It is astonishing that some people still doubt the existence of Santa Claus. Despite the vast amount of photographic evidence, the hundreds of annual reports on Father Christmas’s activities from perfectly reputable news sources, and the bulging stockings full of presents that reliably appear on Christmas morning, somehow the doubters remain unconvinced.

Thankfully mathematics can help.

The conspiracy theorists have already tried turning to science to demonstrate their (clearly incorrect) position. They calculate that if Santa were to visit the 1.9 billion children in the world, he would have to travel at 3,000 times the speed of sound while carrying more than 300,000 tons of presents† (about the weight of six Titanics). Richard Dawkins, king of the skeptics, has insisted that the lack of any noticeable sonic booms from all that zipping about at supersonic speeds is more than enough evidence that Santa cannot possibly be real.

Worse still, some claim that this astonishing weight of parcels travelling at such a remarkable speed would practically vaporize the leading reindeer, who would have to withstand the full hit of air resistance. Meanwhile, sitting in the back of his sleigh, Santa would be subjected to forces tens of thousands of times stronger than gravity, making it impossible for him to breathe or to retain any of the physical structure of his bones or internal organs, thus reducing him to a liquefied mess. While this would admittedly explain how he was able to slip down some of the narrower chimneys on his route, it probably wouldn’t make for very attractive Christmas cards.

Sure, all these scientific spoilsports sound convincing enough. Although their arguments totally depend on the assumption that Santa isn’t a macroscopic quantum object capable of being in two places at once. And that he’s unable to manipulate time (though how else do they think he manages not to age in photographs?). And that he hasn’t constructed a NASA-style heat shield to protect his reindeer. Or invented a device to suppress sonic booms.

They also assume that any of these simple explanations is more far-fetched than the idea that the vast majority of the adult world is participating in a massive conspiracy, with parents cheerily lying to their children on behalf of a mystical non-existent figure, postal services fiendishly filtering out letters to Santa rather than returning them to sender as they normally would, and news agencies annually publishing blatant falsehoods that go against all their journalistic ethics, simply to maintain the whole pointless charade. Riiiggght. Sure.

The skeptical scientists’ arguments also illustrate an important point. The great difference between scientific and mathematical proof.

The scientific method takes a theory—in our case that Santa is real—and sets about trying to prove that it is false. Although this may seem a little counterintuitive on the surface, it actually does make a lot of sense. If you go out looking for evidence that Santa doesn’t exist and don’t find any … well then, that is pretty revealing. The harder you try, and fail, to show that Santa cannot exist, the more support you have for your theory that he must. Eventually, when enough evidence has been gathered that all points in the same direction, your original theory is accepted as fact.

Mathematical proof is different. In mathematics, proving something “beyond all reasonable doubt” isn’t good enough. You have to prove it beyond all unreasonable doubt as well. Mathematicians aren’t happy unless they have demonstrated the truth of a theory absolutely, irrefutably, irrevocably, categorically, indubitably, unequivocally, and indisputably. In mathematics, proof really means proof, and once something is mathematically true, it is true forever. Unlike, say, the theory of gravity—hey, Newton?

If we want to silence the doubters once and for all we have to turn to mathematical proof.

The Indisputable Existence of Santa Claus: The Mathematics of Christmas