Why is Mathematical Reasoning not a separate field from Mathematics in general? Mathematical reasoning has more to do with psychology and requires the development of mental skills and an evident progression linking one concept to another, rather than the common approach of maths that's focused on proving and memorizing.Currently maths is like managing a library, it organizes a vast list of facts to be consulted, but other than consulting an index and taking for granted what is found, people in general are not able to wield it. Those who are capable of it have developed their math reasoning without help, which is an extremely inefficient way of acquiring the skill, and the reason most people have anxiety towards math.So why has nobody taken the approach to organize math with focus on the different ways to visualize a problem, the different ways to reach a solution and taking notice which procedure is the most intuitive for that?
Take the pythagoras theorem for example. We all know, because it has been proven in many ways, that C2=A2+B2. We use it and build upon it. But how on Earth did Pythagoras even begin to conjecture that? What did he do to first get the idea? How can I trace the discovery of the theorem de novo? Nobody teaches that.
>>16161044What do you think about this visualization/figure for 7.7 elements
>>16161044Thanks doc.
>>16161055Compare to the typical figure
>>16161051math is just another arm of capitalism who the fuck cares about le heckin truth
>>16161070I don't give a shit about le hecking truth. I want to be able to use math because I want to be part of capitalism you bum.
/sci/ can't into geometry
>>16161051Yes they do. Learn math history. The world knew about the Pythagorean theorem and most theorems well before they were conjectured. We know ancient Egypt knew about that famous theorem as they incorporated it into their design. The difference is, it was understood empirically. Pythagorean simply provided the first proof of it showing that it was necessarily true and not just mere observation.
>>16161185>Yes they do>Learn math historyWhere?>The world knew about the pythagorean theoremAnd how did they come to know them? >The difference is it was understood empiricallyAnd this is what I am talking about.You don't have a SINGLE book or source that doesn't shy away from showing how can a mathematical concept be derived empirically. It must be "proven" to begin with, it must be proven in order to exist. Proofs don't just poof into existence, they are conjectured first and there's not a single book dedicated to these initial conjectures.The pythagorean theorem is not obvious to just about anybody in real life, the fact that others discovered it and used it still doesn't replace the absence of that step that goes from empirism to formality. Even a story about "Pythagoras was drawing a square in the sand and decides to inscribe another inside it, then noticed shit looked about the same" should suffice as a method to discover patterns.
Why don't we focus on my visualization of 7.7 since it's the only on topic response of substance
>>16161051>it has been provenproven is a adjective proved is a verb
>>16161218Euclids elements has this line in it on 3.31 so I suggest reading Euclids elements, I expect you to be able to read greek because mathematics is full of greek words and letters
>>16161498You have been retarded
>>16161044psychology is whatever story is most convincing as judged by le common expertswe will never know 'why' something is, we can only know 'that' it is. and even that is subject to debate considering the fallibility of our senses.
>>16161044most places offer an intro proofs & basic set theory class where you learn that. direct proof, induction, contrapositive, contradiction. basic propositional logic. sets and elements. functions and relations. recursive definitions. that's math.
>>16161568Only if you're in university, and specifically in a major that requires it.>that's mathYes, that's math. It's the development of math, it's not the learning and reasoning part. You need reasoning to work with proofs.
>>16161218It is literally self evident when working with triangles. I don't know what to tell you dude. Literally it was obvious to every engineer of the ancient world. Maybe considered a trade secret, but a well known one. There's nothing complex, just observations made full form. Pythagorean just showed that it must be true from basic geometric axioms.
>>16161647>It's self evidentPut it in words.
>>16161044Albert Whitehead - introduction in Mathematics and Bertrand Russell introduction in to math philosophy seems good ones for this subject.but those are only introductionsis there a math reasoning or you have to go trough all math genealogy in order to understand?
>>16162902thanks
>>16161044i don't know.
