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 Nov7 comment What are some examples of notation that really improved mathematics? @NateEldredge I think it is an improvement. Compare vector expressed as a series in usual notation $\sum \langle x,\phi \rangle \phi$ and in bra-ket notation $\sum \langle \phi | x \rangle |\phi\rangle$. The bra-ket notation also can be read not just as sum of vectors with coefficients but also as matrix-vector multiplication just by swapping things around. Also we can treat $\sum |\phi\rangle\langle\phi |$ as an identity and it gives rise to a bunch of useful algebraic manipulations. Nov7 comment What are some examples of notation that really improved mathematics? Einstein's notation is indeed the power of math at its finest! I would add Kronecker and Levi-Civita symbols to this answer. Nov7 comment How to put 9 pigs into 4 pens so that there are an odd number of pigs in each pen? @kriss Thx, next to last was wrong indeed (also the second one), counting to five is hard! Fixed it and also colored the pens for more clearity. Nov2 comment When written in decimal notation, every square number has at most 1000 digits that are not 0 or 1. True or false? [silly]$2^2 = 3.9999999...$ have clearly more than 1000 nines, so it's false[/silly] Jan11 comment Minimum number of steps needed to solve a rubik cube It's not the one I'm looking for. This solution I can easily find everywhere, it's more than just 3 steps. Jan9 comment Minimum number of steps needed to solve a rubik cube @RossMillikan I did solve it with those moves many times, it required some thought to it and I liked it :). Jan7 comment Minimum number of steps needed to solve a rubik cube @RahulNarain Probably... If someone will write these moves down it would be great. Dec25 comment Why is 'abuse of notation' tolerated? Oh I remember how as a freshman I was taking notes on math related lectures and was trying to purify math so that I have no words at all there except titles, names and some minor comments and it should be as compact as possible. Now I can make a 10 page theorem proof in to one page so that I can see a full picture just with one glance, it helps a lot. Dec15 comment Change of variables in Belousov-Zhabotinsky reaction Well, that's what you do when you nondimensionalize your equations. It's a chemistry, so $x,y,z$ are some concentrations so as $A,B$. Then to nondimensionalize a variable $z$ you replace it with something like $\frac{z}{B}$. Dec15 comment Change of variables in Belousov-Zhabotinsky reaction Or $z -> \frac{z}{B}$, $t -> \frac{\tau}{B k_5}$, $x -> \frac{k_5 x}{2 k_3 A }$ Dec15 comment Change of variables in Belousov-Zhabotinsky reaction Well just from looking on the 3rd equation I can say, that $z$ was changed to $\frac{z}{k_5 B}$, $t$ to $\frac{\tau}{B k_5}$ and $x$ to $\frac{x}{2 A k_3}$. The rest is easy to do. Dec15 comment Change of variables in Belousov-Zhabotinsky reaction It can be used for further simplification of the system , to get rid if some equations. But I just realized that it's not the question. Do you just need to know what replacements were used? Dec15 comment Change of variables in Belousov-Zhabotinsky reaction Take a look at Tikhonov's theorem Oct1 comment using numbers 1 to 9 only once to equal 1 million @Joren If the question didn't say anything about 'one million' and just stayed that the answer should be 1000000 then it works :)