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I'm interested in alternative systems of notation for mathematics. I've often heard how mathematical notation is illogical, inconsistent, filled with grandfather clauses that serve no purpose, and suggests deprecated ideas (e.g .the $\rm{dx}$ of the integral and derivative).

It seems reasonable to suppose someone has tried to come up with some alternative notation.

My interest in this is mostly curiosity. I'm very interested in what people have come up with to rectify the perceived faults. I vaguely remember seeing a link to some alternative notation of logarithms, but I seem to have lost it.

I know that using highly non-standard notation is a bad idea for many reasons. I highly doubt I will use it.

Also, I don't mean good notation or even consistent notation. I'm just interested in something different, preferably a lot of it, and in one place.

I'm labeling this as a soft question, but I'm not really looking for suggestions or discussions for alternative notation. I just want a good source(s).

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Maybe you were thinking of this posting for logs math.stackexchange.com/questions/30046/… ? Regards – Amzoti Jan 15 at 19:31
Nope, it was actually something else, though I've seen this too. What I remember involved squiggly lines, kind of like a square root. – Greg Ros Jan 15 at 19:37
One "folklore" alternative notation is write functions in postfix notation, like $xf$ or $(x+3)f$ instead of $f(x+3)$. This way the compositions are naturally read left to right: $(x)fgh$ instead of $h(g(f(x)))$. (NB: This is not to say that LTR is more natural than RTL, just that the rest of mathematical formulas are read LTR). With linear operators, for which parentheses are often omitted, one could write things like $2xAB$, with linearity (or at least homogeneity) built-in. I don't have any references, unfortunately. – user53153 Jan 15 at 19:37
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Attend a course taught by an analyst. I guarantee you'll see weird and inconsistent notations. – Git Gud Jan 15 at 19:39
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I don't know if this counts as "alternative" enough: In the preface of Structure and Interpretation of Classical Mechanics, Sussman and Wisdom reject the traditional notation for the Euler-Lagrange equations, $\dfrac{\mathrm d}{\mathrm dt}\dfrac{\partial L}{\partial\dot q_i}-\dfrac{\partial L}{\partial q_i}=0$, as ambiguous and inconsistent, opting instead for a computer-algebra-like notation $D(\partial_2 L\circ\Gamma[q])-\partial_1 L\circ\Gamma[q]=0$. All the math in the rest of the book is written in this style. – Rahul Narain Jan 15 at 20:50
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