I am working on memorizing the multiplication tables up to 100 x 100.
I am currently up to 30 x 30. I was never very good at math in my youth but I now realize the importance of math.
The more I work with numbers, the more I keep seeing interlocking patterns in their structures. These patterns are very interesting so I will keep practicing for now.
Please share your number memorizing discoveries here, if you are inclined to. 
I just want to comment that I am trying to find math tricks and magic games to astound to my son, because like you say, in the youth we can not see the importance of math, but we can try to show how to appreciate math.
I did all the squares from 00-99. It took me less than 30 minutes. I basically used my 2 digit images for people for the 2 digit number, then the 2 digit person and 2 digit action for the square.
93 = 8649
(nicholas cage) = (running around)(a football)
Next to memorizing the table, here is another way to do the calculation mentally:
About squares, I think most MCWC competitors I know, have memorised the first 100 squares. Then, some like W. Bouman memorised the first 1000.
It depends on how much info you wanna hold in long-term memory.
About tables, I think most competitors know the 20x20 by heart. Before competitions, I usually study the 30x30 or the 50x50 table, but it’s not necessary to know it by heart, since most of us can find such 2x2 digit answer in 3 seconds