Mathematicians kick away the ladder

[g.lemaitre]

Definition: to kick away the ladder: to rely on someone else for help, then when you get to the top and don't need help anymore you kick away the ladder so that no one else can get the help you received.

This is what mathematicians do. Math textbooks are written in a highly opaque, jargon-laden style so much so that you need a private tutor to sit down with you and tell you what it means. As the student finally gets the hang of it, and becomes a full-fledged mathematician rather than write textbooks so that beginners can understand it and won't be in need of a private tutor they instead kick away the ladder so that anyone else who reads it will have to resort elsewhere in order to get the hang of it.

Here's a quote from Peter Woit that backs up directly what I'm saying:

The culture of mathematics values highly precision, rigor, and abstraction, not the sort of imprecise motivational material and carefully worked out examples that make a subject accessible to someone from the outside trying to get some idea of what is going on. This makes the research literature often impenetrable to all but those already expert in a field. There is often a somewhat intellectually macho attitude among some mathematicians, an attitude that since they overcame great hurdles to understand something, there’s no reason to make it easier and encourage others less talented and dedicated than themselves

 

[pwsnafu]

This is true of all academia: you're target audience are your colleagues, not students. You can't just pick up a book on physical chem without having done basic chem and physics. And no, it is not the job of academia to make it accessible. By the time you are at university you should have your own motivations to do the work.

 

[Stephen Tashi]

There is often a somewhat intellectually macho attitude among some mathematicians, an attitude that since they overcame great hurdles to understand something, there’s no reason to make it easier and encourage others less talented and dedicated than themselves.

You find some people with that outlook in all technical fields - and you find similar complaints: "Why isn't configuring Linux systems explained simply/ Why isn't there a book that will teach me to be a chess master? Why isn't there a book that shows me how to draw well?".

When it comes to encouraging those less talented and dedicated, there are some people that take an interest in doing that and others that say "What's the point?". There are arguments for both outlooks.

I suppose it's theoretically possible to write a "...for Dummies" book on any complicated technical subject, but writing such a book is not a trivial endeavor and few people who understand technical subjects are also talented writers. I think people who expect to find simple step-by-step instructions for doing sophisticated things like discovering mathematical proofs or drawing portraits are naive. If you think that mathematics is "really simple" and not innately sophisticated then you have cause for complaint.

 

[Number Nine]

This is what mathematicians do. Math textbooks are written in a highly opaque, jargon-laden style so much so that you need a private tutor to sit down with you and tell you what it means.

I've never had this problem. There are a few bad textbooks in different branches of mathematics, but I've never had any trouble finding a good explanation for what I needed to know. Modern mathematics is intrinsically rigorous and abstract; you have to work at it, and nothing is going to change that.

 

[pwsnafu]

not the sort of imprecise motivational material and carefully worked out examples that make a subject accessible to someone from the outside trying to get some idea of what is going on

Except these books do exist in their relevant fields. If you pick up a good textbook in inorganic chemistry, it will list all the representations of the symmetry groups a chemist will need. It will have a section with explains all the group theory a chemist needs.

A book on encryption will teach group and ring theory. And so on.

And then you have books like Five Golden Rules which is aimed at the general public. There's no shortage of these.

 

[Jolb]

This isn't a new phenomenon, either. C. F. Gauss was notorious for stripping away all traces of how he came up with his ideas before he would publish.

There is a reason for this, however. If a mathematical result is correct, it often contains subtleties that even the author has not yet fully grasped. If the author includes whatever "aides" he used to formulate the result, these aides might cause the reader to miss out on the greater generality that the result has. In other words, if you include a picture to explain your mathematical result, there is a great likelihood that the picture is a somewhat incomplete or inaccurate, and if the author puts a picture into the reader's head, the reader might not find his own new (and possibly productive) way of looking at it.

 

[chiro]

This is just not true in general although it does exist.

There are books out there that take a more casual approach and explain exactly what it is they are trying to do and what the point of the book/article/whatever is in English.

I've just finished reading a few monographs in statistics and the first part of the monograph goes into detail exactly what the whole thing is about, why it's useful, and how it's used.

The demand for these kinds of expositions is increasing and some of the demand is being met. These monographs do require knowledge of statistics, but the point is that the goal of the work and what it sets out to achieve is in plain english and not in a whole bunch of greek symbols.

The other thing is that there are "For dummies" books on very technical topics like Quantum Field Theory, but they have a completely different goal in mind in comparison to say a graduate textbook on QFT.

Also, remember that if one source doesn't do this, a combination of sources may do.

 

[micromass]

There are indeed quite some textbooks which do not give intuition at all. Rudin comes to mind as an example. But Rudin is not the sort of text to learn the material from, it is more a text to learn it for a second time. As such, Rudin is an awesome book.

So perhaps the problem is that you're trying to tackle too advanced books? I noticed that you said in a previous thread that Stewart was hard for you. If that's the case, then advanced math books are not for you yet.

Also, how do you do math?? Math is not a spectator sport. Just reading something over and over again is not going to teach you math. You'll have to actually do the work. You'll have to actively find examples and counterexamples to theorems. You'll have to do a lot of exercises (and not just computational exercises). You'll have to draw pictures to guide your intuition. You'll have to make your own conjectures and ponder on them.

This is the only way to properly learn mathematics. Reading a text is not sufficient. Yes, this takes a lot of time. But there is not other way.

Here's a nice quote by Paul Halmos on reading mathematics:

Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?

 

[chill_factor]

This is true of all academia: you're target audience are your colleagues, not students. You can't just pick up a book on physical chem without having done basic chem and physics. And no, it is not the job of academia to make it accessible. By the time you are at university you should have your own motivations to do the work.

except for Atkin's Quanta, Matter and Change book which I think was really poorly written, I think most physical chemistry books are easy to read.

 

[g.lemaitre]

Also, how do you do math??

I really have no way of knowing since I don't take any tests and I'm completely isolated so I can't compare myself to other students. However, it is true that I often have to stare at a text for about 3 minutes before I get it and that happens quite a lot, so I'm guessing that there is something that does not click naturally for me.

I was getting a little discouraged with math, however, richard hill's text on linear algebra has restored my confidence and I'm cruising again. That said, in about 3 months I'm going to put my path studies on hold indefinitely since i have other projects in the humanities that i want to complete.

 

[genericusrnme]

Definition: to kick away the ladder: to rely on someone else for help, then when you get to the top and don't need help anymore you kick away the ladder so that no one else can get the help you received.

This is what mathematicians do. Math textbooks are written in a highly opaque, jargon-laden style so much so that you need a private tutor to sit down with you and tell you what it means. As the student finally gets the hang of it, and becomes a full-fledged mathematician rather than write textbooks so that beginners can understand it and won't be in need of a private tutor they instead kick away the ladder so that anyone else who reads it will have to resort elsewhere in order to get the hang of it.

I've never had this problem with maths textbooks.. True, some are written pretty badly, I don't think that the intent was to make it hard for others to understand - it's just that once you understand a subject it's hard to step back and look at it as if you didn't understand it which leads to writing a textbook like baby rudin. Most textbooks I've read have been pretty nice, even some of the bourbaki books which have a reputation for being super rigorous and abstract.

I really have no way of knowing since I don't take any tests and I'm completely isolated so I can't compare myself to other students. However, it is true that I often have to stare at a text for about 3 minutes before I get it and that happens quite a lot, so I'm guessing that there is something that does not click naturally for me.

3 minutes is pretty quick, you shouldn't expect to breeze through a textbook without having to pause and think every few pages.

 

[g.lemaitre]

3 minutes is pretty quick, you shouldn't expect to breeze through a textbook without having to pause and think every few pages.

I meant a paragraph of text or a text that describe a problem. It's probably more like 10 minutes.

 

[jgens]

I meant a paragraph of text or a text that describe a problem. It's probably more like 10 minutes.

This still is not very long. Why do you think 10 minutes a page is slow?

 

[g.lemaitre]

This still is not very long. Why do you think 10 minutes a page is slow?

Because when reading philosophy, physics, biology or psychology I rarely have to do that.

 

[Hurkyl]

Because when reading philosophy, physics, biology or psychology I rarely have to do that.

But maybe you should be spending 10 minutes a page! e.g. while you can often read a philosophical argument as if it were a short story, you certainly aren't going to learn much by doing so.

 

[g.lemaitre]

But maybe you should be spending 10 minutes a page! e.g. while you can often read a philosophical argument as if it were a short story, you certainly aren't going to learn much by doing so.

Not really. You can understand what's going on in philo by reading it straight through. I know this is true because I'm not asking myself what's going on here, whereas in math I often have to ask myself what's going on.

 

[Hurkyl]

Not really. You can understand what's going on in philo by reading it straight through. I know this is true because I'm not asking myself what's going on here, whereas in math I often have to ask myself what's going on.

Without analyzing what you read (or some other sort of active learning), you can only gain superficial knowledge at best. What are the strengths of a philosophical argument? What are its weaknesses? In what context is it being made? What parts are the central ideas and what parts are fluff? Can you refute the points of the argument? What would the rebuttals be? Are the ideas applicable elsewhere? You don't get answers to these questions simply by reading it straight through.

 

[g.lemaitre]

Without analyzing what you read (or some other sort of active learning), you can only gain superficial knowledge at best. What are the strengths of a philosophical argument? What are its weaknesses? In what context is it being made? What parts are the central ideas and what parts are fluff? Can you refute the points of the argument? What would the rebuttals be? Are the ideas applicable elsewhere? You don't get answers to these questions simply by reading it straight through.

Don't worry, I get it. I've written quite a lot of philo essays for fun. Plus I actually read 10% of each book 3 times. I didn't feel like going into this because it sounds like bragging, but I digitize all the books I read with my homemade book scanner. I can scan a 400 page book in 20 minutes. then as i read through i put a symbol on the beginning of a key passage and a symbol at the end. when I'm done with the click of one button my macro built for MS word will pick out all the important passages, usually about 10% of the book. I will then reread them a second time, then with my text to voice software I will listen to them a 3rd time in the car. that homemade book scanner has enabled me to increase my learning experience by about 5 times. if you're interested, even though you can't do it with math books check out diybookscanner.org

 

[micromass]

I don't quite get how you can read physics books while only spending 10 minutes on each page. I think you're not doing it right.

Mathematics and physics are sciences which have a very high signal-to-noise ratio. When reading a math book, every single sentence is important and can contain vital information. Even books which are considered very wordy and verbose have a very high signal-to-noise ratio.
Humanities texts are very different. I've seen texts where they literally spend pages after pages making a single point. In the end, I could summarize a text of 300 pages in a 10 page word document. This is of course not possible with math texts (or even physics books).

I'll make my point again: you cannot read a math book. You have to fight a math book. You have to think about it. You have to make pictures. You have to make mindmaps. You have to work out arguments for yourself. You have to connect all the little dots in a text. This will take you way more than 10 minutes each page.

 

[coolul007]

This is the "Country Club" syndrome, one tries all ways to get excepted as a member, then as a member your efforts are to keep others out. It is practiced daily on freeways, in commute traffic, people try to keep you from getting on the freeway, then once on, you do the same. I find this most annoying in proofs.

 

[jgens]

Because when reading philosophy, physics, biology or psychology I rarely have to do that.

It is a fallacy to think that a mathematics text ought to read anything like a work of philosophy or physics.

 

[Dembadon]

Definition: to kick away the ladder: to rely on someone else for help, then when you get to the top and don't need help anymore you kick away the ladder so that no one else can get the help you received.

This is what mathematicians do. Math textbooks are written in a highly opaque, jargon-laden style so much so that you need a private tutor to sit down with you and tell you what it means. As the student finally gets the hang of it, and becomes a full-fledged mathematician rather than write textbooks so that beginners can understand it and won't be in need of a private tutor they instead kick away the ladder so that anyone else who reads it will have to resort elsewhere in order to get the hang of it.

Here's a quote from Peter Woit that backs up directly what I'm saying:

It would be more accurate to say "insecure egotists kick away the ladder." I've yet to meet a professor who isn't eager to help a genuinely interested student understand difficult concepts.

 

[Vanadium 50]

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