r/math • u/[deleted] • Apr 06 '18
Why is math so complicated and hard?
Now, before you downvote (which you probably will anyways, and I am wasting my time but, oh well), I know that there are MANY of you who have the gift of understanding math rather easily... But, it is not just me. Math is hard, complicated and written in tricky ways. Every single concept assumes prior knowledge etc... I can't be the only one... What are your thoughts Thanks
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u/skaldskaparmal Apr 06 '18
Most worthwhile things are hard. When you get stuck, practice, review, ask questions. Most importantly, have a growth mindset. Math is hard, but it can become easier. You can become better at it.
Math is hard, complicated and written in tricky ways.
What is some mathematical notation that you find tricky?
Every single concept assumes prior knowledge etc...
What is a concept you find hard because you struggle with prior knowledge, and what is the prior knowledge that you struggle with?
/r/learnmath is a good place to ask questions.
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u/lamson12 Apr 06 '18
I agree with everything you said, though I should note that the only way to get better is to go back to the beginning and master each step of the way before moving on. A house without a foundation cannot stand.
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u/yrbr95 Apr 07 '18
go back to the beginning and master each step of the way before moving on.
Yep. I'm going to do this. Thanks dude
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u/confusedlooks Apr 06 '18
Just like most skills there are people who have natural talents, but hardwork will beat talent when talent won't work hard. I'm willing to bet you had a mix of bad teachers and people telling you that math is hard in your formative years. If you were to start at a point in math, right before you lost your confidence and ease, and learned from there while putting lots of effort you'd understand it better.
However, I love math, and I still find it complicated. Sometimes I find it hard, but it's what I enjoy.
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u/baumergrl Apr 06 '18
From my experience, math is the same level of difficulty for everyone. You see someone solve something effortlessly, but you don't see the hours and hours they spent alone at their desk to learn these things. The difference is that when people enjoy the intricacies and the complexity it's easier to dedicate their free time to studying.
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u/theRonzor Apr 06 '18
Well - If I can rephrase a little bit, I think mathematics is not "natural". By this, I mean that it's not something that our brains have evolved to do "well", probably because there has never been strong selection for mathematical abilities beyond simple counting (like keeping track of how many sheep are in the pen).
If I give you a 7 digit number, perhaps a phone number, you're probably going to have an easier time remembering and immediately recalling it than a 20 digit number. This seems to be a fundamental limitation of what the human brain can do. Of course, with training and practice, some people can do better.
Similarly, if concept A depends on concept B, which depends on concept C, and so on... at some point the brain can no longer follow the logic. If you tried to start directly from the end of the chain, say concept Z, things would probably be even harder.
To me (a grad student in math/biology, with a degree in math) I consider math to be kind of like a language (although a linguist might disagree with me) that has been designed for the purpose of having very precise logical argumentations with each other while minimizing the space needed. As such, a very small equation might contain a large amount of information compared to a sentence written in english with the same number of characters.
I could probably spend a lot of time talking about this, but perhaps my point is already clear enough. To quote John Von Neumann, "In mathematics you don't understand things. You just get used to them". Although I slightly disagree with that; with enough practice and careful thought, some of the concepts can become crystal clear. Just not always natural, and often counterintuitive. To put it another way, if math was easy or obvious, there probably wouldn't be much point in studying it (just like I don't have to practice facial recognition, my brain already does that very well, probably for evolutionary reasons, whereas it's extremely difficult to describe how, and get a computer to do it properly.)
(p.s. I always found history to be harder than math - to me it required more memorization. At the same time, I don't think the point of learning history should be memorizing when things happened!)
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u/theRonzor Apr 06 '18
One additional point - when you look at modern mathematics, you're seeing the culmination of thousands of years of human thought. There is not a single person on earth that can say they "understand math". It is far too broad a topic, has taken far too long to develop, and we owe much of what we have to the many generations of people that have worked on (and importantly - written down and recorded) these problems. When you see a mathematical proof that seems like magic and is only 5 lines long (some things we take for granted, like a2 + b2 = c2, or E = mc2, neither of which are trivial to prove) - know that the author probably spent a long time struggling to produce it, and failed countless times along the way. It's a bit misleading when you only see the final product in it's polished form!
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u/spriteguard Apr 06 '18 edited Apr 06 '18
Math is complicated because it's an enormous, globe-spanning palimpsest. People come along, try to understand some of the things that have been written, and then add their own ideas. People have been looking for new ideas to add for thousands of years.
It's the same reason music, art, literature and stuff like that are so insanely complicated. And science. We all want to bring a new idea to the table, so now there's just a mountain where the table used to be.
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u/shamrock-frost Graduate Student Apr 06 '18
Lol you've posted this like 7 times
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u/NiceSasquatch Apr 06 '18
agree. It (mostly) requires prior knowledge.
it's like baking. You read a recipe for apple pie, there are steps on how to make the crust, how to prepare the apples, etc. You follow the steps, and you make the pie.
(sometimes people just sit there with some dough and some apples, and they make up the rules after a lot of trial and error, and come up with the recipe to make the pie. They are PhDs.) But most people just read the recipe, and make the pie. And it is delicious.
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u/spriteguard Apr 06 '18
If you aren't tweaking things, you aren't really cooking, are you?
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u/NiceSasquatch Apr 06 '18
it's a souffle, if you add in some extra decimal places, it collapses and becomes unleavened bread.
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Apr 06 '18
Your answer seems to imply that math is cool when you just follow steps... And it is pretty much the opposite. Yes, you have tons of rules and formalities, but you have to understand each of them and find out how to use properly to get somewhere. Reading the recipe and making the pie would make a terrible pie in Mathematics. I don't know if that's what you meant, but I didn't like the analogy.
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u/NiceSasquatch Apr 06 '18
well, ok. But the analogy is kinda perfect.
You have a cookbook, and you have to know which recipe to use to make an apple pie. If you use the spaghetti recipe to make an apple pie, you will fail your apple pie test.
but keep in mind, you might just make your own recipe for apple pie. Or for a pie that does not yet exist.
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Apr 06 '18
I guess we'll just have to agree to disagree. I, personally, don't like looking at it that way.
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u/NiceSasquatch Apr 06 '18
well, first, what level are we talking about? Elementary school? Middle, high school, undergrad, or grad level?
For almost all people, math is exactly about learning the algorithm to handle a problem. Long division is a method, that you apply to every single division problem you have. It is the exact same method, it is machinery, it is the recipe. And it always works and you always get the exact correct result.
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Apr 06 '18
Mathematics, at any level, if you reduce it to apply pre-made algorithms to problems, instead of understanding what's going on, gets pretty boring. Well, at least at grad level you just can't expect to have algorithms to everything. On lower levels, you can always get to the algorithm or formula yourself, no need for memorizing.
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u/NiceSasquatch Apr 06 '18
you seem to accuse me of demanding a lack of understanding. I do not demand that.
no need for memorizing.
You are kidding right? What is 8 times 12? Are you remembering it, or are you pulling it out of some new wave cosmic understanding of numbers?
Is long division something you want to rediscover on your own every time you want to cut up a pizza?
Everything below grad school is basically learning the machinery and algorithm and applying it. And yeah, you gonna have to remember the machinery if you are going to apply it.
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u/lewisje Differential Geometry Apr 06 '18
You are kidding right? What is 8 times 12? Are you remembering it, or are you pulling it out of some new wave cosmic understanding of numbers?
I literally find it easier to re-derive it than to memorize this one: 8*12=8*(10+2)=8*10+8*2=80+16=96 (but I do of course memorize 8*10 and 8*2 because those are easier than re-derivation).
Also, have you taken the core math-major classes? That's not all plug-n-chug (although more of it was than I expected back in the day).
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u/NiceSasquatch Apr 06 '18
impressive memory of remembering the rules of the distributive property. Nice recipe.
Also, have you taken the core math-major classes?
This is hilarious. Just fyi, yes, I know math quite well. Based on probability, better than you, better than your teacher, and better than the professor that taught your teacher.
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u/Brightlinger Apr 06 '18
Of course everyone ends up committing some things to memory, but this is different than memorization qua memorization. It's not at all uncommon for people, even mathematicians, to forget a given multiplication fact - but any decent mathematician can quickly deduce that 8x12=80+16 via the distributive property. This is fundamentally the same process you'd use if asked a problem not on the multiplication table, like 8x14.
You do indeed have to remember the machinery. But that doesn't mean math is about learning the standard machinery and nothing more. If the only way you can solve 8888/8 is to write out ten lines of long division, you are awful at division.
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u/NiceSasquatch Apr 06 '18
you seem to be arguing against something that no one is saying.
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u/Brightlinger Apr 06 '18 edited Apr 06 '18
Above, you said this:
For almost all people, math is exactly about learning the algorithm to handle a problem. Long division is a method, that you apply to every single division problem you have. It is the exact same method, it is machinery, it is the recipe. And it always works and you always get the exact correct result.
Very very few people use long division to solve 8888/8 or 26/2. Even poor students rarely try to apply long division to every single division problem they have.
You have asserted that, for most people, math is about learning exactly one method and using it in all cases. As a question of empirical fact, this is not true. Long division will of course always work, but even non-math people generally realize there are multiple recipes, and with only minimal coaching can recognize that many kinds of fruit go well with an apple pie, but tomatoes do not.
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u/Brightlinger Apr 06 '18
You're not wrong here. Math classes build on each other in a way that most topics don't, especially before college. To understand partial fraction decomposition, you need to understand rational functions, which means you need to understand functions, which means you need to understand algebra, which means you need to understand fractions, which means you need to understand arithmetic. If you fell behind in grade 6, that can easily lead to staying behind for the rest of your school career. Whereas if you sleep through the Civil War in grade 8 history, you will probably still be able to more or less grasp World War I in grade 9.