books about [...] are not the [...]
the whole point of mathematics is its awesome, godlike, almost spiritual like predictive power
philosophy, history and all these other humanities type things are pseud gypsy fortune telling compared to it in predictive power, hence why math filtered these topics into /x/
you have to have double digit iq to live in the intellectual ghetto of humanities after the enlightenment
Math isn't even real. The frick does addition even mean? No one knows. One apple and another apple makes two apples. Actual nonsense, there aren't any separate objects.
I'd rather read a story about how apples are the cause of all suffering, than sit around counting apples like an autist. "B-but I can predict how many apples will fall from the tree using non-linear retroactive eucledian difractal whatever"
So what.
While we're at it numbers are also fake and mind parasites. 1 is the only number that exists. There is nothing greater or less than one. Split something in half you don't have half, but just a smaller 1. Add another 1 to 1 you don't actually add anything unless the two fuse together in which case it still remains one thing. If they remain separate you don't have two, but just 1 and 1.
Mathlets btfo
Loeb did two volumes called Greek Mathematical Works that covers everything from Thales to Euclid. You can read Nichomachus On Arithmetic too. There are bunch of Arabic works that don't have English translations but Al-Khwarizmi's Algebra does have a few but they are hard to come by. Then you have Lobachevsky's New Principals of Geometery with a Complete Theory of Parallels.
Morris Kline, Loss of Certainty
Morris Kline, History of Mathematics
Jacob Klein, Greek Mathematical Thought and the Origin of Algebra
Edmund Husserl, Origins of Geometry (read this one before Klein)
E.A. Burtt, Metaphysical Foundations of Modern Science (read this one together with or before Kline's Loss of Certainty)
>Morris Kline, Loss of Certainty >This book is about the profound changes that have taken place in the way people view the nature and role of mathematics. We now know that mathematics does not possess the qualities that once earned it universal respect and admiration. Our predecessors saw mathematics as an unrivaled model of rigorous reasoning, a set of immutable "truths in themselves" and truths about the laws of nature. The main theme of this book is the story of how man came to realize the falsity of such ideas and to the modern understanding of the nature and role of mathematics.
>Kline was born to a israeli family in Brooklyn and resided in Jamaica, Queens.
We don't do that here.
"For centuries, Euclidean geometry seemed to be a good model of space. The results were and still are used effectively in astronomy and in navigation. When it was subjected to the close scrutiny of formalism, it was found to have weaknesses and it is interesting to observe that, this time, it was the close scrutiny of the formalism that led to the discovery (some would say invention) of non-Euclidean geometry. (It was several years later that a satisfactory Euclidean model was devised.)
This writer fails to see why this discovery was, in the words of Kline, a "debacle". Is it not, on the contrary, a great triumph?...
Professor Kline does not deal honestly with his readers. He is a learned man and knows perfectly well that many mathematical ideas created in abstracto have found significant application in the real world. He chooses to ignore this fact, acknowledged by even the most fanatic opponents of mathematics. He does this to support an untenable dogma. One is reminded of the story of the court jester to Louis XIV: the latter had written a poem and asked the jester his opinion. "Your majesty is capable of anything. Your majesty has set out to write doggerel and your majesty has succeeded." On balance, such, alas, must be said of this book."
>pilosop
1) George Soros book "finance is alchemy," springs to mind, published in a era of rapid currency debasement and unpayable debt.
2) Numerology appeals to the same piece of the brain as random chance and, intellectually speaking, is reductionism.
>hist
3) Mathematics, originally had very little to do with numerology, and 'advanced numbers' (algebra, etc.) was only introduced about two hundred years ago.
>fundatore
4) algebra is an arabic term from medicine meaning "to break a bone to set a bone," referring to the rewriting of the human mind into a reductionist engine.
I study maths but I feel like a fraud because I don’t understand it on a deep, intuitive, holistic, philosophical level. I get first class marks in all my exams but that’s simply because I work with the definitions and rules to solve the question, much like a logic puzzle. The way maths is taught is partly to blame for this. A maths uni course is basically a game show where you have to prepare to solve some logic puzzles at the end. Unlike in philosophy exams, where they’ll ask you open-ended things like, “Are there any synthetic a-priori truths?” and expect you to think independently, maths exams are purely “objective” with no room for critical thought. The result is you can just memorise some algorithms, rules, and definitions, without understanding them, and get top marks like I do. Also the Definition—Theorem—Proof structure of the textbook rarely gives motivation for the results discussed. If you take the Platonic view of knowledge, as I do, then learning should be a rediscovery. The student should be placed in the shoes of the mathematician who discovered these things, and should rediscover it for himself. That requires discussing the idea which motivates the definitions in depth, since that is the most important thing. It requires putting forward different hypotheses and definitions and working around the problem until you get the answer. Instead most maths textbooks just present a finished end product as though it just pops out of nowhere. And how is the student supposed to learn these things on his own with the constant pressure of the exam looming over his neck? Yes, I could spend a few days/weeks learning some concept so that it becomes intuitive, or I could just write down the theorem that I know I’ll have to use and commit it to memory. Euclid is very easy to understand, but I think that’s because Euclidean geometry is just intuitive
You learn to use the tools, and then you start working on some unanswered question, even if you flip burgers to make ends meet.
But to succeed in answering math open questions requires turboautism, it ain't for everyone.
Schopenhauer calls the modern method of mathematical proof "mouse-trap" proofs because rather than giving you the actual intuition and construction that actually generated (and thus guarantee/found) the mathematical insight, they give you an indirect "trap" that snaps onto you and makes you think "I guess I can't disagree with this..." but without any intuition or satisfaction.
You'd probably like Poincare's form of intuitionism, which isn't like Brouwer's. You'd probably also like pragmatist philosophy of maths. Whitehead was a pragmatist and Morris Kline follows him. That doesn't mean they don't believe in truth, it means they think that truth is diverse because it's rooted in human cognition which is diverse. Mousetrap proofs are only secondary things, ultimately what we want to do is to re-travel and intuitively integrate the actual constructions and understanding that created mathematical entities and solutions in the first place.
I find Wildberger's approach to be interesting because he's a very talented traditional mathematician trained in modern proofs but he thinks instinctively in terms of a constructivist plurality of frameworks or languages in which different constructions (and thus proofs) become possible, rather than trying to work backwards from a single unified proof "framework" like set theory. Set theory is just the result of a badly mistaken obsession with mousetrap proofs and a desire to create the ultimate omni-mousetrap.
>proof "mouse-trap" proofs because rather than giving you the actual intuition and construction that actually generated (and thus guarantee/found) the mathematical insight, they give you an indirect "trap" that snaps onto you and makes you think "I guess I can't disagree with this
Which is exactly what they're supposed to do. A proof is not required to provide intuition concerning whatever it's about only to show logically that it's claim is true. Intuitions can be false. Just go to IQfy and see the 0.999...<1 threads come back over and over.
History of mathematics is an unsatisfying field, by the 18th century mathematicians were already doing work more advanced than a highschool-level of mathematical knowledge would be able to understand. Better to just read pop math books about whatever you're interested in, they'll walk you through the relevant work.
books about [...] are not the [...]
the whole point of mathematics is its awesome, godlike, almost spiritual like predictive power
philosophy, history and all these other humanities type things are pseud gypsy fortune telling compared to it in predictive power, hence why math filtered these topics into /x/
you have to have double digit iq to live in the intellectual ghetto of humanities after the enlightenment
Stemtard, define set.
a set is a collection of different things, for example ur mom's vegana is a set that contains muh dick
>a set is a collection of different things
Excellent. Now define empty set, based on that definition.
number of hoes you got by baiting (you)s from me
>mfw stemtard got rekt by the second post
Bait.
Anyways picrel
Math isn't even real. The frick does addition even mean? No one knows. One apple and another apple makes two apples. Actual nonsense, there aren't any separate objects.
I'd rather read a story about how apples are the cause of all suffering, than sit around counting apples like an autist. "B-but I can predict how many apples will fall from the tree using non-linear retroactive eucledian difractal whatever"
So what.
While we're at it numbers are also fake and mind parasites. 1 is the only number that exists. There is nothing greater or less than one. Split something in half you don't have half, but just a smaller 1. Add another 1 to 1 you don't actually add anything unless the two fuse together in which case it still remains one thing. If they remain separate you don't have two, but just 1 and 1.
Mathlets btfo
What a cool illustration. Crazy that it took them centuries to figure out how to print a properly straight line.
Elements by Euclides
i don't like the mathematical philosophy.
Why?
everything is number? intutionism can't be maintained, and realism is also true
Loeb did two volumes called Greek Mathematical Works that covers everything from Thales to Euclid. You can read Nichomachus On Arithmetic too. There are bunch of Arabic works that don't have English translations but Al-Khwarizmi's Algebra does have a few but they are hard to come by. Then you have Lobachevsky's New Principals of Geometery with a Complete Theory of Parallels.
Morris Kline, Loss of Certainty
Morris Kline, History of Mathematics
Jacob Klein, Greek Mathematical Thought and the Origin of Algebra
Edmund Husserl, Origins of Geometry (read this one before Klein)
E.A. Burtt, Metaphysical Foundations of Modern Science (read this one together with or before Kline's Loss of Certainty)
"you need to go back"
>Kline was born to a israeli family in Brooklyn and resided in Jamaica, Queens.
We don't do that here.
>Morris Kline, Loss of Certainty
>This book is about the profound changes that have taken place in the way people view the nature and role of mathematics. We now know that mathematics does not possess the qualities that once earned it universal respect and admiration. Our predecessors saw mathematics as an unrivaled model of rigorous reasoning, a set of immutable "truths in themselves" and truths about the laws of nature. The main theme of this book is the story of how man came to realize the falsity of such ideas and to the modern understanding of the nature and role of mathematics.
LIKE CLOCKWORK
"For centuries, Euclidean geometry seemed to be a good model of space. The results were and still are used effectively in astronomy and in navigation. When it was subjected to the close scrutiny of formalism, it was found to have weaknesses and it is interesting to observe that, this time, it was the close scrutiny of the formalism that led to the discovery (some would say invention) of non-Euclidean geometry. (It was several years later that a satisfactory Euclidean model was devised.)
This writer fails to see why this discovery was, in the words of Kline, a "debacle". Is it not, on the contrary, a great triumph?...
Professor Kline does not deal honestly with his readers. He is a learned man and knows perfectly well that many mathematical ideas created in abstracto have found significant application in the real world. He chooses to ignore this fact, acknowledged by even the most fanatic opponents of mathematics. He does this to support an untenable dogma. One is reminded of the story of the court jester to Louis XIV: the latter had written a poem and asked the jester his opinion. "Your majesty is capable of anything. Your majesty has set out to write doggerel and your majesty has succeeded." On balance, such, alas, must be said of this book."
get algebra 1 at any school library
work your way up to calculus
then keep going
>pilosop
1) George Soros book "finance is alchemy," springs to mind, published in a era of rapid currency debasement and unpayable debt.
2) Numerology appeals to the same piece of the brain as random chance and, intellectually speaking, is reductionism.
>hist
3) Mathematics, originally had very little to do with numerology, and 'advanced numbers' (algebra, etc.) was only introduced about two hundred years ago.
>fundatore
4) algebra is an arabic term from medicine meaning "to break a bone to set a bone," referring to the rewriting of the human mind into a reductionist engine.
I study maths but I feel like a fraud because I don’t understand it on a deep, intuitive, holistic, philosophical level. I get first class marks in all my exams but that’s simply because I work with the definitions and rules to solve the question, much like a logic puzzle. The way maths is taught is partly to blame for this. A maths uni course is basically a game show where you have to prepare to solve some logic puzzles at the end. Unlike in philosophy exams, where they’ll ask you open-ended things like, “Are there any synthetic a-priori truths?” and expect you to think independently, maths exams are purely “objective” with no room for critical thought. The result is you can just memorise some algorithms, rules, and definitions, without understanding them, and get top marks like I do. Also the Definition—Theorem—Proof structure of the textbook rarely gives motivation for the results discussed. If you take the Platonic view of knowledge, as I do, then learning should be a rediscovery. The student should be placed in the shoes of the mathematician who discovered these things, and should rediscover it for himself. That requires discussing the idea which motivates the definitions in depth, since that is the most important thing. It requires putting forward different hypotheses and definitions and working around the problem until you get the answer. Instead most maths textbooks just present a finished end product as though it just pops out of nowhere. And how is the student supposed to learn these things on his own with the constant pressure of the exam looming over his neck? Yes, I could spend a few days/weeks learning some concept so that it becomes intuitive, or I could just write down the theorem that I know I’ll have to use and commit it to memory. Euclid is very easy to understand, but I think that’s because Euclidean geometry is just intuitive
You learn to use the tools, and then you start working on some unanswered question, even if you flip burgers to make ends meet.
But to succeed in answering math open questions requires turboautism, it ain't for everyone.
Schopenhauer calls the modern method of mathematical proof "mouse-trap" proofs because rather than giving you the actual intuition and construction that actually generated (and thus guarantee/found) the mathematical insight, they give you an indirect "trap" that snaps onto you and makes you think "I guess I can't disagree with this..." but without any intuition or satisfaction.
You'd probably like Poincare's form of intuitionism, which isn't like Brouwer's. You'd probably also like pragmatist philosophy of maths. Whitehead was a pragmatist and Morris Kline follows him. That doesn't mean they don't believe in truth, it means they think that truth is diverse because it's rooted in human cognition which is diverse. Mousetrap proofs are only secondary things, ultimately what we want to do is to re-travel and intuitively integrate the actual constructions and understanding that created mathematical entities and solutions in the first place.
I find Wildberger's approach to be interesting because he's a very talented traditional mathematician trained in modern proofs but he thinks instinctively in terms of a constructivist plurality of frameworks or languages in which different constructions (and thus proofs) become possible, rather than trying to work backwards from a single unified proof "framework" like set theory. Set theory is just the result of a badly mistaken obsession with mousetrap proofs and a desire to create the ultimate omni-mousetrap.
>proof "mouse-trap" proofs because rather than giving you the actual intuition and construction that actually generated (and thus guarantee/found) the mathematical insight, they give you an indirect "trap" that snaps onto you and makes you think "I guess I can't disagree with this
Which is exactly what they're supposed to do. A proof is not required to provide intuition concerning whatever it's about only to show logically that it's claim is true. Intuitions can be false. Just go to IQfy and see the 0.999...<1 threads come back over and over.
This book might be okay for a start:
https://jontalle.web.engr.illinois.edu/uploads/298/HistoryMath-Burton.85.pdf
History of mathematics is an unsatisfying field, by the 18th century mathematicians were already doing work more advanced than a highschool-level of mathematical knowledge would be able to understand. Better to just read pop math books about whatever you're interested in, they'll walk you through the relevant work.