, from which the rest of the subject is built from. How to limit population growth in a utopia? This is not how the real world operates. Math can be used to describe reality or construct useful fictions. Do mathematician always agree at the end? There have been plenty of false theorems and proofs. For example – how can there be a straight line when everything is moving? We can only solve for 1 variable while holding other variables constant. There are many examples to prove that math cannot work in nature. In my opinion (I am a 10th grader in Turkey yet I am also a math nerd), if you are looking through the eyes of a mathematician and see a correct result derivable from a set of axioms that we have accepted that does not suggest a paradox. This will help support your answer and make it less of a personal opinion. Do you have references to other philosophers who take a similar view to yours? Read my Forbes blog here. And what about the theorem Fermat is thought to have had in mind, that proved not to work? and there are of course different ways to define the same thing. Its often their final form, or rather the form that they are expressed in to bring out their most important properties and to make it look as though they are almost inevitable. Now here are two: ll. There is a great deal of truth to what social constructivists maintain, that mathematical truth is socially constructed, but that doesn't mean to say that it is solely that, and that it doe not have some sophisticated relation to reality too. Why are Stratolaunch's engines so far forward? Why Is an Inhomogenous Magnetic Field Used in the Stern Gerlach Experiment? It may be totally unrelated to physics or workings of our universe, or it may be related and very similar but with important deficiencies, still, within its own framework it's correct as long as no (stupid) mistakes have been made along the way. Indeed still mathematics is the true means in which we communicate with nature as we always say nature's lingua franca is mathematics. formulating the Erlangen program amongst others): Quite often you may hear non-mathematicians, especially philosophers, say that mathematics need only draw conclusions from clearly given premisses and that it is irrelevant whether those premisses are true or false – provided they don’t contradict themselves. Do fundamental concepts in physics have any logical basis? Caloric? Therefore mathematics doesn't have to constantly refine itself as science does. I made some edits. How do we get to know the total mass of an atmosphere? You can, for example, build the, @Kevin: How do you define symbol manipulation without using. Can the President of the United States pardon proactively? and a lot of formulas becomes simpler using $\tau$ instead of $2\pi.$. Now, it took a while to actually define things like limits, groups etc. A scientist advances his field by testing hypotheses. How many ls is that? Strictly, you don't really need "logic" per se if all you want to do is arithmetic and mechanical computation. FOR EACH STATEMENT STATE WHETHER IT IS ALWAYS TRUE SOMETIMES TRUE OR NEVER TRUE. It also tells you that if we make certain other assumptions (such as that the axioms of set theory hold), we can derive that we'll find something fulfilling those axioms. Now the mathematics follows by building upon that theorem, always with a little disclaimer "Assuming X's theorem is correct", and meanwhile there's a race between enthusiasts to produce a full proof, or alternatively disprove the dubious theorem. The following quote by Einstein is apropos: "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. However, both geometries are meaningful and have real-world applications. Cutting out most sink cabinet back panel to access utilities. One could argue, that the axioms are derived empirically, by understanding what important questions can be cast into this kind of language, but surely logic remains a priori. Unlikely to be settled here. Since then this 'equivalence-theorem' is considered of the highest importance in set theory." You are saying that mathematics is "completely wrong". The earliest known mathematics appear to be attempts to quantify time and make calendars, with other early efforts directed towards accounting, astronomy, and engineering. Science can be seen as working in the opposite direction as mathematics. All the past experiments of physics remain experiments of physics, and all the technologies that result from the applications of past physics also remain valid, even when the physics on which they originally relied is modified. But these few should be sufficient. Again, this is not so simple. It's very fun to play around with and its essential for understanding a lot of subjects. For all we know, there are much easier ways to describe physics than through complicated systems of equations, but our minds may not be capable of symbolically interpreting the world in a way that allows us to use those tools, any more than we're capable of a tool that requires the use of a prehensile tail. In the same way, since the only truly good mathematicians among the animals are ourselves, we assume that if we encounter other systems of intelligence that they'll have the same concepts of math was we do. It's very fun to play around with and its essential for understanding a lot of subjects. Timer STM32 #error This code is designed to run on STM32F/L/H/G/WB/MP1 platform! I think of mathematical truths existing prior to human cognition and abstraction. Mathematics is nothing more and nothing less a tool that's useful for humans in solving particular problems. Famous mathematicians offer a hypothesis with a faulty proof, with known fault - the proof covers a large part of cases but some remain unproven. Yet we make space shuttles and fighter jets using them not because they are perfect but because they are a good enough approximation. Of course after a time the error will be found and the necessary corrections made. The numbers 1, 2, 3 are points on the real line; they cannot be apples and oranges. I see you have quotes to questions in the Physics SE in a comment. By "axioms of mathematics are unchanging" I meant for a particular mathematical theory. Now, mathematicians also deals with definitions, Statistical mechanics needed to explain all of Carnot's results. It was of course noticed that these 'fluzions' were not fully rigorous, and Berkelys criticism of 'ghosts of departed quantities' stung. Anybody who works productively in mathematics, however, will talk in a completely different manner. But it was also wrong. But that doesn't make Euclidian geometry useless for everyday life. I don’t think I get the concept of ‘two-ness’ from seeing two apples, and then two people, and then two houses and abstracting away from the objects to see what they have in common.