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What's the point of dropping the multiplication sign before a parenthesis? Sure,2(5+5) is shorter than 2*(5+5) - but I prefer readability before shortness - especially when someone else will be reading my calculations.

Is there something that I am missing; or does just people disagree with me? Argue on, if that is the case.

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Just to reduce the clutter of unnecessary notation. We agree that juxtaposition denotes multiplication unless ambiguity arises. So. e.g. $2\cdot3$ or $(2)(3)$, but not $2\,3$. –  David Mitra Jan 17 '12 at 22:54
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Your argument presupposes that $2\cdot(5+5)$ is more readable than $2(5+5)$. I don't see why it is. –  joriki Jan 17 '12 at 22:54
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Depends. To an audience with a fairly good mathematical background, the dots would be a nuisance, distracting. –  André Nicolas Jan 17 '12 at 22:58
    
The place where ambiguity can arise is when you are dealing with functions as well as numbers: does $a(b+c)$ mean $a$ multiplied by $b+c$ or the function $a$ evaluated at $b+c$? Context is generally used to decide (which is why this sort of parsing is hard for computers). –  Robert Israel Jan 17 '12 at 23:30
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To a programming audience, the * is important. To a purely mathematical audience it is not. Multiplication by juxtaposition notation is pretty universal in the math world with some notable exceptions. In the computing world, juxtaposition is not multiplication, since most symbols have more than one character in them. –  ncmathsadist Jan 17 '12 at 23:33

2 Answers 2

up vote 4 down vote accepted

People can and do argue in favor of one way over the other via aesthetics, but if you're looking for a point, there is none. Mathematical notation has grown in fits and spurts based on authors and fashions of the times. Some innovations catch on; others languish and are forgotten.

I hypothesize, along with David Mitra and Robert Israel, that a mathematical author introduced it in a paper one day, and it caught on with other mathematicians because it saved them a symbol. While we can argue over the causes, it is the way it is by an accident of history.

According to Doctor Peterson of The Math Forum, using juxtaposition to denote multiplication arises out of the spoken form of saying $2x$ as "two-ex".

Jeff Miller says that this can be found as early as the 15th century in Europe, and as early as the 10th century in India. The cross $\times$, dot $\cdot$ and asterisk * are first attested in the 17th century.

You can read more about the history of mathematical notation at Wikipedia and from Stephen Wolfram.

See also the related question about ambiguity of the juxtaposition by multiplication in conventional notation, here.

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I would recommend, rather, Cajori's book on the History of Notations. –  Mariano Suárez-Alvarez Jan 18 '12 at 0:02

Math culture gradually sheds redundant notation. It's the same reason it uses single letter variables.

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