In my opinion, today is a magical date: 4/8/16 (dd-mm-yy; as I write on my notebook). So let me tell you what I think about “mathematics” and “magic”. I believe that magic is an art of concealing facts leading to astonishing results. Magic trick is interesting from perspective of both observer and performer. Performer gets satisfaction of being able to fool observer (by making him/her believe that he/she can’t do it), and on the other hand observer gets satisfaction of being able of witness an act which he/she can’t perform (a quality of appreciation is expected).
Now, as many of you have observed, mathematics (or nature in general) is very much magical in the same sense. Only experts (algebraist/number theorists…) can “understand” the rules (called theorems) behind the actions (called computations) they ask you to perform (which amaze you). So, in general, whenever you are using a result (for example, an integer has unique factorization into prime numbers) without “knowing” the proof, you are performing “mathemagic” for yourself. When you take magic out of mathematics, you get what mathematicians called rigour.
I believe that the most important rule for performing a magic trick is to never reveal the secret rule (though the audience is free to conjecture and prove the possible secret rule). This is very much different from first rule of cryptanalysis, since while doing cryptanalysis you “must” know the algorithm/rule used to encipher the message and task is to find the key to decipher the cipher. Trying to find the secret rules for a magic trick is much more interesting that trying to decipher a cipher. So, I will leave you with a classic “mathemagic” trick and you as observer of this trick, try to find the secret rule governing it (but never reveal it to others!!!):
Write down the year you were born and under that the year of some great event of your life (like year of graduation, the time you saved somebody…). Now write the only even prime number. Write down your age by the end of this year (i.e. 2016) and the number of years ago the great event (quoted above) took place in your life. Now add all these. I know what the total will be! Today it’s 4034.