Is Math Nothing but Problems?

[Hunter]

In the math without curriculum thread, I stated that math is not just problems. Regentrude asked me what math was not problems. I'm in way over my head here, or just wrong.

 

Is math nothing but problems? I've spent decades reading literature trying to convince me that it isn't, or at least I thought it was trying to convince me of that.

[regentrude]

OK, maybe we have a semantics issue. For me, a math problem is anything that poses a question/puzzle and lets me find an answer using math.

All the following are "math problems" to me:

325*464=

or

3x-25=50, solve for x

or

sketch the graph and find all zeros of the following polynomial....

or

prove the Pythagorean theorem

or

find the length of the line xy in the sketch (complicated geometric figure included)

or

"word problems" of any kind

or geometric constructions of any kind

or

applied math problems in a physics situation

 

What do YOU consider math that is not a problem?

 

[Ellie]

You always ask such deep questions!

 

When I was growing up a gazillion years ago, my math texts were very similar to R&S's math series--probably the first editions, which had the most wonderful word problems. Because of those word problems, I have a very good foundation in basic arithmetic, and have no problems in using math in my every-day life: how much gas mileage my car gets, which product is a better buy at the grocery store, how much paint or wall paper to buy, balancing my checkbook (ACK), and so on. If there's more to math than that, I don't care. I know some people love math, and they love to mess with x's and y's and parentheses and everything. For those people, maybe math is more than problems. Or maybe it is that the problems they're trying to solve are more complex than what I am trying to solve. Good for them. Just don't make me solve for x, lol.

 

Which may or may not answer your question, but it's all I got. :laugh:

[Alte Veste Academy]

:ph34r:

 

DS10's favorite drinking vessel is a cup that says, "Dear Math, I am not a therapist. Solve your own problems."

 

:leaving:

[My3girls]

You always ask such deep questions!

 

When I was growing up a gazillion years ago, my math texts were very similar to R&S's math series--probably the first editions, which had the most wonderful word problems. Because of those word problems, I have a very good foundation in basic arithmetic, and have no problems in using math in my every-day life: how much gas mileage my car gets, which product is a better buy at the grocery store, how much paint or wall paper to buy, balancing my checkbook (ACK), and so on. If there's more to math than that, I don't care. I know some people love math, and they love to mess with x's and y's and parentheses and everything. For those people, maybe math is more than problems. Or maybe it is that the problems they're trying to solve are more complex than what I am trying to solve. Good for them. Just don't make me solve for x, lol.

 

Which may or may not answer your question, but it's all I got. :laugh:

 

By figuring mileage and unit prices, you are solving for x and just not realizing it. ;)

[Ellie]

By figuring mileage and unit prices, you are solving for x and just not realizing it. ;)

 

Figuring out those things with basic arithmetic makes sense to me. Solving for x does not. I learned how to figure out those things by 7th grade. I did not need algebra. :-)

[kiana]

FWIW, I agree with regentrude.

[Alte Veste Academy]

Mathematics as truth? Mathematics as nature? Mathematics as it is expressed and witnessed in life? Mathematics just is.

 

We make lots of problems out of it though. :tongue_smilie:

[sunnyday]

Here's the summary from my Mathematical Thinking class on Coursera: 
 

Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world. This course helps to develop that crucial way of thinking.

 
Math is more than *procedures* , but mathematical thinking is a way to puzzle the truth out of an abstraction...and this is, ultimately, problem-solving.

 

I hope the author doesn't mind if I share the course introduction here, it's pretty relevant to this distinction between "doing problems" and "creating mathematical thinkers": http://spark-public.s3.amazonaws.com/maththink/readings/Background_Reading.pdf

[Farrar]

Is language nothing but sounds and words?

 

I'm sort of seriously asking...  I don't know if my metaphor works or not, but I think it does.  I mean, language is more than sounds and words, but if you don't learn the sounds and words, how could you get to the more part, right?  I think of math the same way.  Mathematical thinking and reasoning is more than problems or "doing math" but what is mathematical thinking without problems?

 

 

[kiana]

But in my viewpoint, the mathematical thinking and reasoning is still to solve a problem, even if it is not explicitly posed as a mathematics problem.

[Tsuga]

I believe that it would be helpful to discuss the difference between computation (a part of mathematics) and mathematics qua mathematics.

 

Mathematics is the science of quantity, space and number. Computation is mathematical calculation, or solving problems.

 

Mathematics includes theories about why numbers relation to each other in certain ways, and whether this is an intrinsic property of spatial and temporal relationships, or not.

 

In between mathematical theory and computation lie word problems. While these are problems, they require either explicit or implicit understanding of the theories that underlie the mathematical procedures (a.k.a. computation or calculation skills) that we use to solve the problems.

For example, let's take multiplication and time. If I tell my child, "James has six apples at one o'clock p.m. Every hour starting at 2 o'clock p.m., he gets four more apples and no more, and he doesn't give any away or lose any. How many apples does James have by 9:30 p.m.?"

Here, the child must understand the concepts of whole and half, and you can see whether the child uses multiplication as a concept (8*4 or 4+4+4...etc.), and then you remember that the temporal repetition must be added (not subtracted from or substituted for) the original quantity. It requires an understanding of the concepts to translate a situation into a computation problem. Then the child can solve the problem. But at some level, there is something other than problem-solving going on. There is implicit or explicit theorizing.

Does that make sense? In that respect, word problems require both conceptual, theoretical knowledge (even implicit--some people can do word problems but not explain them, some could explain but get muddled in the details) and computational skill.

BUT! And here is the cool part... you could ask someone to only explain how they would figure out the problem, and why they would do that, without actually solving it. This is not a mathematical "problem" in the sense that you are speaking about, right? It would consist of a theory about how quantities and time work.

 

While, in the academic sense, that might be considered a "problem" to solve, I think it is a good example of how you can have math without computation.

[Belacqua]

Is language nothing but sounds and words?

 

I'm sort of seriously asking...  I don't know if my metaphor works or not, but I think it does.  I mean, language is more than sounds and words, but if you don't learn the sounds and words, how could you get to the more part, right?  I think of math the same way.  Mathematical thinking and reasoning is more than problems or "doing math" but what is mathematical thinking without problems?

 

I think your metaphor works. Language is phonemes and syntax, but it is also Whitman and Akhmatova. Solving an arithmetic problem is math, but so is searching for the most elegant, concise proof of a problem you've already solved. The Olympiad kids get separate scoring for "math" and for "style." Would we call both sides of that "problems"? Not sure.

[Seasider]

Love your thread title! Made me think, "Yeah, with some kids more than others!"

[regentrude]

 Mathematical thinking and reasoning is more than problems or "doing math" but what is mathematical thinking without problems?

 

 

But you have to think mathematically and reason mathematically about something.

That something is your problem.

 

[regentrude]

I believe that it would be helpful to discuss the difference between computation (a part of mathematics) and mathematics qua mathematics.

Mathematics is the science of quantity, space and number. Computation is mathematical calculation, or solving problems.

 

Disagree. You can solve problems that involve absolutely no computation. Geometrical constructions. Proofs. Finding a general relationship between any function and its slope at any point -i.e. inventing the concept of calculus.

 

I also do not think we should call math a science. It is not.

 

Mathematics includes theories about why numbers relation to each other in certain ways, and whether this is an intrinsic property of spatial and temporal relationships, or not.

 

Temporal relationships belong in the realm of physics. THAT is science. It may use math as a tool, but math itself knows no "time".

 

 

BUT! And here is the cool part... you could ask someone to only explain how they would figure out the problem, and why they would do that, without actually solving it. This is not a mathematical "problem" in the sense that you are speaking about, right? It would consist of a theory about how quantities and time work.

While, in the academic sense, that might be considered a "problem" to solve, I think it is a good example of how you can have math without computation.

 

Exactly. But now you are contradicting yourself - see beginning of post.

 

[Farrar]

But you have to think mathematically and reason mathematically about something.

That something is your problem.

 

Yes, I see. Math is more than numbers, notations and formulas, but not more than problems.

 

Maybe language isn't more than expression? Sorry, I always need metaphors.

[Tsuga]

Quote

I believe that it would be helpful to discuss the difference between computation (a part of mathematics) and mathematics qua mathematics.

Mathematics is the science of quantity, space and number. Computation is mathematical calculation, or solving problems.

 

Disagree. You can solve problems that involve absolutely no computation. Geometrical constructions. Proofs. Finding a general relationship between any function and its slope at any point -i.e. inventing the concept of calculus.

 

I also do not think we should call math a science. It is not.

 

 

 

I was using the term "problem" in a most narrow sense. If you include proofs, etc. as I said later, then not only is mathematics only problems, but pretty much all learning involves problem-solving, even drawing. I am not suggesting you're wrong to use that term to apply to proofs. I just thought OP meant "problems" as in "computation problems" because that is what most kids see.

 

Moreover, I could easily leave the term "science" but that is a theoretical question. Does mathematics exist outside of spacetime? Is it sensical to speak about identity and the law thereof, without invoking a notion of space, which is to say, the material world? This is where theoretical physics, analytic metaphysics, logic, and mathematics overlap and I wouldn't be so hasty to say that math is not a science. However, I agree that it's debateable! "There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.^{[7][8]" (From Wikipedia, sorry :blushing: ).}

 

 

Quote

Mathematics includes theories about why numbers relation to each other in certain ways, and whether this is an intrinsic property of spatial and temporal relationships, or not.

 

Temporal relationships belong in the realm of physics. THAT is science. It may use math as a tool, but math itself knows no "time".

 

 

 

Now this conversation is getting exciting! Let us say that spatiotemporal relationships are outside the realm of 'pure' mathematics. What, then, do we mean when we say that a=a? Is it possible to conceive of quantity outside of spacetime? How do we know that our concept of quantity is not dependent upon our mental framework, which is structured to process sensory input in terms of space and time? Without time and space, there is no law of identity, as far as we know:

 

http://www.oberlin.edu/faculty/mwallace/LeibnizsLaw.html

 

All the qualities that you could name to me, are spatiotemporal. Even when we move from the metaphysics of God the Final Cause, to describe the attributes of God in a non-spatio-temporal sense is always a struggle. I personally read quite a bit about it and ultimately it was said to be a matter of faith, that all of our metaphors essentially "translated" a non-spatio-temporal god into human terms, but that we could not conceive of the true perfection of god, primarily because we could not get the non-spatio-temporal aspects. Whether it is possible to conceive of quantity or quality without appealing to nature is an ongoing, and extremely lively, philosophical debate.

 

I bring up god because god is the most familiar example of a non-spatio-temporal object to most people. There are other suppositions about non-spatio-temporal objects, particularly if by "space" one only refers to the three dimensions in which we experience our existence daily (without respect to those that we might be existing in, without realizing it on an everyday basis, or time). However, these are so theoretical that to use them as examples here would probably not be fruitful. The point is, just try to explain "1" without using a spatial example. (Spoiler alert: I've probably read a good 20 academic papers on whether or not this was possible and attempts to do so and arguments about whether or not it was done, and believe me, it's harder than you might think!)

 

 

 

Quote

BUT! And here is the cool part... you could ask someone to only explain how they would figure out the problem, and why they would do that, without actually solving it. This is not a mathematical "problem" in the sense that you are speaking about, right? It would consist of a theory about how quantities and time work.

While, in the academic sense, that might be considered a "problem" to solve, I think it is a good example of how you can have math without computation.

 

Exactly. But now you are contradicting yourself - see beginning of post.

 

 

No, I did not say that mathematics did not involve computation, which is a part of determining relationships between things. I did not intend these to be mutually exclusive categories. I was very clear that computation is a part of mathematics. We can distinguish between fruits and apples, but that does not mean an apple is not a fruit.

 

Regarding the use of the word "problem", that is why it is in quotes: because it serves as an example of the use of "problem" in the academic sense, it's not an example of a computation problem.

 

I believe that the OP's question is ultimately semantic so it's not going to be useful to continue on assuming terms. I think they should be defined, which I tried to do, though we may disagree on the definitions. Let's use your sense of "problem", by which, nearly everything in academia (not to mention life) is a "problem" and if you can produce a definition of mathematics I'm perfectly happy to use it.

 

I just don't want to go around in circles.

 

Incidentally, regarding the debate on math as a science: http://en.wikipedia.org/wiki/Mathematics#Mathematics_as_science :001_wub: Gödel...

[Joshin]

My two cents: If not problems, then solutions. Math is all about solutions (to real or imaginary problems, if you will). What math isn't  all about are algorithms. It's also about concepts and abstract problem-solving.

 

 

[duckens]

Math is not just problems.

 

Two phrases in our home:

 

1) Math is all about Patterns.

 

Whether you are seeing the pattern that when you add 1, you get the next number in the sequence, or whether you are graphing y=mx+b, math is about patterns.  We see the pattern in area equations: Area (of a circle) = pi * r * r .   We see it in Calculus when we take derivatives.  Math is all about patterns.

 

2) Math is the Language of Science.

 

We use these patterns to predict what will happen in our natural world.  How long will it take for an object to fall from a tower?  Using the rate the bacteria reproduce, at what point will you have a colony of 1 Billion?  How much force was in the bomb blast?  How much load can the building hold?  How much medicine do I need to heal this sick person?  How likely are twins to be alike in their likes and dislikes and habits?  How old is this bone?  And the standard: Two trains are on the same track, traveling towards each other......

 

We can predict these all because of Math.

 

 

Oh, I love math!!!!!!

 

[Nscribe]

Is literature nothing but reading?  Math clicked for real for me when I realized it was a language, expressing itself and the world in a way that is like a dialouge.  To this day I see a "problem" as a sentence...an expression of a question that needs to be responded to in the language spoken. FWIW

[Hunter]

Math is not just problems.

 

Two phrases in our home:

 

1) Math is all about Patterns.

 

Whether you are seeing the pattern that when you add 1, you get the next number in the sequence, or whether you are graphing y=mx+b, math is about patterns. We see the pattern in area equations: Area (of a circle) = pi * r * r . We see it in Calculus when we take derivatives. Math is all about patterns.

 

2) Math is the Language of Science.

 

We use these patterns to predict what will happen in our natural world. How long will it take for an object to fall from a tower? Using the rate the bacteria reproduce, at what point will you have a colony of 1 Billion? How much force was in the bomb blast? How much load can the building hold? How much medicine do I need to heal this sick person? How likely are twins to be alike in their likes and dislikes and habits? How old is this bone? And the standard: Two trains are on the same track, traveling towards each other......

 

We can predict these all because of Math.

 

 

Oh, I love math!!!!!!

This is all way over my head, but this is the kind of stuff I have heard in the past and just makes so much sense to me. I don't see math as a set of problems. I don't even see arithmetic as nothing but problems. I think of the discovery/development of the base 10 system as so fascinating and beautiful. I like solving problems, but the whole pattern stuff especially doesn't feel like problems to me. It just feels exciting and grounding at the same time, which is saying something, because they are basically opposites.

 

When I read How to Tutor, and the alphabet and the base 10 system are talked about in the same way, I just see glorious patterns. I am just a tad of an aspie, and patterns are...well...exciting and grounding as I already said. Whether they are math or phonics or something else.

 

So, yes, people need to define their terms, but "problems" just doesn't encompass what I feel. I feel something bigger, whether that bigger is just in my imagination I don't know.

 

As a child I taught myself to read by just decoding. I really wasn't given the resources or the idea that I could do the same with math, and then on top of that no one taught me any math. So without teaching or self-education, math lagged so far behind reading. In another life, I think I could have become a mathematician.

 

If I could send myself some things back in time, math resources would be at the top of my list.

[Farrar]

Hunter, might you enjoy a book like Here's Looking at Euclid?  It's a pop science book, but about math.

[Hunter]

Hunter, might you enjoy a book like Here's Looking at Euclid? It's a pop science book, but about math.

I put it on my Kindle wishlist. It looks good. Thanks!

 

Back before the brain damage and PTSD and with his help, my younger son and I used to try and go geometric constructions using the instructions written in Ancient Greek. How geeky is THAT? :lol:

[Hunter]

The website we used is still up.

 

http://mysite.du.edu/~etuttle/classics/nugreek/contents.htm

[Arcadia]

Back before the brain damage and PTSD and with his help, my younger son and I used to try and go geometric constructions using the instructions written in Ancient Greek. How geeky is THAT? :lol:

I'm having fun reading this pdf version of Euclid Elements which has the Greek and English translation side by side on each page.

http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf

 

My younger prefer the pictorial Oliver Bryne version

https://archive.org/details/firstsixbooksofe00byrn

 

My opinion is the Life is a puzzle and math just like anything else is a puzzle.  For me, an unsolved problem seems weird, an unsolved puzzle seems more logical.  Its just how I perceived things.

[Hunter]

I put it on my Kindle wishlist. It looks good. Thanks!

Back before the brain damage and PTSD and with his help, my younger son and I used to try and go geometric constructions using the instructions written in Ancient Greek. How geeky is THAT? :lol:

  

The website we used is still up.

http://mysite.du.edu/~etuttle/classics/nugreek/contents.htm

And here are the Loeb Classic greek math texts.

http://www.amazon.com/Greek-Mathematical-Works-Euclid-Classical/dp/0674993691

[Hunter]

I'm having fun reading this pdf version of Euclid Elements which has the Greek and English translation side by side on each page.

http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf

 

My younger prefer the pictorial Oliver Bryne version

https://archive.org/details/firstsixbooksofe00byrn

 

My opinion is the Life is a puzzle and math just like anything else is a puzzle. For me, an unsolved problem seems weird, an unsolved puzzle seems more logical. Its just how I perceived things.

Cool links. There is something so cool about doing math in greek.

[sunnyday]

Moreover, I could easily leave the term "science" but that is a theoretical question. Does mathematics exist outside of spacetime? Is it sensical to speak about identity and the law thereof, without invoking a notion of space, which is to say, the material world? This is where theoretical physics, analytic metaphysics, logic, and mathematics overlap and I wouldn't be so hasty to say that math is not a science. However, I agree that it's debateable! "There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.^{%5B7%5D%5B8%5D" (From Wikipedia, sorry :blushing: ).}

 

 

 

 

Now this conversation is getting exciting! Let us say that spatiotemporal relationships are outside the realm of 'pure' mathematics. What, then, do we mean when we say that a=a? Is it possible to conceive of quantity outside of spacetime? How do we know that our concept of quantity is not dependent upon our mental framework, which is structured to process sensory input in terms of space and time? Without time and space, there is no law of identity, as far as we know:

 

http://www.oberlin.edu/faculty/mwallace/LeibnizsLaw.html

 

All the qualities that you could name to me, are spatiotemporal. Even when we move from the metaphysics of God the Final Cause, to describe the attributes of God in a non-spatio-temporal sense is always a struggle. I personally read quite a bit about it and ultimately it was said to be a matter of faith, that all of our metaphors essentially "translated" a non-spatio-temporal god into human terms, but that we could not conceive of the true perfection of god, primarily because we could not get the non-spatio-temporal aspects. Whether it is possible to conceive of quantity or quality without appealing to nature is an ongoing, and extremely lively, philosophical debate.

 

I bring up god because god is the most familiar example of a non-spatio-temporal object to most people. There are other suppositions about non-spatio-temporal objects, particularly if by "space" one only refers to the three dimensions in which we experience our existence daily (without respect to those that we might be existing in, without realizing it on an everyday basis, or time). However, these are so theoretical that to use them as examples here would probably not be fruitful. The point is, just try to explain "1" without using a spatial example. (Spoiler alert: I've probably read a good 20 academic papers on whether or not this was possible and attempts to do so and arguments about whether or not it was done, and believe me, it's harder than you might think!)

 

Um, as I read this, you're lecturing to a theoretical physicist about the fact that theoretical physics is mathematics is science, by invoking the existence of God as proof that mathematics, like God, is a scientific construct independent of spacetime...???

 

FWIW, Keith Devlin's introduction that I linked above, defines mathematics as a science of patterns. I like that. 

[Pen]

What about something like the vibrations of two notes an octave apart?   That to me seems like a form of mathematics without a problem.   Explaining why would be a math problem, but experiencing it is already a mathematical experience with no problem.    ????

[Tsuga]

Um, as I read this, you're lecturing to a theoretical physicist about the fact that theoretical physics is mathematics is science, by invoking the existence of God as proof that mathematics, like God, is a scientific construct independent of spacetime...???

 

FWIW, Keith Devlin's introduction that I linked above, defines mathematics as a science of patterns. I like that.

It is supposed to be a discussion, not a lecture.

 

I'm not invoking the existence of god. If you read carefully, I'm discussing the conceptualization of things outside of space time. For the vast majority of people, the only object that they have heard of, which is not in space time, is the idea of a god as the final cause. I don't believe in god but I do think it is interesting that a great deal of progress in theoretical math and philosophy came about from trying to reconcile the idea of god as a cause, god as all-knowing and merciful, etc.

 

Finally, I did not say that theoretical physics IS mathematics IS science. There is a huge difference between an overlap in subject matter at one point (namely, what numbers refer to) and being the same thing.

 

I will engage in meaningful discussion but I am not going to explain myself if explanations are not read. It should be clear that there are many schools of thought regarding math but you must define your terms before beginning the debate.

[Amy in NH]

Math is a language.

[Belacqua]

Math is a language.

 

How much do I love that this was your 3000th post?

[EmilyGF]

Have you seen Math For Love?

 

I'd think they would argue it isn't all problems.

 

E

[Hunter]

I wanted to talk a bit more about "math is a language".

 

My ex-husband is a mathematical genius, but he learned very little math, or anything else in school. After he graduated, he self-educated a little math, but mostly designed his own math language to document the engineering he was doing in his head. No one could use his blueprints, because they were not comprehensible or worse yet, looked wrong, because he had used commonly used symbols to mean something else.

 

When I schooled my son, I insisted that he learn the common math symbols and vocabulary, and to learn to document what he was doing in his head, in this common language. He fought me a bit, but he understood a lot of our poverty was based on Daddy's inability to share math with other people. Daddy had to design and build everything himself from start to finish, rather than pool resources and machines and knowledge with others.

 

My son overheard other men venting in frustration about trying to work with him. He had such genius, but no one could understand his language, and he was too violent and arrogant to teach it to them, or even explain that it was one. And they didn't understand that an alternate language was "correct" as long as it was used consistently. I think one boss would have had the others workers learn the language if he had understood the potential of having them do so. I don't think even the boss understood the concept that "math is a language" and that there is more than one language. He only heard the men yelling about "right" and "wrong".

 

The exhausting day in and day out realities of poverty, partially caused by my ex only knowing an alternative math language has left an indelible understanding that math is a language, and that there is more than one language. Also my son did math in Greek and Latin, along with his classical language studies, and learned those math languages and their limitations.

 

In my ex's language, times 2 and squared meant the same thing! I still don't know what he used to mean squared. But cubed and so on meant the same thing as common language. To the power of 2 was a BIG problem though! Pi r squared meant pi r times 2 in ex's language. And these guys were building machines 3 stories high, so you can just imagine. And worse yet, were selling them to a Japanese company that was trying to read the blueprints. :lol:

[sunnyday]

It is supposed to be a discussion, not a lecture.

 

I'm not invoking the existence of god. If you read carefully, I'm discussing the conceptualization of things outside of space time. For the vast majority of people, the only object that they have heard of, which is not in space time, is the idea of a god as the final cause. I don't believe in god but I do think it is interesting that a great deal of progress in theoretical math and philosophy came about from trying to reconcile the idea of god as a cause, god as all-knowing and merciful, etc.

 

Finally, I did not say that theoretical physics IS mathematics IS science. There is a huge difference between an overlap in subject matter at one point (namely, what numbers refer to) and being the same thing.

 

I will engage in meaningful discussion but I am not going to explain myself if explanations are not read. It should be clear that there are many schools of thought regarding math but you must define your terms before beginning the debate.

 

It sounds pretty lecture-y, what with the "it's harder than you think"s and the "as far as we know"s (mmm, authoritative third person). I'm glad to hear that wasn't the intent.

 

Mathematics is abstract. That's...the whole point. We don't need to worry about whether we can conceptualize God without referring to spatial points of reference. We can just look to Plato's world of idealized forms and see that mathematical constructs have an existence independent of reality. You're referencing God as the only example of something that exists outside of spacetime, to someone who undoubtedly knows a little sumthin' about imaginary numbers and hypothetical dimensions. It's...a bit condescending from where I sit.

You countered the claim that mathematics should not be referred to as a science, by stating that theoretical physics, analytic metaphysics, logic, and mathematics overlap on the subject of identity, therefore it's hasty to state that math is not science. How is that not equating these subject areas, at least on the point of being scientifical or not, at least on the subject of the identity relation?

 

I dunno, I guess I just didn't come for the debate.

 

[wapiti]

From an art or puzzle angle, some of you might enjoy this little video tribute to Escher http://vimeo.com/36296951 (my dd's algebra teacher sent his students this link at the beginning of the school year)

[Pen]

:ph34r:

 

 

DS10's favorite drinking vessel....

 

:leaving:

 

 

Where did you get it?!!  I think my son would love one of those!

[Alte Veste Academy]

Where did you get it?!! I think my son would love one of those!

I got mine on ebay but that picture was from Amazon. http://www.amazon.com/gp/product/B00D61U1QI/ref=ox_sc_sfl_image_3?ie=UTF8&psc=1&smid=A3CNWJSYRKSPG Cafe Press had some too when I was looking.

[regentrude]

I wanted to talk a bit more about "math is a language".

...

In my ex's language, times 2 and squared meant the same thing! I still don't know what he used to mean squared. But cubed and so on meant the same thing as common language. To the power of 2 was a BIG problem though! Pi r squared meant pi r times 2 in ex's language.

 

I completely agree with you about the importance of using standard notation conventions, but that is not what math is.

The mathematical relationship that the area of a circle is pi multiplied by the square of the radius exists independent of notation. We could decide that denoting a square should be done by drawing a daisy on top of the number and that the symbol for pi is a mickey mouse - it would still be the same math!

 

The conventions used to communicate about mathematics are not what math is.

 

ETA: For the person who liked the language analogy: the conventions to capitalize the first letter in a sentence, to put a space between words, to shape the letters a certain way, or to use punctuation are not literature.

[Twigs]

:bigear:

[sunnyday]

I completely agree with you about the importance of using standard notation conventions, but that is not what math is.

The mathematical relationship that the area of a circle is pi multiplied by the square of the radius exists independent of notation. We could decide that denoting a square should be done by drawing a daisy on top of the number and that the symbol for pi is a mickey mouse - it would still be the same math!

 

The conventions used to communicate about mathematics are not what math is.

 

ETA: For the person who liked the language analogy: the conventions to capitalize the first letter in a sentence, to put a space between words, to shape the letters a certain way, or to use punctuation are not literature.

 

Or, I'm sure most of you have seen this, but the music analogy seems to hold up better than the language one, for me. Music is not the symbols you put on staff paper, even if consistency in your symbols does permit you to more clearly transmit the music you conceive of.

 

I'm sorry about your ex-husband's challenges and how they affected your family, Hunter. :(

[regentrude]

but the music analogy seems to hold up better than the language one, for me. Music is not the symbols you put on staff paper, even if consistency in your symbols does permit you to more clearly transmit the music you conceive of.

 

Great analogy!

 

[Hunter]

The mathematical relationship that the area of a circle is pi multiplied by the square of the radius exists independent of notation. We could decide that denoting a square should be done by drawing a daisy on top of the number and that the symbol for pi is a mickey mouse - it would still be the same math!

 

But most people do not know this. Instead of figuring this out, most people would just scream, "wrong" or "You can't do that!".

 

So we discover the math, but invent the notation?

 

If we change the base from 10 to 8, is just the notation different, or do we need to rediscover things?

 

Thank you SunnyDay. Hey, at least I learned something that I probably wouldn't have otherwise learned. I try to always see the silver linings in the clouds, even when it hurts.

[regentrude]

So we discover the math, but invent the notation?

 

We definitely invent the notation. But the question of whether we discover math or invent it is a tricky one.

Can we discover the concept of a "function", of negative numbers, of delta-function? I don't think so. Mathematicians can develop those concepts and then study the properties of the mathematical items and make a theory, and yes, that's where they can discover new relationships that must exist if the item behaves according to some mathematical framework.

 

But one can definitely adopt the POV that integers are the only thing that "naturally" exists, and all other math is invented to describe certain patterns. Algebra has been invented. Calculus too. they have not been "discovered".

[Hunter]

When my younger son was little, he used to take some of his work to show his grandfather to have some sort of outside validation. I was his teacher and his dad had no interest in his education. It was nice for him to get grandparent feedback as a form of "report card". His grandmother had zero understanding of algebra and anything past integers; it makes sense that some people struggle to transition here, if that is where you say we start to invent. She said she liked to look at his pages and pages of equations though. She told him they are "pretty". Thankfully his grandfather understood his work, past "pretty".

 

Math is pretty in so many ways. But I just cannot keep up with many of you. Being married to and raising mathematical genius introduced me to ideas, but I'm not equipped to fully understand what I was introduced to. I joked that in another life I maybe would have been a mathematician, but I probably would have quickly moved into applied math early on, or maybe computer programming.

[ladydusk]

Has anyone seen this? Diagramming Math Sentences. Fun. http://comparativelysuperlative.wordpress.com/2013/04/23/math-sentence-diagram/#comments

[kroe1]

You guys are way too philosophical for me.

 

Let me see if I can sum it all up for those of us philosophically challenged. In the fundamentalist sense, math is merely a problem solver. For those who choose to allow math a broader definition, it can also be a beautiful language predicting a sense of artistic order and repetition to life.

 

Have I got it?

[mama27]

Math sure has been nothing but problems for me most of my life but that's probably not what you meant.

[Hunter]

Has anyone seen this? Diagramming Math Sentences. Fun. http://comparativelysuperlative.wordpress.com/2013/04/23/math-sentence-diagram/#comments

:lol: