/sci/ - Science & Math » Thread #13742568

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Anonymous Tue 12 Oct 11:16:44 2021 No.13742568 View Reply Original Report

Quoted By: >>13742606 >>13743093 >>13743187 >>13743225 >>13745851 >>13745981

How do I get into math?
I'm not really bad at it, nor do I have a bad arithmetic IQ, but I have never mustered the same interest that I have for, say, philosophy, history, linguistics.
I usually saw it as a chore and would get good grades only with a superficial and temporary understanding, such as by backtracking solutions. Is there a "beauty" to math that I've just never noticed?

Anonymous

Anonymous Tue 12 Oct 2021 11:30:58 No.13742606 Report

Quoted By:

>>13742568
Sometimes the beauty of maths is it's abstraction, sometime it it's practical applications. What I like about Maths are mostly subjects related to game theory and it's practical applications but I think someone like you should be looking for videos like 3blue1brow's to get why a lot of peoples talk about "the beauty of maths" because visual representation changes a lot of things. For a fun practical application I'd suggest to learn about the game of Nim (and DrNim, a simple mechanical computer that never loose).

Anonymous

Anonymous Tue 12 Oct 2021 14:21:53 No.13742933 Report

Quoted By:

Navigational mathematics is how I started. In the Navy of course. Read Bowditch's American practical navigator if you're interested.

Anonymous

Anonymous Tue 12 Oct 2021 15:17:18 No.13743093 Report

Quoted By:

>>13742568
Pretty sure they use a lot of math in linguistics at a certain point. Philosophy is closely connected with math too. The front of Plato's university read, " Let no one ignorant of geometry enter". Platonism is a philosophy many in math still hold since we deal with perfect, ideal forms of physical things; perfect line, perfect circle etc. Many logicians were involved in math as well. So if you're interested in philosophy maybe look into Plato and some logic stuff like when Gödel rekt rationalism with his incompleteness theorems.

Anonymous

Anonymous Tue 12 Oct 2021 15:59:04 No.13743187 Report

Quoted By:

>>13742568
start with euclidean geometry

Anonymous

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Anonymous Tue 12 Oct 2021 16:15:26 No.13743225 Report

Quoted By: >>13743234 >>13743797 >>13744227 >>13744687

>>13742568
It's fairly hit or miss.
It seems to me that most people with a genuine interest in mathematics don't care about anything else. There are some exceptions (like von Neumann who apparently had very broad interests) but they don't seem to be the rule.
If you care too much about things like history you're unlikely to love math. People who are really devoted to math believe it is the only truth; they have a "if... the..." view of what truth is, whereas historians have a "fact" view of what truth is. A mathematician is concerned with the validity of an implication, and that's all that really matters: assuming something is true, it follows that something else is also true (whether the assumption is true or not is a secondary issue); while the historian is concerned with a collection of loosely connected facts (that he tries to weave into a narrative a posteriori). Ultimately, the big issue with history from an autistically mathematically perspective is that you can be sure of anything. Did the holocaust happened? Was 9/11 an inside job? Who killed Kennedy and his brother? What happened in Nanjing? There may be some evidence in one direction or the other, but the "truth" will forever elude you; you will never grasp it with any reliable certainty, simply because you weren't there and there is no unproblematic knowledge of the empirical world without experience (and sometimes even experience itself can be problematic). Mathematics is a priori science and does not depend on experience; you can tell whether a math book tells the truth or not simply by reading it and analyzing the statements and proofs. To tell whether a history book is lying or not you have to go outside and actually look at the evidence, which is something few people have the leisure and resources to do (not to mention that a lot of evidence may be inaccessible to the general public or forged).
If you love history you don't have the frame of mind to love mathematics.

Anonymous

Anonymous Tue 12 Oct 2021 16:18:08 No.13743234 Report

Quoted By: >>13743797

>>13743225
>"if... the..."
*if... then...
>you can be sure of anything
*you can't be sure of anything

Anonymous

Anonymous Tue 12 Oct 2021 19:31:39 No.13743797 Report

Quoted By:

>>13743225
>>13743234
this nigga autistic af fr no cap

Anonymous

Anonymous Tue 12 Oct 2021 21:19:59 No.13744227 Report

Quoted By: >>13745781

>>13743225
Very interesting thoughts. Thank you.
>a genuine interest in mathematics don't care about anything else.
What about people with mathematics as just one of their many interests?

Anonymous

Anonymous Tue 12 Oct 2021 23:55:16 No.13744687 Report

Quoted By:

>>13743225
It's posts like these that keep me coming back to /sci/. I don't know to what extent you are correct but I can tell there was some genuine thought behind what you wrote

Anonymous

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Anonymous Wed 13 Oct 2021 07:43:25 No.13745781 Report

Quoted By: >>13745818

>>13744227
>What about people with mathematics as just one of their many interests?
Unless you're a genius polymath, you will be a mathlet and you will never make much progress in mathematics if it's just one of your many interests. I guess this is true of any person who has "many" interests, but it is particularly true when it comes to mathematics. Then again, it's not like everyone has to be a top-class mathematician who knows everything about some narrow math field and plans on doing research in that field, so it's not necessarily a bad thing to have other interests. But I think it is comparatively difficult to gain a genuine understanding of even the most elementary parts of mathematics without a certain particular frame of mind. Many people don't seem to appreciate the value and importance of mathematical proofs. In part this is most likely due to the education system, as Paul Lockhart points out in A Mathematician's Lament. According to Lockhart, people's interest in mathematics is stifled early on by the dogmatic way in which mathematics is presented in school, and he has some beef even with elementary synthetic geometry (which, as usually thought in high schools, it is one of the few math courses that are genuinely proof-based) since it imposes upon students an unnaturally rigid way of thinking with "two-colum proofs" or something equivalent to it, and rarely challenges students to come up with proofs of their own, and thus the student never comes to appreciate how a proof is really thought out in a person's head in natural language (and only later formalized in something like two-column proof, if really necessary; after all Euclid didn't use two-column proofs and just wrote down everything in natural language). Beyond that, I think math is one of the most challenging topics for most people to learn, even disregarding the inadequate approach of the school system.

Anonymous

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Anonymous Wed 13 Oct 2021 07:59:54 No.13745818 Report

Quoted By: >>13745860

>>13745781
>(continued)
Math requires a lot of attention to detail, since even one small mistake can spell doom in the flow of thought and calculations, and I think that's one of the reasons many people develop a fear of math. Making a spelling mistake or a grammatical error is bad but it won't affect the meaning of a sentence too much since anyone reading it can auto-correct it in their head, but with math one small mistake usually doesn't remain "local": it affects everything that comes afterward. So for many people learning languages is not nearly as anxiety-inducing as solving math problems.
At any rate, I don't think anyone devoted to math and science should be completely insulated from history, though I stand by what I said in my other post about the unreliability of history. The kind of history that matters to someone who loves math is intellectual history (the history of mathematics itself, and the history of science more generally) rather than general history (the kind concerned with politics and society at large). Math history depends only on books, so you can acquire a more reliable knowledge of it (barring potential forgeries, but those must be rare since nearly nobody has much to gain from altering the evidence in this field; there has been some controversial attempts to re-evaluate and appreciate mathematics done by non-whites in the past but ethnomathematics remains a novel and thus far largely ineffective movement. It came too late and the growing body of knowledge of math history won't be easily canceled any time soon). A knowledge of older mathematics can often help understand better more recent mathematics (or at least it can lead you to appreciate the improvements) and Joseph-Louis Lagrange was very well acquainted with Newton's works and older mathematical books.

Anonymous

Anonymous Wed 13 Oct 2021 08:16:55 No.13745851 Report

Quoted By:

>>13742568
If you're not interested in math you won't get interested by forcing you. You're either a mathhead or you're not.
But it's ok, everybody is interested by different things, it says nothing about your value or your intelligence. In life you must do things that interests you, otherwise it's counterproductive, and you will never be excellent in a field that you're not naturally inclined to, no matter how hard you work.

Anonymous

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Anonymous Wed 13 Oct 2021 08:24:00 No.13745860 Report

Quoted By: >>13745912

>>13745818
>(continued)
Newton was already outdated by Lagrange's time since he fashioned his physics in the language of ancient Greek synthetic geometry, even though the more modern Cartesian analytic geometry was already available at the time and Newton was familiar with Descartes' methods. There are various hypothesis as to why Newton did this, among them there is the idea that anything French (like Descartes) was automatically suspicious in England and the idea that Newton wanted to deliberately make his book harder to understand by using unwieldy and outdated geometric methods. Yet another hypothesis is that he wanted to make his novel ideas more acceptable by casting them in a form as venerable as that of ancient Greek geometry. But at any rate it took a century (Newton's Principia was published in 1687 while Lagrange's Analytical Mechanics was completed in 1789) to complete the transition from synthetic methods to analytic methods even though most of what was needed was already there but the other scientists of the time never attempted a comprehensive revision of Newton's work. Lagrange wasn't even interested in mathematics early in his life (he was supposed to study law in university) and he disliked Greek geometry, though in the end he became well acquainted with newton's geometric methods and his distaste for them must have motivated him to find a general analytic formulation that didn't depend on synthetic geometry (he boasted that his book didn't contain any geometric diagram).
Being ahistorically obsessed with one or two branches of mathematics can create autistic geniuses of great value; but a swiping revolution requires an appreciation of the works of the past and a desire to improve them.

Anonymous

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Anonymous Wed 13 Oct 2021 08:46:55 No.13745912 Report

Quoted By: >>13745921 >>13745925

>>13745860
>(continued)
The latter part (the desire for change) is difficult for the genuine historian who tends to become something of an antiquarian who loves to preserve the past and is allergic to anything overly innovative. A case in point would be Morris Kline, who deeply disliked the kind of synthetic geometry proposed by books like Edwin Moise's Elementary Geometry From An Advanced Standpoint which tried to embed the notions of the real number system into the axioms of geometry, while Kline favored the kind of "geometry without numbers" that is much more traditional and goes back to Euclid. Morris Kline was interested in the history of mathematics in an antiquarian way and some even question whether he truly loved mathematics at all as he had a philosophically problematic view of the relationship between mathematics and the physical world, seeing mathematics as originating from (and being useful for) physical investigations, which goes against the loftier ideals of mathematicians like G. H. Hardy who viewed mathematics as its own thing and physical applications as merely incidental. Kline's opinion was most likely influenced by his interest in history since both in Antiquity and during the Enlightenment there was a close connection between mathematical progress and progress in the physical sciences (even as late as the early 20th-century, modern vector analysis was invented by physicists like Oliver Heaviside and Willard Gibbs). In the course of the 20th century there was a revolution in mathematical thought (dominated by figures like Frege, Russell, Hilbert, and Goedel) that led to a much more marked divorce of mathematics from physics and from everything else.

Anonymous

Anonymous Wed 13 Oct 2021 08:50:22 No.13745921 Report

Quoted By: >>13745932

>>13745912
Don't want to be mean but you never heard of synthetic thinking and the power of concision?

Anonymous

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Anonymous Wed 13 Oct 2021 08:55:08 No.13745925 Report

Quoted By:

>>13745912
>(continued)
The "New Math" movement of the 1960s was a reaction to the Sputnik crisis but it was also partially motivated by the idea that the more abstract approach in mathematics that had developed in recent years was superior and had to be taught to children in order for the US to keep ahead of the Soviet Union in science and technology (ironically ignoring that Russian textbooks of the time weren't nearly as abstract as the New Math textbooks, though less traditional than the usual US textbooks). The New Math project was almost unanimously deemed a huge failure in retrospective since abstraction is the terminal point (or possibly a terminal point, not necessarily the only one) of mathematics, not the starting point. The New Math was a victim of an ahistorical approach which tried to break away with tradition in a way that was unnatural and unmotivated and ushered in only empty, shallow concepts that posed as highbrow intellectual exercises.

In conclusion the relationship between math and history is a difficult one in my opinion. One may ignore general history but losing track of intellectual history leads to foolishness, as exemplified by American math curricula in schools.

So if you wanna learn math, perhaps your best bet is literally to start with the Greeks (as /lit/ would recommend) and read Euclid, Archimedes, and Apollonius. It may be time-consuming and convoluted to start from so far back in time, but it can definitely help put things in perspective.

Anonymous

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Anonymous Wed 13 Oct 2021 08:58:34 No.13745932 Report

Quoted By: >>13745942

>>13745921
Some things can be synthesized only so much before it amounts to watering them down.
I belong to an older generation and I'm not capable of expressing all my thoughts in a single Twitter post. Anyway I'm done with the multi-post essay now.

Anonymous

Anonymous Wed 13 Oct 2021 09:05:53 No.13745942 Report

Quoted By: >>13745959

>>13745932
>Anyway I'm done with the multi-post essay now.
Thanks. The first post was genuinely good, but the rest was superfluous, boring and out of topic. The thread is about OP, not about you.

Anonymous

Anonymous Wed 13 Oct 2021 09:17:33 No.13745959 Report

Quoted By: >>13745962

>>13745942
>The thread is about OP, not about you.
This isn't OP's blog, nor mine. The thread is about math, not about one person or another, and I talked about math, not about myself. I touched upon history and one philosophical problem (math vs physical world) since OP mentioned history and philosophy among his interests. I don't understand why you're so salty.

Anonymous

Anonymous Wed 13 Oct 2021 09:19:23 No.13745962 Report

Quoted By: >>13745983

>>13745959
>The thread is about math
The thread is about how OP goes into math, and whether or not he should, not math in general.

Anonymous

Anonymous Wed 13 Oct 2021 09:26:20 No.13745981 Report

Quoted By:

>>13742568
>I have never mustered the same interest that I have for, say, philosophy, history, linguistics.
then why get into it?
>I usually saw it as a chore and would get good grades only with a superficial and temporary understanding, such as by backtracking solutions. Is there a "beauty" to math that I've just never noticed?
beauty is subjective but in math an equation is considered beautiful when it cancels out nicely or gives nice answers. Euler's identity is beautiful because an irrational raised to the product of an irrational and an imaginary giving out -1 is beautiful. same case for euler's polyhedron formula. some view complexity as beautiful or simple maths that diverge into very complex maths as beautiful or proofs that use unexpected concepts as beautiful, etc. maths get better the higher you go but if you struggled with basics it won't get better

Anonymous

Anonymous Wed 13 Oct 2021 09:27:41 No.13745983 Report

Quoted By: >>13746068

>>13745962
And I tried to relate math to his other interests and to explain why in my opinion some people (including OP himself) may find it hard to get into math. How is that off-topic?

Anonymous

Anonymous Wed 13 Oct 2021 09:59:08 No.13746068 Report

Quoted By: >>13746087

>>13745983
I liked your posts anon.

Anonymous

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Anonymous Wed 13 Oct 2021 10:05:19 No.13746087 Report

Quoted By:

>>13746068
Thanks.

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