What is the mathematical explanation for this trick?

Solution 1:

1. Let $n$ be the last digit of your mobile number.
2. $2n$
3. $2n+5$
4. $50(2n+5)=100n+250$
5. $100n+250+1764=100n+2014$ (fixed by Daniel R)
6. Let $y$ be your year of birth. Then we have $100n+(2014-y)$.

Since $2014-y$ is your age (assumed to be $<100$), the hundreds digit is $n$ and the last two digits are your age.

Solution 2:

That's elementary. If $d$ is the last digit and $y$ your birth year, you are computing

$$(2d+1)50+1964-y=100d+2014-y.$$

The first term is the digit shifted two positions to the left (times $100$); the other two terms compute your age.

You'll have to increment the constant $1964$ every year, and the trick won't work for centenarians.

Solution 3:

$50(2x + 1) + 1964 - y = 100x + (2014 - y).$

If you were born before August 1st in year y, then (2014 - y) is your age. If you are under 100, then it's a 2-digit number. So the right-hand side of the equation is just a three digit number whose first digit is $x$ (doesn't matter what one-digit number $x$ we started with) and whose last two digits are your age.

edit: fixed lhs as per comments