In class, I make sure my students get practice with their calculators by having them do the calculations (I teach physics). I can do the numbers in my head faster than they can work the calculator. This is partly because they are extremely slow with the calculator and badly need practice with it. See Undercover Mathemati's answer.
One day one of my students got the answer faster than I knew a calculator could provide it. I stared at him briefly and asked "how did you get that". He said that he'd followed my advice. If you want your brain to be good at arithmetic, use it while you're driving. Look at the license plates and do multiplication or addition or division or subtraction problems. You will find yourself getting better and better each day.
The same thing applies to any other type of math. You will slowly become fabulously good at the thing you spend your time doing.
What I'm saying is that the head shapes of mathematicians are not significantly different from those of the general public. What's different is what they find interesting. Make math interesting for yourself and you're halfway there.