Why is math beautiful?

[Sahamamama]

"Math is beautiful." I've heard this for many years, from various sources. I've never understood what some people "see" in math that is beautiful to them. In school, for me it was mostly painful and humiliating. I saw it as utilitarian and/or incomprehensible, except to "mathy" people -- something I was not.

 

My friend's 15yo son is a good ambassador for math. He adores math, thinks it is wonderful, talks about the beauty of trigonometry and calculus and number theory, and so on. I just want to listen to him talk about math, his enthusiasm is so magnetic!

 

I wonder what he "sees?" Why is math beautiful?

[mathmarm]

I could wax poetic about maths beauty, but keep in mind that beauty is in the (minds) eye of the beholder.

[Elisabet1]

I love math. Everything has its place. No one can argue what is right and what is not. It is right or it is not. No one judges. 

[kiana]

I can only say that until I reached real proofs I saw little beauty in it myself. My high school courses had many proofs, and I loved them, but when I took calculus at an average state school I lost my way for a while. I saw math only as a boring yet easy subject that I took to bring my grades up. I was taking my last class for a math minor when I took introduction to proofs -- that was the semester I changed my major.

 

For me, it is the logical thought process and the proof -- closing every last loophole -- that makes it beautiful. Solving an equation? That is pedestrian -- that is boring -- and yet it is all that many see. But proving that a type of equation can always be solved or can never be solved? Solving an entire class of problems? Yes, there is beauty.

 

And in successfully completing a proof, there is accomplishment and pride -- and yes, joy.

[quark]

"Math is beautiful." I've heard this for many years, from various sources. I've never understood what some people "see" in math that is beautiful to them. In school, for me it was mostly painful and humiliating. I saw it as utilitarian and/or incomprehensible, except to "mathy" people -- something I was not.

 

Because in most schools, what is taught is not so much math in the way that math really is. You are taught arithmetic or algorithms or tested in ways that kill any enjoyment math can bring. I told myself for the longest time that I am not mathy and yet there is an aspect of math I was always good at...symmetry. As a budding artist I picked up symmetry so easily. Symmetry is linked to geometry and geometry is linked to probably everything else! I never knew all of this in school and am only now discovering it through the eyes and enthusiasm of my child. Just fold some origami or watch vi hart's videos and you'll get just one little taste of why math is beautiful.

[Sahamamama]

I could wax poetic about maths beauty, but keep in mind that beauty is in the (minds) eye of the beholder.

 

So what do you see? I'm not saying that math is not beautiful, I only want to see what people see when they say this.

 

[Sahamamama]

I love math. Everything has its place. No one can argue what is right and what is not. It is right or it is not. No one judges. 

 

Ah, so it's very different than, say, a group discussion of Mr. Bennett's success and failure as a father in Pride and Prejudice? (which ends up where?)

 

My husband says it was that kind of discussion "garbage" that made him abhor English class. ;) He loved and still enjoys math, precisely because it was either this or that, no opinions necessary.

[Pegs]

I like it because it is universally true. :)

[Joker]

I've never understood it either. Dh loves math, has a math degree, and uses it everyday. I now realize youngest, 12, may be following in his footsteps. When I picked her up from school one day last week the first thing out of her mouth was, "I love linear equations!". :huh:  She was so excited and happy to tell me all about math class that day and I kept thinking I wish I understood what made it so beautiful and wonderful.

[Targhee]

I wonder what he "sees?" Why is math beautiful?

The beauty for me is in the patterns and connections which become visible through mathematics. I enjoying pondering these things from a purely rational standpoint, but also a symbolic standpoint. Math can be a tool, but it can also be something you create, and more awesomely, something you find. I feel like a child, peeking in on the mature universe.

[rdj2027]

To me it is the order and structure that make it beautiful, sort of like a well composed painting.  In addition to that, math just is, it is reality and reason.  Language is modern art, most of the time I have no idea what the painting, sculpture, ... is supposed to show and when I hear the artists interpretation I just shake my head.  

[maize]

I like the way things fit together like a puzzle, the structure and harmony and chance to explore and discover.

 

Math is not algorithms and arithmetic and memorized facts; unfortunately that is all too often the way it is taught.

[Angie in VA]

I love math. Everything has its place. No one can argue what is right and what is not. It is right or it is not. No one judges.

Ds used to think the order of operations was some invention of mine that I made up just to torture him!

[kiana]

Ds used to think the order of operations was some invention of mine that I made up just to torture him!

 

You know, I have said in class "contrary to popular opinion, math is not just something we made up to torture you"

[regentrude]

Math is beautiful because:

 

There is logic and order.

There are patterns to discover - some of them surprising

It is immensely satisfying when  long expression simplifies, or when a proof finally comes together. Have you ever felt satisfaction at solving a puzzle?

One can marvel at the human mind that managed to uncover such relationships

Some relationships are stunning: how can there be such a simply way of finding out a certain thing?

Geometry can be visually beautiful.

 

Many students get turned off math before they even get to the beautiful stuff. Arithmetic is not math.

[Hunter]

Here are some books that showed me the beauty of math.

 

How to Tutor

http://www.amazon.com/How-Tutor-Samuel-L-Blumenfeld/dp/0941995011/ref=sr_1_1?ie=UTF8&qid=1415968925&sr=8-1&keywords=how+to+tutor

 

A Guide to American Christian Education

http://www.amazon.com/Guide-American-Christian-education-school/dp/0961620110/ref=sr_1_8?ie=UTF8&qid=1415968989&sr=8-8&keywords=american+christian+education

 

Mathematicians are People Too

http://www.amazon.com/Mathematicians-Are-People-Too-Stories/dp/0866515097/ref=sr_1_sc_1?ie=UTF8&qid=1415969067&sr=8-1-spell&keywords=mathameticians+biographies

 

The Librarians That Measured the World

http://www.amazon.com/Librarian-Who-Measured-Earth/dp/0316515264/ref=sr_1_9?ie=UTF8&qid=1415969202&sr=8-9&keywords=measured+the+world

 

Waldorf is known for it's beautiful middle school geography drawings. It's taken me awhile, but I'm starting to discover the vintage resources that Waldorf is based off of. SO much of Waldorf is just STANDARD vintage practices.

 

Constructive Form Work

https://archive.org/details/constructivefor00hailgoog

 

Outlines of Industrial Drawing

http://books.google.com/books?id=qjlDAAAAIAAJ&printsec=frontcover&dq=outlines+of+industrial+drawing&hl=en&sa=X&ei=0PplVMCTK6PLsAT1qIDYBA&ved=0CDIQ6AEwAA#v=onepage&q=outlines%20of%20industrial%20drawing&f=false

 

First Lessons in Observational Geometry

http://books.google.com/books?id=PIFTAAAAYAAJ&source=gbs_navlinks_s

 

Lessons in Experimental and Practical Geometry

https://archive.org/details/cihm_76933 

[Hunter]

I hear over and over that arithmetic isn't beautiful; I disagree. I think the first two resources I listed show how amazing the Hindu-Arabic decimal number system is. Have we discovered it, or did we create it? Either way, learning how it works is fascinating.

 

Arithmetic is a more subtle beauty, compared to geometric drawing, but sometimes when we slow down enough to appreciate the subtle, it's even more awesome.

[Orthodox6]

Theoni Pappas has a couple of books conveying her beliefs on the beauty of mathematics.

[carriede]

Have you ever seen Donald Duck in Math Magic Land? I feel that video would give you a simple intro to beautiful mathematics.

[wendyroo]

I see math as a huge jigsaw puzzle.  The marvelous and beautiful thing about it is that I keep finding new pieces that fit perfectly even though I didn't even know a piece of the picture was missing.

 

I've taken Linear Algebra and Advanced Calculus at MIT, and yet there are still missing puzzle pieces in even elementary mathematics waiting for me to discover them like hidden treasure or Easters eggs in a video game or $5 bills pleasantly discovered in the pocket of last year's winter coat.

 

This summer someone started a thread asking about a Singapore math word problem.  I knew how to solve the problem easily enough, but then they mentioned how Singapore explained it.  Convert the fractions to have like numerators!!!  What an elegant problem solving strategy.  Math is beautiful when you find the puzzle piece that lets you reduce a whole bunch of chaotic problems into one united archetype that can all be solved simply...predictably...gracefully.

 

I doubt I will be adding pieces to the periphery of my math puzzle; I don't really have any interest in learning Quantum Computation, the Geometry of Manifolds or any of the plethora of high, higher, highest level math topics.  I delight, however, in filling in the middle of my puzzle, in adding color and detail and depth to the picture by learning all the amazing ways that numbers fit together.

 

I also watch gleefully as my children build their own puzzles.  The moment that Peter realized that five red Cuisenaire rods form the same size rectangle as two yellows.  When Elliot exclaimed, "Wait!!  I can make my number with this finger and this finger and this toe!!"  And watching Spencer put down his very first pieces as he slides beads along a wire or tries to cram one more beanbag into a basket than will actually fit.

 

I find math very beautiful.

 

Wendy

[kiana]

I hear over and over that arithmetic isn't beautiful; I disagree. I think the first two resources I listed show how amazing the Hindu-Arabic decimal number system is. Have we discovered it, or did we create it? Either way, learning how it works is fascinating.

 

Arithmetic is a more subtle beauty, compared to geometric drawing, but sometimes when we slow down enough to appreciate the subtle, it's even more awesome.

 

I think the arithmetic system is beautiful -- but I think that actually doing computation is rather boring. 

[wapiti]

Arithmetic = boring

 

Number theory = beautiful

 

 

The geometry I learned in school ("Bueller? Bueller?") = excruciatingly boring. My friend and I taught ourselves the course the weekend before the Regents exam.

 

AoPS geometry = astonishingly beautiful. I love hearing dd exclaim "yes!!" when she gets a correct answer to an on-line challenge problem.

[Clear Creek]

Nature contains math; in fact, some would argue that it is math that makes it beautiful. Read this blog post, and watch the short movie here.

[Wind-in-my-hair]

I think math is beautiful if it is taught in a way that makes it possible to comprehend it with certainty. There is nothing worse than having to solve problems with "rules" that give you no sense of the truth of why they are correct. Then you have no idea why you got the problem wrong when you get it back a week later and see the red pen. And by that time you have carried your confusion over to the next concept. With luck, one concept taught exceptionally well might strike you and show you the clear way forward, and also help you correct your past misconceptions. That is the beauty of math. But it would be better if the way to understanding were kept clear the whole way, through good teaching. 

[Hunter]

I think math is more beautiful, when you are learning it at your developmental level, rather than having bits and pieces thrown at you, that you are not capable of catching, never mind using or appreciating or asking questions about.

 

The whole international competition push is no different than child labor that is beyond a child's physical development. Now we use schools as places of apprenticeship, instead of having our overwhelmed children training and working at the actual place of employment. 

 

Nothing is beautiful when it hurts.

[Sahamamama]

The beauty for me is in the patterns and connections which become visible through mathematics. I enjoying pondering these things from a purely rational standpoint, but also a symbolic standpoint. Math can be a tool, but it can also be something you create, and more awesomely, something you find. I feel like a child, peeking in on the mature universe.

 

Thank you for this, Targhee.

 

I ask, in part, because I have (at least) one child who thinks this way.

 

Boom finishes eating her oatmeal, and says, "Twenty-seven."

 

I say, "Twenty-seven what, Sweetie?"

 

She answers, "Twenty-seven spoonfuls of oatmeal this morning. Yesterday's bowl was 31, but I used a smaller spoon."

 

:huh:

 

We're on our way to church on Wednesday night. We arrive and Boom says, "Ninety-eight."

 

"Ninety-eight what, Sweetie?"

 

"Ninety-eight cars passed us on the way here. Three of them had one headlight. What do you call those again? Poodles?"

 

:huh:

 

It's like this all the time. Oy, the counting.

 

Her twin is like this, too, but in a different way. With her, it's mental math. She's even faster than my parents, and they are scary-fast. Bang can do things with fractions and percents IN HER HEAD that I have always done on paper. Now that I have more experience (ahem), I can do some things in my head, but I certainly didn't move things around in there when I was six or seven.

 

So I wonder about these two....

 

We were working on a number chart a while ago, skip-counting by threes. They know this. The "exercise" was to satisfy my check-the-boxness. The girls colored in all the numbers from 0 to 99 by threes. We saw so many patterns. 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33 [double], 36... and so on. Just basic skip-counting, right? But plug those into the chart, and you see the patterns. Look at the tens' place and the ones' place.

 

I wonder, is it all like this? This is something that I certainly never did in school. No patterns in math were ever pointed out to me, just nothing. The only thing I remember a teacher saying was that when we multiply any number by 10 we "add a zero" to it and that's the product. So I spent a while literally adding zeros when I multiplied by ten. I was clueless, but obedient. Hey, I did what she said. :glare:

 

We've talked about the patterns in the 9 times table. Who knew? No one ever told me that the digits add up in a pattern, and not just in the beginning of the pattern, but (perhaps?) all the way through.

 

0 x 9 = 0

1 x 9 = 9 (adds up to 9)

2 x 9 = 18 (1 + 8 = 9, or 9 x 1))

3 x 9 = 27 (2 + 7 = 9)

4 x 9 = 36 (3 + 6 = 9)

5 x 9 = 45 (4 + 5 = 9)

6 x 9 = 54 (5 + 4 = 9)

7 x 9 = 63 (6 + 3 = 9)

8 x 9 = 72 (7 + 2 = 9)

9 x 9 = 81 (8 + 1 = 9)

10 x 9 = 90 (9 + 0 = 9)

11 x 9 = 99 (9 + 9 = 18, or 9 x 2)

12 x 9 = 108 (10 + 8 = 18)

13 x 9 = 117 (11 + 7 = 18)

14 x 9 = 126 (12 + 6 = 18)

15 x 9 = 135 (13 + 5 = 18)

16 x 9 = 144 (14 + 4 = 18)

17 x 9 = 153 (15 + 3 = 18)

18 x 9 = 162 (16 + 2 = 18)

19 x 9 = 171 (17 + 1 = 18)

20 x 9 = 180 (18 + 0 = 18)

21 x 9 = 189 (18 + 9 = 27, or 9 x 3)

and so on....

 

Doing this interesting work successfully with my 9 and 7 year olds made me wonder why I never had any math like this? And not only was I never shown this pattern -- which, by the way, I think is fascinating! -- but no one ever presented math as questions, such as, "Does this pattern continue infinitely? How could you prove that this pattern continues infinitely? Does anyone know why the pattern continues (or does not continue)? Does it work if one factor is a negative number?"

 

The mathematically gifted students did have this kind of math. They were the kids (in my same class, tucked in a corner) who were faster and better on tests, so they learned to make equilateral triangles with circles or hexagons with a compass, while the rest of us math-stupid students worked on algorithm dittoes. "Four plus seven is eleven, put down the one in the ones place, carry the one.... "

 

They got to do things like hammer nails in wood and make string art. To see patterns, I guess?

 

They made and flew kites. I remember the kites. With deep resentment, actually. I was always so good at building things, but apparently was too stupid at math. [Huh. Too much reflection for one day.]

 

Reflective pause....

 

Well, I will say that I've been doing some of these "more interesting things" with my young children. They have no problem understanding what was kept behind locked doors for me and my kind.

 

So now I'm asking, Can I get a healthier perspective on what math actually is? Because for me it was pretty much one ditto after another, until middle school. Then it was one textbook after another, until college. Then it was one course that was required (I choose Statistics). Then it was "done." I was so happy when math was finally done.

 

You know, looking back, I think the biggest insight (for me) from this thread has been how much the "You are stupid in math" message was pounded into my head from 2nd grade onward. That's when we were split out into the Smart group and the Dumb group.

 

No wonder I never "liked" math!

 

 

 

[Sahamamama]

Math is beautiful because:

 

There is logic and order.

There are patterns to discover - some of them surprising

It is immensely satisfying when  long expression simplifies, or when a proof finally comes together. Have you ever felt satisfaction at solving a puzzle?

One can marvel at the human mind that managed to uncover such relationships

Some relationships are stunning: how can there be such a simply way of finding out a certain thing?

Geometry can be visually beautiful.

 

Many students get turned off math before they even get to the beautiful stuff. Arithmetic is not math.

 

Regentrude, thank you. Again, I thank those who are explaining this to me.

 

Here's an example of how I was taught:

 

298 + 437 = ?

 

Step 1:  Line up the numbers vertically.

 

   298

+ 437

 

Step 2:  Add the digits in the ones' place; 8 + 7 equals 15, put the 5 in the ones' place below the line, "carry the one to the tens' place above the top number" (seriously, this was how I was taught) -- no terms, such as addend, sum, subtrahend, minuend, difference, etc., until high school. By then I was completely lost).

 

     1

   298

+ 437

       5

 

Step 3: and so on... you get the idea.

 

Imagine my surprise, many years later, when I learned that you could "take two" from the 437 and add that to the 298.

 

437 - 2 = 435

298 + 2 = 300

 

435 + 300 = 735

 

Shoot, even I could do that in my head! We were never encouraged to move things around or play with numbers. The problem was the problem. Do it THIS way! Show your work! Do it ONLY this way. There is only ONE right way!

 

Furthermore, we were never given time to think deeply about any problems. The key determinant of "success" in math was speed. The faster, the better. Never, "Look at this until you see at least one more way to solve it."

 

However, I am persuaded that these tricks and tips -- and this flexible way of thinking -- were explicitly taught to a certain subset of teacher-selected students, while the rest of us were kept in the dark. Am I too cynical?

 

[wapiti]

However, I am persuaded that these tricks and tips -- and this flexible way of thinking -- were explicitly taught to a certain subset of selected students, while the rest of us were kept in the dark. Am I too cynical?

 

Yes, IMO that view is inaccurate.  The examples you present in your post strike me as more of a curriculum-selection issue, procedural vs. conceptual, rather than a tracking issue.

 

FWIW, I was never taught the tips and tricks - which BTW involve concepts rather than "tricks" without understanding - but a lot of that I was able to intuit.  Not everything, but a lot.

[regentrude]

However, I am persuaded that these tricks and tips -- and this flexible way of thinking -- were explicitly taught to a certain subset of teacher-selected students, while the rest of us were kept in the dark. Am I too cynical?

 

I don't know... it was not that I was actively taught stuff like in your example - that's something one just figures out because it make sense and is quicker. A kid with a natural interest in math will naturally begin to play with it an explore.

 

I grant you, however, that a lot of the issues with math education in this country stems from the fact that there is a substantial portion of math phobic teachers, teachers who themselves do not like and fully understand math, yet are "teaching" it. There have been studies how much an elementary school teacher's negative attitude about math affects female students (female students more than male students, because little girls want to please their teachers to a greater extent)... no wonder that kids think math is dumb/they are bad at it when their teachers subconsciously transfer their own attitude.

 

Math needs to be taught by teachers who LIKE math and are GOOD at it.

Until that is the case, the students with a natural aptitude will manage to discover the cool patterns themselves, and the others will be left with a bunch of memorized algorithms.

[wapiti]

Furthermore, we were never given time to think deeply about any problems. The key determinant of "success" in math was speed. The faster, the better. Never, "Look at this until you see at least one more way to solve it."

 

I missed this part - faster isn't smarter.  And, did I hear a call for problem solving?  :) 

[Sahamamama]

Yes, IMO that view is inaccurate.  The examples you present in your post strike me as more of a curriculum-selection issue, procedural vs. conceptual, rather than a tracking issue.

 

FWIW, I was never taught the tips and tricks - which BTW involve concepts rather than "tricks" without understanding - but a lot of that I was able to intuit.  Not everything, but a lot.

 

What I'm saying is that there were two groups of students, from 2nd grade onward. One group ("my" group) was taught that procedural way (e.g., my examples). But I know the "other" group was taught differently, because all their assignments and projects were different (e.g., string art, geometry, kites, math olympiad, etc.). They were never a part of the "lower" math group, they were separate. There were two groups, and two different methodologies.

 

Along with that, this "lower" group of students was continually instructed to leave all the numbers exactly in place and just "do it this way." So I do think that lack of freedom creates a mindset that is less able to intuit independently. The training paradigm was to not think independent thoughts related to math.

 

[Clear Creek]

If you want to learn more about patterns, how far they go (and why), and how you can learn from them...get yourself Harold Jacobs' Mathematics: A Human Endeavor. Or if you are short on time, Jousting Armadillos is based in part on it and teaches all the concepts through patterns, games, and other discovery methods. Both are fun, fun stuff.

[wendyroo]

Well, I will say that I've been doing some of these "more interesting things" with my young children. They have no problem understanding what was kept behind locked doors for me and my kind.

 

So now I'm asking, Can I get a healthier perspective on what math actually is? 

 

Vi Hart is a wonderful role model for math loving kids (especially girls who need to see women excelling in STEM subjects).

She certainly deals with the "more interesting things".  Some of the math in her videos goes over my head, but I find them fascinating nonetheless.

 

[happypamama]

I think math is beautiful because of its order, its sameness, its neat, tidy answers. I like that you can know that you're done, because you got the correct answer all wrapped up in a neat little box. I love the patterns and discoveries, and the way you can take it apart in different ways and still have it come back to the same number. I love that you can add three and eight and get eleven, or you can turn it into two plus eight equals ten plus one more equals eleven. I love that you can add a long column of consecutive numbers together by adding the first and last and multiplying by the numbers of pairs. I love that two fourths make a half; I love the symmetry; I love the balance of an equation. To me, this is poetic.

 

My one son thinks like I do, and he thinks the little tricks and patterns are fun. I think he'd agree that math is beautiful. To my child who doesn't care about the patterns, math probably is not beautiful, but merely functional. To my son and I, the functionality IS beauty.

[happypamama]

 

Math needs to be taught by teachers who LIKE math and are GOOD at it.

Until that is the case, the students with a natural aptitude will manage to discover the cool patterns themselves, and the others will be left with a bunch of memorized algorithms.

I fully feel that this is why I like math and see the beauty in it, because it was modeled for me. My dad was an AP calc teacher for most of my life, so I was never told that math was tough. I was told that math was cool, that it was fun. We did math puzzles for family fun at my house. I have warm fuzzy memories of going with my dad as a sixth grader to keep score for his traveling high school math competition team and stopping by his room at school to get help with a problem for one of my own math classes. If my teachers were lackluster about math, Dad certainly wasn't, and I picked up his enthusiasm. I don't fear or hate math.

 

Ftr, I also highly credit one teacher in particular for why I see the appeal of history. I always enjoyed it, but it never came alive for me the way it did when one teacher taught it. Then, then it was beautiful, and it stuck. The models ahead of us matter!

[Kerileanne99]

I love the systematic, orderly, calming process of it.

 

I just asked my math crazy almost-five-year-old this question out of curiousity. She said " because it has really fun patterns and you can do it whenever you want...oh, and some numbers are extra beautiful, like jewels that sparkle, like the number 1."

 

Oh. Okay? I tried for clarification but she was 'too busy playing pirates and princesses.'

[Kerileanne99]

If you want to learn more about patterns, how far they go (and why), and how you can learn from them...get yourself Harold Jacobs' Mathematics: A Human Endeavor. Or if you are short on time, Jousting Armadillos is based in part on it and teaches all the concepts through patterns, games, and other discovery methods. Both are fun, fun stuff.

Lol, I bought a copy of Mathematics: A Human Endeavor for myself and my dd4 totally confiscated it! She calls it HER textbook an insisted on taking it for preschool Show and Share. Not sure WHAT was made of that:)

It really is awesome. I learned math with the traditional, boring, algorithmic math with zero extras. That book, and researching for my child, ha completely opened my eyes to a different, exciting world of math.

[Tanikit]

For me I think it comes down to the fact that Math is about patterns. If you look at every living thing in creation then there is a symmetry, a pattern. If you look at your favorite bedspread or what you might consider a beautiful advert on a billboard or a beautiful blog then you will see that somewhere in that there will be a pattern - either in the use of color, or in the symmetry, or in the size of the writing (even what I type here has a pattern since all the letters are proportional).

 

Math itself is about that - that is why many like proofs - it proves there is a pattern - they all solve like this because... usually when people can see the patterns then they like Math, if they cannot see them then they miss the beauty. Most kids when they learn to multiply by 0 laugh and think: oh this is easy, but it is really because they have seen the beauty of the pattern - a very easy pattern to see. Some patterns need to be explained (hence the proofs) and sometimes it just takes a lot of work to see there is one - some of the joy in Math lies in finding and being able to see those patterns.

[LMD]

Math is beautiful. I read in a zvonkin book that (paraphrasing) math is the purest of the sciences. It seeks to observe and express the world around us. It also has the satisfaction of lightbulb moments, when you realise how these fit perfectly.

[LMD]

Like this:

 

 

[OneStepAtATime]

I did not understand math in school.  It made me feel insecure and stupid.  Now that I am teaching my own kids and we are learning together and I have finally seen there is a LOT more to math than just algorithms, it really does seem beautiful at times, even fun.

[dragonflyer]

I have seen a lot of comparisons to art, but I always see math more as music.  It is the most basic melody of the universe.  It allows us all a common language in an effort to understand the laws by which the universe operates.

Arithmetic gives a basic rhythm, but trig adds the melody and calculus the harmony.  There is point and counter-point and a huge crescendo when the numbers allow you to deepen your understanding of nature and humanity.  There is always a deeper pattern to discover and a new appreciation for the many components that contribute to the beautiful symphony of numbers being acted around us so consistently that most people do not stop to see within the complexity.

[Orthodox6]

When I was a child, one of my favorite things was the Spirograph and the beautiful designs it made. Whe I was older, I realized that mathematics was related to those designs.

[Ausmumof3]

There was a post a while back with a link about this. It described the way Maths is taught in terms of music. He said its like teaching kids all the names of all the notes and to sit and read music in every key but never actually being allowed to hear music or touch an instrument.

 

I am new to the concept of maths as beautiful though I have always found it satisfying and enjoyable. In architecture there is the golden ratio where things that look pleasing to the eye all follow a certain mathematical pattern. Music notes are all mathematically related. I'm sure I'm doing an awful job of remembering and explaining but not only is maths beautiful but also many beautiful things are beautiful because or sense can detect the hidden maths laws they are following even though we can't see or intellectually define them.