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Why Mathematics is Boring (2007) [pdf]

math.ucr.edu

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Re: Why Mathematics is Boring (2007) [pdf]

#51

Post by Levitz »

datastoat wrote: post #13
abdullahkhalids wrote: post #3

If you read any science papers, they start with a clear introduction with the aims, claims, importance and novelty of the work. A lot of math papers (but not all) just start off with a dry statement of what the theorems being proved are, and jump right into the proofs. I always wonder why editors don't understand the importance of these things and don't enforce them.

Relatedly, a lot of recipe books just have a dry statement of what the ingredients are and how to combine them. They should be more like CS and science papers, and explain the narrative of why the recipe is exciting, and where it comes from, and what it means for the cook. (Posted from a parallel universe.)

As other user commented, cooking books meant to be read rather than used as reference material are actually written like that.

Makes me wonder if that's the difference, do people not check math papers unless they are specifically interested in that very proof or such?

Re: Why Mathematics is Boring (2007) [pdf]

#52

Post by robomartin »

GDC7 wrote: post #27
robomartin wrote: post #23

Earlier quoted context omitted.

Yes, of course. BTW, I don't think my comment covered the fact that I agree with you 100% on the impenetrability of mathematical notation. That said, all notations --including the written alphabets of many spoken languages-- are impenetrable until you learn them. As a personal example, for me, learning French and German was a million times easier than learning Chinese and Japanese. In the first two cases I could read…

> It took less than a minute to explain that this just means a sequence of sums, maybe ten seconds. I just wrote down something like: "(a0 * b0) + (a1 * b1) + ... + (an * bn)" and said: "This is what it means. Summation". Done. I think the real world feedback is quite different, given that math can be explained textually with words , why should we not do it? The burden of the proof is always on the institution trying…

I think the notation is very much needed because it quickly becomes a tool for thought and communication. This is very much the case for every spoken language and other areas, such as music. Your point, which is quite correct, is that the math might not be explained well enough and internalized to the extent where the notation becomes a language for students beyond the simplest levels of mathematics.

A kid can learn the notation for whole, 1/4, 1/8, etc. musical notes and their positions on the staff very easily. An immediate relationship is created to the key on the piano or the fret on the guitar. I have been to math classes where the professor simply vomits formulas on the blackboard for one hour and you are left to figure out what they hell happened. That is a problem. Not the notation. The way math is taught.

Re: Why Mathematics is Boring (2007) [pdf]

#53

Post by BeFlatXIII »

abdullahkhalids wrote: post #3

If you read any science papers, they start with a clear introduction with the aims, claims, importance and novelty of the work. A lot of math papers (but not all) just start off with a dry statement of what the theorems being proved are, and jump right into the proofs. I always wonder why editors don't understand the importance of these things and don't enforce them.

> importance and novelty of the work

That's there for playing the grant funding game. It's a waste for people who care about the content of the research.

Re: Why Mathematics is Boring (2007) [pdf]

#54

Post by Jensson »

abdullahkhalids wrote: post #3

If you read any science papers, they start with a clear introduction with the aims, claims, importance and novelty of the work. A lot of math papers (but not all) just start off with a dry statement of what the theorems being proved are, and jump right into the proofs. I always wonder why editors don't understand the importance of these things and don't enforce them.

You are assuming that the paper is important or novel. Maybe they just created some dry theorems and have nothing more to day? The time I spent at a math institution tells me that many of them doesn't know or care about why or how their work matters.

Re: Why Mathematics is Boring (2007) [pdf]

#55

Post by GDC7 »

robomartin wrote: post #52
GDC7 wrote: post #27

Earlier quoted context omitted.

> It took less than a minute to explain that this just means a sequence of sums, maybe ten seconds. I just wrote down something like: "(a0 * b0) + (a1 * b1) + ... + (an * bn)" and said: "This is what it means. Summation". Done. I think the real world feedback is quite different, given that math can be explained textually with words , why should we not do it? The burden of the proof is always on the institution trying…

I think the notation is very much needed because it quickly becomes a tool for thought and communication. This is very much the case for every spoken language and other areas, such as music. Your point, which is quite correct, is that the math might not be explained well enough and internalized to the extent where the notation becomes a language for students beyond the simplest levels of mathematics. A kid can learn…

> A kid can learn the notation for whole, 1/4, 1/8, etc. musical notes and their positions on the staff very easily. An immediate relationship is created to the key on the piano or the fret on the guitar

I don't know about that. How many people can read music?

But also music, much like Chinese and Japanese is at a comparative disadvantage compared to math because there are no other tools to explain how high or low a note is.

You can use words to explain math, just like you did with your son.

Internalization is key, if you miss the window as a kid then it's gonna be an uphill battle and life being complicated as it is would mean people giving up on it.

And real world feedback is telling us that such window will be missed, that's why I had thought about math being always explained using the familiar English language which is almost always never missed as a kid.

Re: Why Mathematics is Boring (2007) [pdf]

#56

Post by Jensson »

amcoastal wrote: post #12
_Microft wrote: post #9

Earlier quoted context omitted.

The idea that unfamiliar symbols and alphabets are a huge problem for the accessibility of math is common. As physicist I do not agree. Math is hard. It's damned difficult. Symbols and alphabets are the least of your concerns when dealing with a math paper. I know a lot of these symbols by name, I sometimes understand the notation or could familiarize myself with it but the math itself? Nope, no chance, usually. If o…

I'll disagree. I read many papers with mathematics in them, and I get a lot of the concepts but the symbology used doesn't make sense to me so its hard for me to understand what is exactly going on. The sentence after the equation that explains each symbol is necessary for me, and many others as well. Not everyone has taken 8 math classes to know each kroniger delta by heart.

> I read many papers with mathematics in them

That is the problem, non-mathematicians usually doesn't fully understand the math they use in their papers and thus the math becomes opaque. Papers written by real mathematicians are usually much easier to read, although of course the math in them is much much harder.

Re: Why Mathematics is Boring (2007) [pdf]

#57

Post by abdullahkhalids »

enriquto wrote: post #25
taneq wrote: post #20

Earlier quoted context omitted.

As a non-mathematician this seems to be lacking a little something. Would you not want your paper to provide some indication of what you're attempting to communicate and why? Or is that information (as the joke goes) possible, and therefore trivial, to infer?

A great deal of maths is that you get to use theorems for purposes that they were not intended for. Presenting the theorem in a "pure" form thus allows to approach it without pre-conceptions. I love the analogy with cooking recipes in another comment. Math papers are like recipe books, deliberately devoid of their social context. The same recipe may mean different things to different cooks, even contradictory! Having…

> A great deal of maths is that you get to use theorems for purposes that they were not intended for. Presenting the theorem in a "pure" form thus allows to approach it without pre-conceptions.

Plenty of physics papers end up being useful in ways the authors never conceived. I don't think the authors writing down their best guess of the importance of their results, prevents others from using the results or techniques in alternate ways. In fact, I frequently see this happening.

But the authors writing down their best guess of the importance of their results helps others judge the minimum importance of the results, and decide whether they want to read the paper in the first place.

Re: Why Mathematics is Boring (2007) [pdf]

#58

Post by enriquto »

abdullahkhalids wrote: post #57
enriquto wrote: post #25

Earlier quoted context omitted.

A great deal of maths is that you get to use theorems for purposes that they were not intended for. Presenting the theorem in a "pure" form thus allows to approach it without pre-conceptions. I love the analogy with cooking recipes in another comment. Math papers are like recipe books, deliberately devoid of their social context. The same recipe may mean different things to different cooks, even contradictory! Having…

> A great deal of maths is that you get to use theorems for purposes that they were not intended for. Presenting the theorem in a "pure" form thus allows to approach it without pre-conceptions. Plenty of physics papers end up being useful in ways the authors never conceived. I don't think the authors writing down their best guess of the importance of their results, prevents others from using the results or techniques…

> But the authors writing down their best guess of the importance of their results helps others judge the minimum importance of the results, and decide whether they want to read the paper in the first place.

In many cases it will be unlikely that the authors even know the importance of the results. Forcing them to come up with an explanation would be useless at best, and an unbearable burden at worst (e.g., when a student has proved a theorem proposed by his advisor).

There are mathematical reviews, where mathematicians with a higher-level view on the field point to particular papers and explain their importance. Also, many journals have an editorial column that explains the papers on each issue.

Re: Why Mathematics is Boring (2007) [pdf]

#59

Post by Jtsummers »

GDC7 wrote: post #27
robomartin wrote: post #23

Earlier quoted context omitted.

Yes, of course. BTW, I don't think my comment covered the fact that I agree with you 100% on the impenetrability of mathematical notation. That said, all notations --including the written alphabets of many spoken languages-- are impenetrable until you learn them. As a personal example, for me, learning French and German was a million times easier than learning Chinese and Japanese. In the first two cases I could read…

> It took less than a minute to explain that this just means a sequence of sums, maybe ten seconds. I just wrote down something like: "(a0 * b0) + (a1 * b1) + ... + (an * bn)" and said: "This is what it means. Summation". Done. I think the real world feedback is quite different, given that math can be explained textually with words , why should we not do it? The burden of the proof is always on the institution trying…

> Given that (unlike foreing languages) math can be explained WITHOUT having to teach a new notation, then why don't we do it?

Can you explain, say, orbital mechanics, without math notation? In a way where someone can determine where a satellite will be at a particular time given its position and velocity at a prior time taking into account disturbances to the ideal orbit caused by the Moon and Sun (we'll stick with just those 2 and pretend the Earth itself is a perfect sphere).

I don't mean explain in a pop-sci sense. That's actually feasible with very little math (though you will probably want some diagrams), I mean explain in a way that the audience can then apply this math-but-not-in-math-notation to solve real world problems.

Re: Why Mathematics is Boring (2007) [pdf]

#60

Post by GDC7 »

Jtsummers wrote: post #59
GDC7 wrote: post #27

Earlier quoted context omitted.

> It took less than a minute to explain that this just means a sequence of sums, maybe ten seconds. I just wrote down something like: "(a0 * b0) + (a1 * b1) + ... + (an * bn)" and said: "This is what it means. Summation". Done. I think the real world feedback is quite different, given that math can be explained textually with words , why should we not do it? The burden of the proof is always on the institution trying…

> Given that (unlike foreing languages) math can be explained WITHOUT having to teach a new notation, then why don't we do it? Can you explain, say, orbital mechanics, without math notation? In a way where someone can determine where a satellite will be at a particular time given its position and velocity at a prior time taking into account disturbances to the ideal orbit caused by the Moon and Sun (we'll stick with…

Again, you are assuming that math is only done at the frontier.

I don't care about the frontier, I care about improving standards of living and quality of life, and that you can do by moving the needle in a concrete manner for HS and college math proficiency.

Not to mention that the satellite operations you mention will benefit a lot thanks to a higher standards of living/quality of life which are synthetized in the GDP metric.

One can only imagine the GDP growth that would happen if math proficiency levels were to suddenly become on par with coastal China.

At that point the satellite operations you'd speak of would become much smoother without even needing to move the math frontier forward.

You'd see collapsing costs everywhere ranging from personnel, raw materials, building operations, security and so forth.

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