Proving Jo Chen’s Conjecture

A long-coveted result in mathematics is the solution to the tooth integral of the existential quantifier dotted with d7, or


After seconds and seconds of speculating upon what the correct result of this integral is, Jo Chen conjectured that


It turns out that Jo Chen correctly predicted the answer to the integral, as the solution has been found. Our first crucial step is to realize it is very difficult to conceptualize the dot product of an existential quantifier and a d7. We thus divide both sides of the equation by ·.

Canceling out the ·s in the numerator and denominator on the left hand side of the equation, we arrive at


Now comes a clever manipulation: we take the antitooth integral of both sides of the equation. It is thus now inverted at the end of the second side:


Intuition now tells us that too many things are upside down, motivation to reciprocate:


It may now be tempting to carry out the cross product, but we must be patient and deal with the fact that the order of operations requires us to deal with the leftmost operations first, as all operations involved in this expression are equally dignified. We can initially simplify by moving a denominator of the denominator to the numerator:


Then, we take care of the smiley at the start of the denominator. It is wildly obscure enough of a smiley to be well approximated by the random number function:

We now see why we don’t carry out the cross product in the first place: the expression will end up being randomized anyway. Yet our result could still be further simplified. We magnify the numerator. We can do this without magnifying the denominator because the random number function can account for all magnifications and contractions:


Notice we now have two divisions going on. Thus, we move the denominator of the denominator to the numerator. Of course, no limits of integration were provided, thus making our original integral an indefinite integral, requiring a +C. Our end result, ,

is read “A random person drowns in the C.” Since all our steps are perfectly reversible and our conjecture is equivalent to a coherent statement, Jo Chen’s conjecture has been proven to be true. //


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