Abstract

In this article, we discuss the classic proof that girls are evil. The author will briefly discuss the origins of the problem and review the classic proof. The author then indicates a mathematical flaw in the argument, invalidating the statement. The article concludes with a revised and corrected statement of the result.

I. Introduction

I recently received an email discussing the differences between men and women from various mathematical and engineering points-of-view. Most of it was extremely funny, and sooner or later all shall certainly appear within the mathematico-humorist community, properly researched, and appended with standard references in the literature.

However, one portion of the email included a mathematical “proof” of the fact that girls are evil. This proof is doubtless familiar to many readers, having circulated a few times in mathematicians’ inboxes. However, for those readers unfamiliar with this well-known proof, we present it now.

II. Statement and classical proof of result

Theorem. Girls are evil.

Proof. It is axiomic in all cultures that girls require both time and money, and any man with either a deficiency in available “quality time” or “disposable income” knows that this a joint-proportion, whence

Similarly, it is has been proved that “time is money”..

Therefore, the Substitution yields

We also know that “money is the root of all evil”, whence

Substituting again yields

Squaring on the right-hand side of the equation yields

establishing the result. Q.E.D.

III. Identifying and resolving the flaw

The above “proof,” so-called, is widely known to mathematicians, leading to the widespread belief that girls are evil.

It will therefore come as a surprise to find that the proof above is flawed, and indeed, the result is incorrect. There is a subtle flaw in the above argument that seems to have escaped most diligent readers for quite some time. In the interest of correcting this mis-truth, which has improperly vilified girls as being evil, we present now the correct statement and its proof.

Theorem (Corrected). Girls are absolute evil.

Proof. Arguing as above allows us to conclude

However, let us more intently examine the consequences of money being the root of all evil. A moment’s thought shows that it is incorrect to conclude that

To see this, recall that evil is a inherently negative concept . We cannot take square roots of negative quantities in the real world, lest we are will to assume that money is imaginary. (Graduate students in particular may choose to investigate this concept further ) Thus, we are therefore forced to conclude that

Substituting again yields

Squaring on the right-hand side of the equation yields

establishing that girls are absolutely evil. Q.E.D.

IV. Conclusion

We sincerely hope this clears things up.