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I took a history of mathematics course at the University of Virginia. One of the I interesting things I learned was that people used to write out equations as s

I took a history of mathematics course at the University of Virginia. One of the I interesting things I learned was that people used to write out equations as sentences before symbolic notation was invented. And so you would realize that a single moderately large equation (such as the quadratic equation) might be equivalent to a full paragraph or more of text. So if you ever get discouraged at how long it takes you to read mathematics, remember that equations can be as information-dense as entire paragraphs, or even more so, and just because it is presented in a spatially compact format doesn't necessarily mean that it shouldn't take you at least as long as a text paragraph to read and comprehend.

JumpCrisscross 14y ago
Happen to remember the text you used?
- Dn_Ab 14y ago
  I've read a couple of texts on the history of math. Most of them were dry, a few were very entertaining like Crowe's on Vector Analysis. But I haven't found anything that beats mac tutor. I used to read it nearly everyday many years back. The section on Al-Khwarizmi, a key innovator in algebra shows how laborious the task was (site down linking cache): http://webcache.googleusercontent.com/search?q=cache:nOT6h0c7J2oJ:www-history.mcs.st-andrews.ac.uk/Biographies/Al-Khwarizmi.html+&cd=1&hl=en&ct=clnk http://webcache.googleusercontent.com/search?q=cache:nOT6h0c... a square and 10 roots are equal to 39 units. The question therefore in this type of equation is about as follows: what is the square which combined with ten of its roots will give a sum total of 39? The manner of solving this type of equation is to take one-half of the roots just mentioned. Now the roots in the problem before us are 10. Therefore take 5, which multiplied by itself gives 25, an amount which you add to 39 giving 64. Having taken then the square root of this which is 8, subtract from it half the roots, 5 leaving 3. The number three therefore represents one root of this square, which itself, of course is 9. Nine therefore gives the square.
- rcthompson 14y ago
  I'm sure I have the text lying around somewhere. I can't remember the title and author, but in any case the text was just a compilation of relevant excerpts from primary sources to be used as reference. It didn't provide any analysis. All the analysis was provided by the professor, Karen Parshall, whose courses I can enthusiastically recommend for anyone at U.Va. interested in the history of math or science (bonus: they satisfy your 2nd writing requirement). Her website is here: http://www.math.virginia.edu/~khp3k/ http://www.math.virginia.edu/~khp3k/ I credit her for pointing out the fact that I note in my original comment, that an equation can be equivalent to a large tract of text. She made the point in the context of why more "advanced" mathematics couldn't have developed before symbolic notation had matured sufficiently to support it. Here, I'm generalizing her point to explain why reading a mathematical text dense in equations might take longer than the page count alone might suggest.
- jacobolus 14y ago
  This book is pretty good: http://www.amazon.com/The-Nature-Growth-Modern-Mathematics/dp/0691023727 http://www.amazon.com/The-Nature-Growth-Modern-Mathematics/d... For original source material (more essays than papers, but a pretty big mix of stuff), this set is fabulous: http://www.amazon.com/The-World-Mathematics-Four-Volume-Set/dp/0486432688 http://www.amazon.com/The-World-Mathematics-Four-Volume-Set/... Both can be found pretty cheap used online.
- tylerneylon 14y ago
  I took a course that used this book (Boyer and Merzbach, A History of Mathematics), which I enjoyed: http://www.amazon.com/A-History-Mathematics-Second-Edition/dp/0471543977/ http://www.amazon.com/A-History-Mathematics-Second-Edition/d...
alister 14y ago
> equations can be as information-dense as entire paragraphs And generally the equation is easier to understand than the same thing written in prose. But did you notice this from the original article: “When you add consecutive numbers starting with 1, and the number of numbers you add is odd, the result is equal to the product of the middle number among them times the last number.” (Levi’s theorem) It's one of those rare cases where the English is much easier to understand than the equation.
- lusr 14y ago
  The problem I have with the way equations are often presented e.g. on Wikipedia is that the authors are so focused on conciseness that they don't stop to explain the idea in straightforward terms. For example, a while ago I was looking into the Radon Transform. The wikipedia page is full of concise technical explanations and equations: http://en.wikipedia.org/wiki/Radon_transform http://en.wikipedia.org/wiki/Radon_transform After reading a number of articles and eventually stumbling across one on MathWorks (http://www.mathworks.com/help/toolbox/images/f21-25938.html http://www.mathworks.com/help/toolbox/images/f21-25938.html) with some great worked out examples I immediately got the idea: if you put your x-ray glasses on and look at an object from many different angles, and make note of what you're seeing at each angle, you can use your notes to rebuild the image or figure out how similar this object is to another object. Pretty intuitive. With that understanding of the idea, the Wikipedia article made much more sense. Most mathematics is only difficult for me because I spend all my time trying to understand why the author is " the integral transform consisting of the integral of a function over straight lines". Once I get that, the rest is straightforward.
  - AlexDanger 14y ago
    +1 absolutely agree. Wikipedia is terrible for learning mathematical concepts, not surprising given that its a reference site. Its appropriate to be concise in this context. People are getting excited about education being an area ripe for disruption. What about a site that rips all the Wikipedia maths topics and allows people to add some worked examples and arrange the content to be more pedagogically pleasing? Providing a nice little HTML5 widget toolbox to create simple interactive visualisations would be cool...

JumpCrisscross 14y ago

Happen to remember the text you used?

Dn_Ab 14y ago
I've read a couple of texts on the history of math. Most of them were dry, a few were very entertaining like Crowe's on Vector Analysis. But I haven't found anything that beats mac tutor. I used to read it nearly everyday many years back. The section on Al-Khwarizmi, a key innovator in algebra shows how laborious the task was (site down linking cache): http://webcache.googleusercontent.com/search?q=cache:nOT6h0c7J2oJ:www-history.mcs.st-andrews.ac.uk/Biographies/Al-Khwarizmi.html+&cd=1&hl=en&ct=clnk http://webcache.googleusercontent.com/search?q=cache:nOT6h0c... a square and 10 roots are equal to 39 units. The question therefore in this type of equation is about as follows: what is the square which combined with ten of its roots will give a sum total of 39? The manner of solving this type of equation is to take one-half of the roots just mentioned. Now the roots in the problem before us are 10. Therefore take 5, which multiplied by itself gives 25, an amount which you add to 39 giving 64. Having taken then the square root of this which is 8, subtract from it half the roots, 5 leaving 3. The number three therefore represents one root of this square, which itself, of course is 9. Nine therefore gives the square.
rcthompson 14y ago
I'm sure I have the text lying around somewhere. I can't remember the title and author, but in any case the text was just a compilation of relevant excerpts from primary sources to be used as reference. It didn't provide any analysis. All the analysis was provided by the professor, Karen Parshall, whose courses I can enthusiastically recommend for anyone at U.Va. interested in the history of math or science (bonus: they satisfy your 2nd writing requirement). Her website is here: http://www.math.virginia.edu/~khp3k/ http://www.math.virginia.edu/~khp3k/ I credit her for pointing out the fact that I note in my original comment, that an equation can be equivalent to a large tract of text. She made the point in the context of why more "advanced" mathematics couldn't have developed before symbolic notation had matured sufficiently to support it. Here, I'm generalizing her point to explain why reading a mathematical text dense in equations might take longer than the page count alone might suggest.
jacobolus 14y ago
This book is pretty good: http://www.amazon.com/The-Nature-Growth-Modern-Mathematics/dp/0691023727 http://www.amazon.com/The-Nature-Growth-Modern-Mathematics/d... For original source material (more essays than papers, but a pretty big mix of stuff), this set is fabulous: http://www.amazon.com/The-World-Mathematics-Four-Volume-Set/dp/0486432688 http://www.amazon.com/The-World-Mathematics-Four-Volume-Set/... Both can be found pretty cheap used online.
tylerneylon 14y ago
I took a course that used this book (Boyer and Merzbach, A History of Mathematics), which I enjoyed: http://www.amazon.com/A-History-Mathematics-Second-Edition/dp/0471543977/ http://www.amazon.com/A-History-Mathematics-Second-Edition/d...

alister 14y ago

> equations can be as information-dense as entire paragraphs And generally the equation is easier to understand than the same thing written in prose. But did you notice this from the original article: “When you add consecutive numbers starting with 1, and the number of numbers you add is odd, the result is equal to the product of the middle number among them times the last number.” (Levi’s theorem) It's one of those rare cases where the English is much easier to understand than the equation.

lusr 14y ago
The problem I have with the way equations are often presented e.g. on Wikipedia is that the authors are so focused on conciseness that they don't stop to explain the idea in straightforward terms. For example, a while ago I was looking into the Radon Transform. The wikipedia page is full of concise technical explanations and equations: http://en.wikipedia.org/wiki/Radon_transform http://en.wikipedia.org/wiki/Radon_transform After reading a number of articles and eventually stumbling across one on MathWorks (http://www.mathworks.com/help/toolbox/images/f21-25938.html http://www.mathworks.com/help/toolbox/images/f21-25938.html) with some great worked out examples I immediately got the idea: if you put your x-ray glasses on and look at an object from many different angles, and make note of what you're seeing at each angle, you can use your notes to rebuild the image or figure out how similar this object is to another object. Pretty intuitive. With that understanding of the idea, the Wikipedia article made much more sense. Most mathematics is only difficult for me because I spend all my time trying to understand why the author is " the integral transform consisting of the integral of a function over straight lines". Once I get that, the rest is straightforward.
- AlexDanger 14y ago
  +1 absolutely agree. Wikipedia is terrible for learning mathematical concepts, not surprising given that its a reference site. Its appropriate to be concise in this context. People are getting excited about education being an area ripe for disruption. What about a site that rips all the Wikipedia maths topics and allows people to add some worked examples and arrange the content to be more pedagogically pleasing? Providing a nice little HTML5 widget toolbox to create simple interactive visualisations would be cool...