Are there Physics and Mathematics Texts for Holistic Learners

[Jarvis323]

Linear learners learn most thoroughly and efficiently, when material is presented to them in a logical, ordered progression. They will often attack problem solving with a series of ordered steps. They often will understand in part before understanding the whole.

Holistic learners work through material most thoroughly and efficiently in "fits and starts." They may often feel overwhelmed with confusion for a while, but understanding will often suddenly click. When the material does suddenly click in understanding, the holistic learner will usually not only see the big picture, but in a more clear and creative perspective that other learners may not. Often, holistic learners will take more time to understand information than their peers. This can often be so discouraging, that a holistic learner may be more tempted to give up on a particular subject. However, when holistic learners do finally understand the material given, more extensively. Holistic learners are usually extremely creative.

http://www.pssc.ttu.edu/techhort/lasrvy/l_h.htm

My learning style seams to be more holistic than linear, but it appears to me that physics and especially mathematics texts are written in a way that is best suited for linear learners. They very often give little or no context or motivation as they move along. I can work through these texts, and even do the practice problems, but very little will stick. I will forget most of it almost as fast as I process it, as if my brain has deemed it unimportant, or likely to be, and just throws it away, trying to save space for stuff worth thinking about. On the other hand, when I have the motivation to learn something, I seam to be able to learn at a much accelerated rate, and end up retaining what I learn.

I'm looking for some mathematics texts which tell stories, give some history, motivation, a bigger picture, some intuition, and some context. They should spark my curiosity, excite me, and cause me to ponder before they expect me to dive in, learn the details, and do practice problems. I would like to read such texts to get some inspiration, intuition and vision, and then go back to fill in the blanks and learn the details as I need them. In the long run, I want to have a knowledge set and understanding that enables me to read graduate level texts or research papers from select topics in physics and mathematics.

Anyone have any suggestions? Anyone have any insight on the issues that holistic learners face when learning mathematics, and how they can overcome them?

 

[Mondayman]

You could try Mathematics and the Physical World by Morris Kline.

 

[DiracPool]

I will forget most of it almost as fast as I process it, as if my brain has deemed it unimportant, or likely to be, and just throws it away, trying to save space for stuff worth thinking about.

You mean important stuff like shrimp tacos?!

I'd say as far as math is concerned I'm a bit of a "holistic" learner myself, whatever that means. I'm guessing you mean more "right-brained" than left-brained? Because I'm slated to enter a machine intelligence graduate program in the fall, I've been accelerating my math studies so I don't show up as a complete boob in the lab. However, I have great difficulty doing math by reading math texts. For me, it's beyond stiff and boring. As you mentioned, my brain rejects it almost immediately and I start thinking about shrimp tacos.

The saving grace for me has been you-tube videos and video lectures from open-access universities such as Stanford and MIT. When learning math and physics, I need to have it "spoon-fed" to me with a colorful character at a white-board who is skilled in communicating difficult concepts. Then I can maintain attention and focus. Give me a dry, stiff book and I'm out the door and on my way to the local taqueria.

Contrast this with neuroscience material which is exactly the opposite. My background is in neuroscience so I already know it forwards and backwards. Therefore, I don't have the patience to sit through any neuroscience lectures so I don't watch any of them. Instead, if I want to know something about it, I already know where to look and exactly what journals or other resource has the information I'm looking for. So when I research a neuroscience-related issue, I go straight to the written text and can scan probably on the order of a dozen or two scholarly publications per hour because I know what I'm looking for. There have been days when I've reviewed probably close to 100 papers, mostly just reading the abstracts and conclusion for clues as to whether the body of the text contains what I came to find.

So, it does present something of a bizarre dichotomy with my learning techniques here. Maybe you can sympathize. As far as math per se is concerned, the videos I like the best are those that put up a problem on the board and then give you a chance to pause the video and try to work the problem out yourself. When you restart the video, the tutor then begins to present a fully worked out solution without skipping steps. Even though they sometimes can skip steps and I'd still be able to follow the solution, I'd rather they didn't even though it takes more time. Why? Because I like thoroughness and I like to consistently reinforce the basics. For mathematical physics, DrPhysicsA is great at this: https://www.youtube.com/user/DrPhysicsA

For straight math, I like PatrickJMT: https://www.youtube.com/user/patrickJMT

Those are free on you-tube. For a little bit of money, or they may have these at your local public library (where I ran into them), I'd highly suggest mathtutordvd.com

http://www.mathtutordvd.com/

If you're just starting your math and physics journey, especially at a later stage in life as myself did, Jason is your man.

Also the "recitation" videos at the MIT website (also on youtube) are great for putting up problems on the board and working out solutions after giving you the opportunity to do it yourself.

I hope this helps. If you or anyone else know of a resource where I can find more videos as the ones I've listed above, please do post them.

 

[OrangeDog]

I am a holistic learner too.

I had the same problem with high level math. While I could learn procedural things like integration and differentiation easily, when it came to proofs I found that they were presented with no context, and no motivation. That made it hard for me to learn. I remember going through various proofs and thinking to myself "Why the hell would anyone think to do that in first place." I would get tripped up trying to figure out why I should be thinking a certain way rather than following the procedure they provided. It doesn't help that a lot of mathematics texts (and many mathematicians I know) are kind of snotty in that they like to present their material in the most unapproachable way possible or sometimes overly terse without any context or insight into the problem they are solving. I found I could understand problems by coming up with my own way to visualize the problems they are trying to solve.

What I found worked for me but took some extra time was to research and acquire background information on problems I was solving. Maybe your homework will take longer to solve, but you will be much more knowledgeable.

 

[DiracPool]

What I found worked for me but took some extra time was to research and acquire background information on problems I was solving. Maybe your homework will take longer to solve, but you will be much more knowledgeable.

I do share this same sentiment with you and the OP's post:

"when holistic learners do finally understand the material given, more extensively"

It takes me a long, long time to understand a mathematical-physics concept. However, when I finally "get it," I feel I have a much deeper understanding of it than most people do. Again, I think that this is a left brain-right brain thing. The "shut up and calculate" crowd (IMHO) are really just blindly executing formal operations in their left hemisphere without any (much) extrapolation as to what these calculations "mean" in a greater context.

I think the distinction may be that the "holistic" crowd may not take the calculations on blind faith but require some kind of conceptual visualization of what is going on that the left-brain thinkers don't require. This requires much more work/effort and is not always successful. But if you can connect with this, i.e., connect the right and left hemisphere understanding of these concepts, you do have a much deeper and richer understanding of the mathematical physics.

 

[bcrowell]

Learning styles are a myth.

Pashler et al., "Learning Styles: Concepts and Evidence," http://psi.sagepub.com/content/9/3/105.abstract

 

[DiracPool]

Learning styles are a myth.

Well, I strongly disagree with that sentiment and believe I can back it up sufficiently:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3787275/
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3728072/
https://www.amazon.com/dp/1111833354/?tag=pfamazon01-20

To name just a few references..

 

[OrangeDog]

I do share this same sentiment with you and the OP's post:

"when holistic learners do finally understand the material given, more extensively"

It takes me a long, long time to understand a mathematical-physics concept. However, when I finally "get it," I feel I have a much deeper understanding of it than most people do. Again, I think that this is a left brain-right brain thing. The "shut up and calculate" crowd (IMHO) are really just blindly executing formal operations in their left hemisphere without any (much) extrapolation as to what these calculations "mean" in a greater context.

I think the distinction may be that the "holistic" crowd may not take the calculations on blind faith but require some kind of conceptual visualization of what is going on that the left-brain thinkers don't require. This requires much more work/effort and is not always successful. But if you can connect with this, i.e., connect the right and left hemisphere understanding of these concepts, you do have a much deeper and richer understanding of the mathematical physics.

For me, it is knowing the context of the problem. Specifically, I need to know WHY I should be thinking a certain way. How does solving the problem in this manner lead me to getting the answer vs just applying the formula and getting a number. I have found as well that my line of thinking has lead me to being particularly good at extrapolating knowledge. Maybe I didn't get the highest marks in the class, but I could usually figure out some higher level concepts that weren't touched on until a later semester or in graduate work. Ironically, one of the reason I left graduate school was because I felt like all my classes were "shut-up and calculate". At the expense of actually understanding the material I felt one had to just do what they had to do to get the answer given the lack of time that was available. It was quite disheartening. I might go back though.

EDIT:
In some sense the holistic approach eliminates the "why not". There are many ways to solve a problem, without knowing the context why can't it just be solve in another, maybe faster or more simple way. What are the problem solving methods limitations? Again, it comes back to context.

 

[Jarvis323]

I see this has been moved to Math and Science Text Books. It's understandable, but unfortunately I think that means I'm most likely not going to get much help finding the books I'm looking for. For one reason, I'm not really looking for textbooks; I'm not sure the books I am looking for exist as textbooks. Another is that I don't think there is much traffic here. I guess I should be asking this on a Q&A site like Quora or something.

I'm looking for some mathematics texts which tell stories, give some history, motivation, a bigger picture, some intuition, and some context. They should spark my curiosity, excite me, and cause me to ponder before they expect me to dive in, learn the details, and do practice problems.

If you took a normal textbook in mathematics and added 5 to 20 extra pages to give context before each section, that might be sort of what I'm looking for. But I'm not sure this exists. I would settle for a book that just gives the context, and I can pair it with a textbook if I need to. Is there a name for these types of math books, that are not written for use in a classroom, but rather for enlightenment, that don't actually teach you how to do math, but covers topics like topology, differential geometry, algebra, dynamical systems, complex analysis, real analysis, etc.

 

[Sophia]

Learning styles are a myth.

Pashler et al., "Learning Styles: Concepts and Evidence," http://psi.sagepub.com/content/9/3/105.abstract

Try teaching and you will see that they are real. That's all I can say.

 

[bcrowell]

Try teaching and you will see that they are real. That's all I can say.

I've been teaching full time for 20 years. Scientific evidence trumps anecdotal evidence.

 

[Sophia]

I've been teaching full time for 20 years. Scientific evidence trumps anecdotal evidence.

Ok, that's a matter of opinion. I think that each teacher has to find what worked for him and his class. If the teacher "anecdotally" finds out that certain methods work for certain students, he has to use that method, even if some science paper says it doesn't work.
And finding my learning style helped me in my studies.
For me, it's reality.
Sometimes I trust real experiences of real people more than research. Especially in social sciences. But that's a matter of world view.

 

[Jarvis323]

Learning styles are a myth.

Pashler et al., "Learning Styles: Concepts and Evidence," http://psi.sagepub.com/content/9/3/105.abstract

I've been teaching full time for 20 years. Scientific evidence trumps anecdotal evidence.

FYI, your reference doesn't support your argument.

 

[OrangeDog]

I've been teaching full time for 20 years. Scientific evidence trumps anecdotal evidence.

I don't think this is always true honestly. This is outside the topic of the thread, but the whole "publish or perish" culture in academia gives people incentives to publish useless research. And ignoring everyday/anecdotal/life experience just makes a person naïve and not functional in society.

 

[Student100]

I don't think this is always true honestly. This is outside the topic of the thread, but the whole "publish or perish" culture in academia gives people incentives to publish useless research. And ignoring everyday/anecdotal/life experience just makes a person naïve and not functional in society.

Huh, I've tried reading that twice now and still can't make out what the point was or how it was supported by what you said. Here's a suggestion OP, why don't you get a textbook at the level of where you need to be, read each section and then Google the rest of the ancillary information that you find useful. It's all there on the internet, and nothing is stopping you from expanding on texts by Googling more information.

 

[jasonRF]

Jarvis323,

I'm not sure exactly what you are looking for, but for complex analysis perhaps a book like "an imaginary tale", followed by "Dr Euler's fabulous formula" , both by Nahin, may be along the lines of what you are looking for. They give lots of history and some interesting applications of complex analysis, cover some of the important topics like Cauchy's theorem, but do not really teach complex analysis with all of the gory details that you would get from a real math book.

jason

 

[mathwonk]

i don't have time to write a complete answer, but I agree this is somewhat of a myth. It is on you to modify how you learn rather than the book to accommodate you. Try what professionals do: read the statement of a theorem and then try to prove it yourelf before reading the proof in the book. Try to think up examples and applications of the material. I.e. work at it. mind you i agree there are very dry books that do not speak to me and others that seem user friendly, but to really learn takes a struggle and neither type of book will make this unnecessary. the best books are the ones written by the masters of the subject. so for algebra, try euler, and for geometry try euclid, maybe with hartshorne as a guide. and try reading your books non linearly. you can really open to any page you choose. its allowed. the book "what is mathematics" by courant and robbins is recommended. Russian books are also very good at pedagogy. the book Geometries and groups by Nikulin and Shafarevich is excellent. Also read the introduction to the books where the author gioves his overview. E.g. in Matsumura's intro to his Commutative Ring Theory, he says the most important theorem in commutative algebra is krull's princip[al ideal theorem. This is very valuable knowledge.

 

[Kilo Vectors]

I don't believe in learning style, but the way a teacher goes about explaining and the presentation of information can really affect students knowledge and motivation (not the same thing as learning style IMO) but maybe the "for dummies" series might help (no really, I use it and its a great series for everything) or schaums outlines

 

[DiracPool]

i don't have time to write a complete answer

If you do find the time, please write it, even if it's in piece-wise bits.

I agree this is somewhat of a myth. It is on you to modify how you learn rather than the book to accommodate you.

Really? So you should just pick up the first book on a subject you're interested in, and if it doesn't speak to you, then engage in a laborious process of modifying how you learn rather than looking for other books in the category that are talking more your language?

Try what professionals do: read the statement of a theorem and then try to prove it yourelf before reading the proof in the book.

You mean the left-brained biased professionals right? Not the right-brained, more creative and visually minded biased "holistic" professionals?

It's easy to call differences in learning strategies a myth when your bonded to a particular way of looking at things. It's like a shark telling a human that the reason he can't swim is because he's deficient in is caudal-fin propulsion strategy rather than encouraging him to work on his "free-style" technique. The shark has no conception of any other method of swimming than the caudal-fin propulsion mechanism so he tells the human that "learning styles" are a myth and the reason you can't swim is that you're not getting your "caudal fin" technique on and you better study it. That's a naive and one-dimensional way of looking at the learning process.

 

[mathwonk]

diracpool, i am also a holistic/creative learner, but practically that means i need to learn how to provide myself with the sort of "aha" moments that illuminate me. i have tried to give you some techniques. my key point is that holistic learners can make it in the linear world if they work at it.

 

[vanhees71]

There's only one way to learn math: Do it! That's all I can say from my experience. Of course, there are types of books you like more or less, and everybody likes a different style of presentation. E.g., I abhorr Bourbaki-like math books and prefer more oldfashioned ones, where you get not only the formalism but also the intuitive ideas behind the abstract formalism, but that's maybe because I'm a theoretical physicist rather than a mathematician, but still the only way one can learn math is to think a lot for yourself, try to prove theorems for yourself etc.

Also math is by definition deductive, i.e., you have to start from the beginning (axioms and simple theorems) up to the more advanced topics. If you don't like this structured way of the subject, math is simply not for you. There are many more fascinating subjects to study out there ;-).

 

[mathwonk]

this discussion reminded me of a famous quote by the great mathematician and teacher, Emil Artin: It appears at the bottom of the first page of this interesting looking article by Hyman Bass:

http://www.aimath.org/WWN/kleinproject/MathematicsandTeaching.pdf

 

[Mastermind01]

Wow! I though I was the only one who found maths textbooks with rigid proofs boring! It appears I'm a holistic learner too.

 

[PeroK]

this discussion reminded me of a famous quote by the great mathematician and teacher, Emil Artin: It appears at the bottom of the first page of this interesting looking article by Hyman Bass:

http://www.aimath.org/WWN/kleinproject/MathematicsandTeaching.pdf

I don't buy this "mathematics is an art" view. Art is bound up in culture and perception, and has an instrinsic freedom. The mathematician is constrained by what is ultimately true by well-defined criteria, whether the result is rigorously proved or not.

A writer, poet, artist or composer can create whatever he or she likes, but inescapably $\sum_{n = 1}^{\infty} = \frac{\pi^2}{6}$ - there is no choice and no artistic freedom. Mathematics is beautiful, but it's not an art.

If mathematics were art, you could submit a blank piece of paper as your mathematical thesis and demand a PhD for it, following the theme of John Cage's 4'33":

 

[DiracPool]

Mathematics is beautiful, but it's not an art.

It is kind of art in a way. I've heard some say that, where differentiation is fairly straightforward, integration is somewhat of an art. There's many different ways and techniques to solve equations. I mean, do you cross multiply in a certain instance, or divide by both sides? Do you want to clean up the left side of the equation first or the right side? The level to which you simplify your terms may depend on your audience. Do you set c and h-bar and G to 1 for this exercise or do you want to leave them in? By watching a lot of lecturers at work, I see a great deal of individualism in how each goes about massaging equations into a form where they can solve them. It's not a one-size fits all prospect. I look at a science lecture as a performance and, dare I say, there's a lot of art going on in these performances, even those that are heavily mathematics-based.

I'm not a mathematician and maybe I don't know what I'm talking about, but I really got a feel for mathematics as art; well, mathematical physics anyway, by watching Lenny Susskind's famous Stanford "theoretical minimum" lectures. This guy is like a maestro up at the white board. Sometimes he takes shortcuts, sometimes he doesn't. Sometimes he only works out half an equation, sometimes he tells you to go home and figure it out for yourself, etc. I consider this art--perhaps art within a boundary of axiomatic-mathematical constraint--but art nonetheless. What seals it for me is when he (Lenny) puts, or should I say "paints" a mathematical expression on the whiteboard and then steps back from it for a second and looks at it with a curious eye and twist of the neck. After a brief pause, he will then extend his arm with his marker brush in hand and, with a touch a delicate as rose petal, change a negative sign into a positive sign. Magnificent. It reminds of one of the "old masters" such as Michelangelo or Raphael putting a finishing touch on a work of art.

 

[Cruz Martinez]

You mean the left-brained biased professionals right? Not the right-brained, more creative and visually minded biased "holistic" professionals?

But creativity, originality and visualization are all heavily engaged when proving almost any theorem in math which is not trivial (look at the proof of Urysohn's lemma for example). Your statement seems to imply that people who are good at mathematics are somehow less creative.

 

[DiracPool]

Your statement seems to imply that people who are good at mathematics are somehow less creative.

As an old-timer street junkie in Hawaii I knew years back once said to me, "Generalizations suck, but it's the best we have to go by."

I think that you're comment is well established. Of course you can find exceptions to the rule so please don't go there. But if you look at the broad scope of it, creative/artistic people are not typically good at nor really desire to be good at mathematics. On the other side of the coin, mathematicians are typically good at math, desire to be so, and are oblivious to the fact that they may not be as creative or more creative than a painter or a songwriter, because, after all, being good at math means that your good at everything, right? Your post really spells this out even more clearly than I can explicate. But this is not the case. The reality is that is it is simply easier to quantify the differences in mathematical capacity between two individuals than it is to quantify a creative capacity, for obvious reasons.

Present to me a mathematical algorithm that is a formula for success in writing a hit pop song. I don't think you'll be able to do it. Mathematically minded left-brain thinkers typically do not write hit pop songs. I am a songwriter and have studied songwriters and songwriting. There's not very many math geeks (and I use the term adoringly, not disparagingly), that are pumping out the creative juice. That said, there are many excellent musicians, studio musicians in particular, that are very left-brain mathematically minded. This is because mathematical capacity and the capacity to manually play scales on the piano or guitar, say, are hierarchically organized sequential-operation skills, for which the left hemisphere of the brain is particularly specialized. But if you look around, the more technically proficient studio musicians are some of the worst songwriters, from my experience (think TOTO ). It's the more sloppier right brain guitarists that are the ones that write the most creative songs.

But creativity, originality and visualization are all heavily engaged when proving almost any theorem in math which is not trivial (look at the proof of Urysohn's lemma for example).

How do you defend this statement? I read the wiki article on the subject and didn't abstract your conclusion from it at all: https://en.wikipedia.org/wiki/Urysohn's_lemma

Perhaps you were talking about this passage?

"This construction proceeds by mathematical induction."

Are you confusing "induction" with creativity, originality and visualization?

 

[micromass]

How do you defend this statement? I read the wiki article on the subject and didn't abstract your conclusion from it at all: https://en.wikipedia.org/wiki/Urysohn's_lemma

Perhaps you were talking about this passage?

"This construction proceeds by mathematical induction."

Are you confusing "induction" with creativity, originality and visualization?

Why would he confuse induction with creativity and originality?? That statement of yours makes no sense.

The truth is that mathematics requires lot of originality. For the uninitiated, it is not easy to recognize this though. They see mathematics as a very logical discipline, as something very linear and rigid. This is far from the truth.

I don't blame you for not understanding Urysohn's lemma and for not understanding how amazing and original the argument really is. You need quite a lot of background to really recognize this.

Both math and music/art/etc. requires creativity and originality. It is very divisive to not recognize this. The difference however, is that music and art are pretty much open for everybody. Sure, few people will be top musicians or will be able to make a beautiful painting. But enjoying music and art is something everybody can do. Enjoying the originality and creativity of mathematics however, that is only there for the patient.

I've read quite a bit on holistic learning due to this thread. I would definitely identify myself as a holistic learner. But what's more, every mathematician I know approaches math in a holistic learning perspective. I don't think it is possible to be a mathematician without being a holistic learner. This is not apparent in high school math, since high school math isn't really the kind of math that mathematicians do, it is more following procedures and fixed steps. This is not at all what actual math is about.

On the other hand, I would definitely agree that math books are not user friendly and are difficult to read. But again, every mathematician I know, thinks the same way. It's just written this way because it induces the maximum amount of clarity and the least amount of ambiguity. Everybody will have to fight math books. I don't know anybody who can read math books in a linear way devoid of connections, meaning, philosophising, creativity, etc.

 

[Cruz Martinez]

Present to me a mathematical algorithm that is a formula for success in writing a hit pop song.

Present to me a method for being innovative in any field, including mathematics. Any innovation requires creativity, and this is something for which there is no method.

Mathematically minded left-brain thinkers typically do not write hit pop songs.

Pop-song writers typically do not excel at math, so? You speak as if not writing songs, not making art or anything else you catalogue as coming from the 'right-side' of the brain means you are not creative. If this is how you define creativity then it is a self-serving defiition on all accounts.

How do you defend this statement? I read the wiki article on the subject and didn't abstract your conclusion from it at all: https://en.wikipedia.org/wiki/Urysohn's_lemma

Perhaps you were talking about this passage?

"This construction proceeds by mathematical induction."

Are you confusing "induction" with creativity, originality and visualization?

Of course I did not confuse those. It would actually be very difficult for me to make you see the originality in the proof if you don't have a fair knowledge of topology, but that's besides the point. To be honest, the wiki article does not even begin to do justice to the lemma. The proof does proceed by induction (or recursive definition rather), but to find the construction that works requires outstanding originality.

 

[vanhees71]

Wow! I though I was the only one who found maths textbooks with rigid proofs boring! It appears I'm a holistic learner too.

This is not what I was implying. Math is about rigid proofs. What else should it be about? I'm only against textbooks that are written like Bourbaki without any motivation for the reader and the intuitive thinking leading to the rigid proofs. There should be a difference between textbooks and scientific research papers!

 

[Jarvis323]

Wow! Thank you all for your great insight.

IMO, it may just simply be that some require intuition or motivation more than others, maybe in part because they need it to maintain interest and focus, or maybe simply because of the way that their brains try to put pieces together and organize information.

Whatever the case, it's surely true that a student needs to have focus to do well. They have to be paying attention. I just need some 'help' with this or my mind will wander; I will find myself pondering abstract philosophical concepts, trying to work out mental experiments, or working out the details of some invention or potential project. I think these same qualities that I think make the thinker, day dreamer, and problem solver, are very beneficial for a mathematician, but potentially detrimental to the beginner student in a linear, and ridged educational path. No doubt, math requires this to some extent as things are built on layers of foundational axioms, theorems, formulas, algorithms and concepts.

You need to wade through a lot of tedium to get to the level where you can productively daydream up coherent and useful mathematical inventions. It's not a lack of love for mathematics that is holding me back, it's more my dislike for tedium and inability to force the aim of my focus arbitrarily. I love mathematics, particularly abstract mathematics, especially the type which requires little background knowledge, but lots of ingenuity and cleverly structured logical deduction.

I don't buy this "mathematics is an art" view. Art is bound up in culture and perception, and has an instrinsic freedom. The mathematician is constrained by what is ultimately true by well-defined criteria, whether the result is rigorously proved or not.

A writer, poet, artist or composer can create whatever he or she likes, but inescapably $\sum_{n = 1}^{\infty} = \frac{\pi^2}{6}$ - there is no choice and no artistic freedom. Mathematics is beautiful, but it's not an art.

If mathematics were art, you could submit a blank piece of paper as your mathematical thesis and demand a PhD for it, following the theme of John Cage's 4'33":

If mathematics is not an art, just because it is a reflection of something real or inflexible, then is photography also not an art? Is non-fiction writing not an art? It's my opinion that the process of bringing together select pieces and then building a beautifully, and logically structured representation of something true, and then communicating it elegantly, and moreover, assigning it some truth based conceptual meaning, is altogether perhaps one of the most creative and artistic endeavours of all; mathematics may be the purest and richest art we have.

 

[vanhees71]

Well, that's a delicate question and not easy to argue about. I think doing mathematics and also the natural sciences is to a certain extent also comparable to the work of an artist. You need ideas and intuition to figure out something new. It's a creative endeavor. Of course the rules are much stricter for math and for natural sciences you have to make observable predictions and test these predictions in experiments. So in some sense you also have to be more focused than an artist who is completely free in his expressions, but you also must not be so focused that you cannot find something new.

 

[PeroK]

If mathematics is not an art, just because it is a reflection of something real or inflexible, then is photography also not an art? Is non-fiction writing not an art? It's my opinion that the process of bringing together select pieces and then building a beautifully, and logically structured representation of something true, and then communicating it elegantly, and moreover, assigning it some truth based conceptual meaning, is altogether perhaps one of the most creative and artistic endeavours of all; mathematics may be the purest and richest art we have.

So, we now have three possibilities:

1) Mathematics is not an art.
2) Mathematics has some artistic elements and may be considered an art.
3) Mathematics is the purest and richest art we have.

Atlhough, I think if you went along to the Arts Council and looked for funding for a PhD in Mathematics, you might come away empty handed! I also like the idea of taking a class at the London Royal College of Art and teaching them differential equations! You wouldn't get away with that, for the pure and simple reason, that mathematics is not art. How could you teach mathematics (as an course in Art) at an Art College? It's absurd.

It's all very well for mathematicians and physicists to convince themselves they are artists - anyone can do that. Everyone is an artist in their own eyes.

The real test is to persuade others that you are artists. To be truly an artist, you would have to persuade the wider public and bodies who support and fund Art. To get people to attend maths lectures purely for the aesthetic pleasure of seeing someone paint (incomprehehensible) equations.

I believe the argument that maths is the purest and richest art would cut no ice outside a maths and physics forum!

 

[micromass]

So, we now have three possibilities:

1) Mathematics is not an art.
2) Mathematics has some artistic elements and may be considered an art.
3) Mathematics is the purest and richest art we have.

Atlhough, I think if you went along to the Arts Council and looked for funding for a PhD in Mathematics, you might come away empty handed! I also like the idea of taking a class at the London Royal College of Art and teaching them differential equations! You wouldn't get away with that, for the pure and simple reason, that mathematics is not art. How could you teach mathematics (as an course in Art) at an Art College? It's absurd.

It's all very well for mathematicians and physicists to convince themselves they are artists - anyone can do that. Everyone is an artist in their own eyes.

The real test is to persuade others that you are artists. To be truly an artist, you would have to persuade the wider public and bodies who support and fund Art. To get people to attend maths lectures purely for the aesthetic pleasure of seeing someone paint (incomprehehensible) equations.

I believe the argument that maths is the purest and richest art would cut no ice outside a maths and physics forum!

So something is only an art because other people think it's an art. I don't accept that definition.
I don't consider somebody an artist because he gets good criticism or funding from famous people. Rather, I take the following definition: "Art is the most individual expression of the most individual emotion". Meaning that art is very personal. You don't consider math art? Fine, then don't. But I do, and that's what art is about: individualism.

 

[vanhees71]

I vote for 2+3) :-))).