A beginner's guide to producing new results in mathematics

• First, choose a problem that nobody’s ever solved before. Be careful, though: the most common beginner’s mistake is to choose a problem that’s much too difficult. Fermat’s Last Theorem was an old favorite, but since Andrew Wiles proved that a while back, the new favorites are the Riemann Hypothesis and the Poincaré Conjecture. Rather, as a beginner, you want to pick something that’s within your grasp. I suggest picking two random 200-digit numbers (no need to make them up on your own; get your computer to do that) and adding them together. With probability 1, nobody in the history of the world has ever added these two numbers together before.

• Next, plug it into Mathematica or Maple. No red-blooded, God-fearing mathematician would ever dream of trying to solve a problem without plugging it into a computer and seeing what the answer is first. Sure, the numerical solution will probably be so vague as to be worthless, but this is how things are done.

• Now it’s time to get down to business: write the problem up on the chalkboard in your office. Of course, you could just write it down on a sheet of paper, but there are several objections to that. First, paper is much too permanent; if you end up getting stuck and you’re working on a blackboard, you can always just claim the janitor erased your chalkboard at a crucial stage. Second, it’s extremely important to always have cryptic and incomprehensible scribbles filling your chalkboard to intimidate students and colleagues that might drop by. It’s even better if you have three or four calculations overlapping eachother on the board.

• You’ve got the problem written down on your chalkboard, so now there’s nothing left to do but to solve the damn thing. Remember to take your time. Cross pieces out, even though you could just erase them. Once you’ve made some progress (and built up a goodly amount of chalk on your fingers), step back to ponder the next step. Rub your chin. Run your hands through your hair. Smooth down your shirtfront. Take a bathroom break. Do whatever it takes to transfer the chalk on your hands to various other parts of your anatomy and attire. Under no circumstances should you try to remove any of this chalk before going to teach your next class. Remember, having chalk smeared all over your face, hair, shirt and crotch is all part of the cachet.

• At some point throughout the course of the above, we’ll assume you’ve actually solved the problem. Contemplate the beauty of your solution. Write it down on paper in an indecipherable hand. If you feel like it, consider typing it up, but be sure to include a few errors. This is necessary so as to confuse the readers of your solution and throw them off your track. Whenever there’s a difficult calculation, simply gloss over it and state the end result; odds are none of your readers will actually expend the effort to do the calculation themselves, so you’ve covered your ass in case you flipped a sign somewhere.

Congratulations! You’ve just proved a new result in mathematics. Of course, if you really just added two random gigantic numbers, the probability that anybody cares is 0. Better luck next time.