How the fuck do I understand math as a humanities-minded person? I've always been fond of the arts, history, languages, politics, religion, literature, philosophy, and even some metaphysics since it was the only way I could "understand" reality, math was never my thing.

Now I'm trying to give math a chance and I still don't understand how math explains reality. I always heard mathematicians say that "math is the language of the universe" yet humanities, to me atleast, always seemed clearer and easier to understand when it comes to explaining our reality.

Are there any books I can read to help me understand math?

>>24533373 (OP)
What the fuck are you talking about?
"Humanities" are completely incapable of explaining reality

>>24533373 (OP)
>How the fuck do I understand math as a humanities-minded person?
Take double maths in your BA. Maths is a fundamental part of the BA.

>>24533373 (OP)
math doesn't explain reality, it's a tool

>>24533373 (OP)
What have you been looking at? If you’re trying to explain reality, calculus is a good place to start. Any introductory book will have word problems that are engineering lite which should connect the concepts to reality.

>>24533373 (OP)
Math isn’t just about numbers. It’s about patterns, structure, logic, relationships, symmetry, infinity, paradox, and imagination.
These are all things that the humanities minded brain already cares about. Try some of these:
>“The Mathematical Experience” by Philip J. Davis & Reuben Hersh
A deeply philosophical and reflective work on what math is, who does it, and why it matters. Reads more like literature than a textbook.
>“Love and Math” by Edward Frenkel
A memoir mixed with poetic reflections on math as a creative, passionate pursuit. Frenkel treats math almost like art or music.
>“A Mathematician’s Lament” by Paul Lockhart
Short and beautiful. This is a manifesto arguing that the way we teach math destroys its beauty. Perfect for someone who loves the humanities, especially if they feel school ruined math.
>“Infinity and the Mind” by Rudy Rucker
Ya like metaphysics? this one dives into infinity, logic, consciousness, and paradoxes. It’s weird and wonderful.
>“Gödel, Escher, Bach” by Douglas Hofstadter
This is dense, but for someone who enjoys philosophy, art, and recursive ideas, this is the holy grail. It connects math with music, art, cognition, and self-reference.
>“The Joy of X” by Steven Strogatz
Light, clear, and playful essays on why math matters in the real world. Very accessible.
>"Unreasonable Effectiveness of Mathematics in the Natural Sciences" by Eugene Wigner
A philosophical essay on the eerie way math fits the universe.
>“What Is Mathematics, Really?” by Reuben Hersh
Explores the humanistic side of math, arguing it’s a social and cultural construct, or something

>>24533376
>>24533385
sounds like somebody doesn't have Knowledge of the Hyperborean Tradition

Study it historically as an emergent set of reductions of complexity, stacked and added upon one another, to create a continuously evolving system. Math is not a platonic entity. People who think it is are retarded. The ancient Greeks thought it was, because they had a metaphysical, substantial (in the sense of ousia, substance) conception of math. (If you want to read one of the hardest but most rewarding books ever written on exactly this note, check out Jacob Klein's Greek Mathematical Thought and the Origins of Algebra.)

What this means in practice is that when the Greeks thought of mathematical entities, they thought of metaphysical entities first, and derived necessary truths about mathematical entities from that. The central example of this is also the most concrete and easiest to understand: In Greek metaphysics, One is not a "number." One is the BASIS of all number. It is a transcendental (transcendens), meaning it transcends the category of things of which it is the cause. Numbers have their cause and origin in the One, or the primal Unit. The One itself is not itself a "countable unit," it is the source and ground of all GROUPS of countable units.

You don't have to believe this or subscribe to it, but it's important to know that the Greeks thought it for various reasons, the chief of which (for your purposes) being that it's an example of how mathematics is not a self-evidently closed, self-evidently interrelated system. There is no "mathematics." Mathematics as WE think of it arises in the early modern period as the earlier Greek mathematics is lost sight of for various reasons, especially the increasing sophistication of algorithms and algebraic abstractions for carrying out what used to be called "computation" (what we now call calculation), and the coupling of this increasingly sophisticated and interrelated set of mathematical notions to problems of mechanics (in observational astronomy and engineering) in the 16th and 17th centuries.

Another good example of how mathematics can change its "basis" and how this can change the tone of the whole system built upon that basis is the gradual death of "intuitive" Euclidean geometry. Intuitive here doesn't mean "intuitive" in the colloquial sense of "coming naturally," it means based on imagined spatial representations. All practical mathematics was founded on geometry until the early modern period, but as it gets attached to increasingly sophisticated algebra and algorithms for manipulating that algebra, it comes (GRADUALLY) to be seen more the way we see it today, as the manipulation of symbols on paper. But prior to this slow transformation, what mathematicians were really "doing" when they did mathematics was imagining geometry along Euclidean lines. At first, the new algebra developed as a means of clarifying and enhancing this Euclidean geometry.

>>24533474
Over time, algebra becomes sort of free-floating, and people realize that you can manipulate the symbols without ever bothering to visualizing a Euclidean manifold, and then people realize that you can actually question the axioms and postulates of Euclid's system (a big move) and "algebraize" geometry entirely, effectively making the manipulation of "true in the symbols/ true on paper" statements into the main thing that mathematicians "do" when they do mathematics, to the point that visualization is optional or even considered a crutch only needed by mathematically inferior minds.

Descartes himself, who was so important in this algebraizing transformation (with the publication of his Geometry), definitely "thought in" Euclidean geometry and used algebra as an aid, not seeing it as the main event so to speak. Morris Kline's books are good on this, especially The Loss of Certainty.

Once you realize this basic fact, that mathematics grows contingently over time (to put it in the usual parlance, it's invented, not discovered, although it feels like discovery, because the relationships between entities are experienced as holding apodictically and self-evidently - it's just that the apodicticity of these relations depend upon preconceptions baked into the entities, as we saw in the case of the Greeks' view vs. the modern view), you can see mathematics from both the outside and the inside: from the outside, as a historian of thought watching its frameworks mutate and emerge, and from the inside, as a mathematician witnessing the unfolding of these mutations and emergences "as if" apodictically. Suddenly you can see WHY Descartes' Algebra or Newton's Principia were so exciting. They "worked," and they seemed to do so of their own accord. They felt like discoveries, not inventions. If you want, you can watch, blow-by-blow, as what modern mathematicians feel in their gut was always necessarily just Math, what they feel is a platonic atemporal realm of mathematical truths and self-evident entities, unfolding and dawning on people historically.

>>24533476
Tracing the development of calculus from Descartes to Newton and beyond is very exciting, as is tracing the development of algebraic geometry and the modern synthesis (or rather, lack of one). Suddenly what Cantor was DOING by proposing transfinite sets as an explanation to the problem of infinity goes from looking like an autist making arbitrary combinations of tinker toys to a man in his living context coming up with a solution to a problem that everybody felt, and you can feel that feeling too, even if you can't feel the same self-enclosed certainty of Cantor or subsequent set theorists. You can FEEL why people thought infinity was a pseudo-concept. You can also fully appreciate books like Ian Hacking's The Taming of Chance and The Emergence of Probability because your mind will be trained to see how epistemes grounded in radically different fundamental assumptions about the world made sense of, and had to invent, the modern notion of probability, after thousands of years of it being suspiciously absent. You can also understand why purported calculus proofs to Zeno's paradox of infinite motion are silly, because they are solutions that make intuitive sense in one framework of thought to a problem posed within an entirely different framework.

This also opens up and pluralizes mathematical epistemes, so you can enjoy thinking about radically "other" mathematics.

I recommend doing something as simple as trying to understand why basic arithmetic works. Not in the dumb logicist sense, wherein all the accomplishments of centuries of slow sedimentation of algorithms is inverted and treated like it was self-evidently necessary all along, but by tracking the algorithmic innovations themselves as they happened historically. Why did a Europe grounded in Greek mathematical thought have such trouble seeing zero as a number (zero = a null value in a column, so the number 101 really translates to "one hundreds, zero tens, one ones)? What does it mean that, even when zero entered into common use because it's so useful, people still couldn't think of it as a "number" in its own right? What does it mean that we now find it hard to imagine thinking that it ISN'T a number in its own right? Or take another example: why does prime factorization "work?" What does it mean that all non-prime numbers are "composed" of primes? How did the modern notation for describing fractions (or ratios) develop, and at each stage of its development, WHY did it develop? What did the Greeks think a "fraction" was? Why is the Cartesian coordinate system so useful? Why do people keep "getting close to" calculus (but never quite making the leap? How was the leap finally made (with help from Fermat, Descartes, etc.)? What was novel about Galileo's intuition of abstract mechanical space? Why was astronomy the proving ground for mathematics and eventually the birthplace of calculus in a sense?

>>24533478
Once you see enough of this, you will realize that modern math (math of the last 150-200 years) is just an exponential acceleration of this sedimentation process, combined with a systematizing impulse. When something worked (was "true"), it was absorbed into the system and became a special application of it. And conversely, every time the system got more robust by integrating some new algorithm, there was crosstalk and new discoveries were made, and often these would prove surprisingly useful for modelling some aspect of the external world. It just so happens that calculus is really useful for modelling something that is all over the real world: continuous change. Everything that undergrads torture themselves to memorize by rote in Calc 1 was originally some beautiful, time-saving, hard-fought algorithm that "worked" and that integrated well with the system, and was probably then simplified and purified, which mathematicians at the time experienced as "discovering its true form, what it really was all along," because the messier forms were contingent applications or extensions or expressions of the simplified purified form. With this in mind, you can understand things as sophisticated as the heat equation and Ricci flow, at least conceptually, and trace their long history back to Newton and then to Fermat and so on.

Math is a gigantic mess, nobody just "does math," what they do is learn the basics of the system as it has been purified and transformed and as it has accumulated new components over centuries, and then they specialize in some extremely abstruse application of an application of a subset of this overall system, which requires absolutely mastering one or several aspects of the overall system the exclusion of others. There are shockingly brilliant continuous-rate-of-change-visualizers who "think in" equations for modelling the change, and there are logicists who completely lack the ability to picture geometric manifolds but who accomplish great things in pure algebraic geometry or number theory as a result. These people are not doing "mathematics," they are doing a dozen or a hundred different things of which the human mind is capable and forcing these things to be faithfully isomorphic to some phenomenon, either notional or physical, and then they are coming back with their results and proving them in terms of the other guy's favorite entities, which have already been reconciled with their own favorite entities by generations of reconcilers.

>>24533478
>Why do people keep "getting close to" calculus (but never quite making the leap? How was the leap finally made (with help from Fermat, Descartes, etc.)?

Why ? I think you could have said a couple words about https://en.wikipedia.org/wiki/Straightedge_and_compass_construction and why it was solved this late

>>24533373 (OP)
Maybe proof theory or model theory is for you

>>24533493
Yes, that's really important too. Pre-algebraic geometry was originally about construction, not proof. It also had a a hazy notion of what a proof even is. "Proof" is not a self-evident concept. Much of what's in Euclid (especially earlier parts) is probably originally "hey bro you need to make a shape and be sure it's even? I got you" guides, with later "check out this crazy shape I can make" showoff constructions added.

>>24533373 (OP)
>How the fuck do I understand math as a humanities-minded person? I've always been fond of the arts, history, languages, politics, religion, literature, philosophy, and even some metaphysics since it was the only way I could "understand" reality, math was never my thing.

sociology? its about explaining human society and actions through science and math (statistics). all you nigger retards just think its nothing but worshiping niggers or something because you "ironically" read salon or whatever

i mean there are even sci-fi novels like foundation that are about this

When you peer behind the curtain you'll learn its a humanities at its core

>>24533373 (OP)
Find something applicable and start doing it.

>>24533373 (OP)
>I'm trying to give math a chance and I still don't understand how math explains reality
Study physics instead if you find math by itself to be too abstract.

>>24533373 (OP)
I had the same problem... until I read Leibniz and Spinoza. Through Leibniz's monadology and metaphysics I came to understand physics and in turn mathematics. I am hopeless at math, I believe I have dyscalculia based on the fact that I absolutely love geometry and is the area in math I passed in high school. But reading Leibniz helped me to appreciate bits of physics and math.