The world of mathematics, often perceived as a realm of cold, irrefutable truths, occasionally finds itself entangled with the seemingly frivolous domains of games and entertainment. On April 22, 2025, a surprising intersection of these worlds occurred: the complex strategy card game Magic: The Gathering (MTG) has unexpectedly found itself at the heart of an age-old mathematical enigma – the twin prime conjecture. This article delves into this bizarre confluence, exposing not just the intricate mechanics of MTG, but also the tantalizing allure of unsolved mathematical problems.

Magic: The Gathering, for the uninitiated, is far more than a simple card game. It’s a collectible card game, or CCG, where players construct decks from a vast pool of over 30,000 unique cards, each with its own distinct abilities and strategic purpose. A CCG requires a player to engage in deep metagaming, by analyzing the strengths and weaknesses of their deck, as well as those of their opponents. Deck construction is a critical part of the game that requires in-depth knowledge of all of the available cards and the ability to predict the meta, the popular decks and playstyles in the current game environment. This immense variety gives rise to staggering complexity, so much so that software engineer Alex Churchill, along with other MTG enthusiasts, demonstrated in 2019 that MTG is Turing Complete.

A Turing Machine, named after the brilliant mathematician Alan Turing, is a theoretical model of computation that can simulate any computer algorithm. For a system to be considered Turing Complete is to say that, given enough resources, it can perform any calculation a computer can. Churchill et al. proved that MTG possesses sufficient complexity to function as a universal computer, meaning any computation could theoretically be carried out through a sequence of card plays.

While this discovery solidified MTG’s position as one of the most complex games ever devised, practically using it to solve real-world problems seemed a fool’s errand. Coding a Turing Machine with cards is exceptionally time consuming, so trying to solve a difficult math problem with a deck of cards is highly impractical. That is until Reddit user its-summer-somewhere unveiled a mind-bending combination of cards that could potentially inflict infinite damage, with a caveat: the damage is contingent on the truth of the twin prime conjecture.

The twin prime conjecture, first posited by Alphonse de Polignac in 1849, concerns the distribution of prime numbers. A prime number, as most remember from school, is a number divisible only by 1 and itself (e.g., 2, 3, 5, 7, 11). Twin primes are pairs of primes that differ by only two (e.g., 3 and 5, 17 and 19). The conjecture proposes that there are infinitely many such twin primes. Despite centuries of effort by mathematicians, this tantalizing proposition remains unproven.

Enter Zimone, All-Questioning, a card from the Duskmourn: House of Horror set. This card’s effect is triggered by controlling a prime number of lands (cards representing mana sources in the game), generating creature tokens. Its-summer-somewhere devised a convoluted sequence of card plays where the game state and the damage inflicted upon the opponent hinges on the existence of infinitely many twin primes. If the player’s number of lands results in a twin prime, Zimone triggers, creating tokens that become more lands, potentially creating infinite damage.

This elaborate setup, while unlikely in an actual game, provocatively ties the game’s outcome to a profound mathematical problem. While this connection is mostly a playful thought experiment, it underscores the inherent complexity of MTG and its capacity to unexpectedly intersect with seemingly unrelated fields. Will MTG players accidentally stumble upon a proof of the twin prime conjecture? Probably not. But this intriguing connection highlights the enduring appeal of both mathematics and games, and their ability to spark curiosity and inspire even the most unconventional collaborations.

Cet article a été fait a partir de ces articles:

https://www.scientificamerican.com/article/magic-the-gathering-fans-harness-prime-number-puzzle-as-a-game-strategy/, https://www.scientificamerican.com/article/how-plastic-glass-and-paper-move-through-the-recycling-system/, https://www.scientificamerican.com/article/fight-flee-or-freeze-this-tiny-caterpillar-does-a-secret-fourth-thing/, https://www.scientificamerican.com/article/child-asthma-will-worsen-with-trumps-pollution-rollbacks-and-rfk-jr-s-cdc/, https://www.scientificamerican.com/article/why-narcissists-emerge-as-leaders-even-in-childhood/