Learning times tables? I have some weird gaps in my learning, I can do lambda calculus and some basic category theory, but I do not know how to do some of the most basic of arithmetic.
(I am in my mid 20s)
Seeing this gap in my knowledge, I have worked up the courage to create this anonymous account and ask for advice. How do I learn my time tables? (probably need to multiply instantly up to $19\times19$)

also I am going through Khan Academy

 A: I learned times tables up to $12 \cdot 12$ as a child through force of my parents and buckets of tears because I hated it. As an adult I fell in love with math and took a master's degree in applied mathematics with 4.0 distinction. A big turn around.
I second the rote memorization up to $10 \cdot 10$ (or better yet $9 \cdot 9$ as you probably already know the tens), and get fast at long multiplication of large numbers by throwing your calculator in a drawer and replacing it with long multiplication on paper. You will accidentally memorize lots of arithmetic by doing lots of it, and that is really the way to go. Do more math, and change your paradigm to a positive one on the topic. It is sort of like tennis. It is really fun even if you are not very good, and the better you get the more rewarding it becomes.
Now I will suppose you do not currently know all of the table up to $10 \cdot 10$. Here are two things for you to do:


*

*Eventually, get or make a stack of flash cards. Shuffle them. Hold them up, or have someone do it for you. When you know one immediately, put it in a elimination pile, and when you do not know one immediately put it in a repeat pile. Put the elimination pile in the drawer beside your calculator and leave it there. Shuffle the repeat pile and ... repeat that process on just those cards for a while. Discard more when you are absolutely sure you know them. You may surprise yourself.

*Right now, if you know say some of the times table, but not all, try computing the unknown in your head by counting from the known. For example, say you do not know $7 \cdot 8$, but you know that $7 \cdot 7 = 49$. Then count $49 + 7$ in your head and you have $7 \cdot 8$. The idea is that multiplication is a sort of shorthand for repeated addition. When you are sitting somewhere with only your mind to entertain you, try "arriving" at the solutions by starting with what you do know, or just by pure repeated addition. Don't be afraid to use your fingers by the way, people have been doing it for millenia. You may also find it useful to count fingers (or dice etc.) on a mental picture in your mind. Above all, have fun doing your enumeration. In the end it is neither trivial nor inconsequential. Strong numeracy skills will definitely enhance your future math ventures. 
A: Memorize up until $10\times 10$. For double digit numbers use:
$$(10a+b)\times(10c+d)==100ac+10(cb+ad)+b\cdot d$$
For higher digit numbers, just ignore all but the first two, and if you need the accuracy, use a calculator.
A: It's easier to memorize the smaller products (like $2\times 3$) than it is to memorize larger products (like $7\times 8$) because it's easier to visualize the former.  I recommend you memorize the smaller products (up to $5\times 5$), then use a method such as finger multiplication to handle the larger products (up to $9\times 9$).  Search the internet using the key phrase "finger math" for more information.  (YouTube has a lot of videos on these.)
