Aggro is the Foundation
Today I want to review a concept present in many domains, but most clearly articulated by TCG players. In a game like Magic the Gathering or Hearthstone, gameplay divides neatly into two phases: deck-building and execution. Deckbuilding involves all the choices and calculations that go into preparing your custom deck of cards before you even sit down (or log in) to draw your first hand. Execution is playing your deck, and your particular draws, as well as possible in the moment.
Execution is hard, but essentially learnable. Deckbuilding is the truly difficult and creative part: it requires not just extensive game knowledge and creativity, but a deep understanding of the metagame – what decks other players are likely to bring and how to counter them. One core philosophy that I learned from great deckbuilders is the understanding that aggro decks – fast, simple decks that try to kill the opponent as quickly as possible – are the foundation upon which the entire metagame is built. Of all the kinds of decks, building an aggro deck is the least difficult; usually your choices are limited to cheap, efficient early-game cards that end the game as quickly as possible, and there isn’t a huge amount of room to optimize for metagame.
In contrast, other decks (typically classified as “midrange” or “control” decks) need to be built contextually with aggro in mind – the dominant aggro deck in the metagame sets a pace you have to match. If the fastest aggro deck can ends the game in three turns, then you need to have cards you can afford to play in the first three turns. If they play a lot of minions on the board, you need a lot of removal to kill those minions. If they play many damage spells, you need counterspells or healing. In a sense, aggro is the foundation upon which the other layers of the metagame are built in layer upon layer of abstraction.
Many other games have the feature that there are a few pure aggro strategies – which is not necessarily even a good strategy – upon which any deep understanding of the game must be built. In Starcraft and other RTS games, the rush strategies that are possible dictate the pace of the game: if the earliest enemy rush can come at 3 minutes and 30 seconds into the game, then your strategy must make sure to start building defenses at 3 minutes (or at least leave the possibility open conditional on scouting information). In real life geopolitics, war, especially nuclear war, is the foundation: even if no military conflict actually happens, military strength must factor into negotiations at every higher level of consideration. In contrast, the execution of nuclear war is straightforward and unfettered by metagame considerations.
I write all this to suggest that there is also a basic aggro strategy in mathematics research upon which all other metagame considerations must be built, and that strategy is the simplest one of working on a hard technical problem by yourself. You will be told to spend lots of time going to learning seminars and talks, you’ll be told to network and hobnob, and you’ll be told (by me, in the very last post) to attend to meta-considerations and learn how to play a supporting role in research. All of this, however, must rest upon a solid foundation of knowing how to play aggro, how to carry out productive research. Without this foundation, you’ll have no idea what to focus on in a seminar, not a clue what to learn from and ask of other researchers, and only a fuzzy model of what support you can provide to another mathematician trying to carry out their research.
Just as not every Magic player plays aggro decks, not every mathematician needs to do solo research to be effective. But every Magic player needs to know what aggro decks are in play, and every mathematician needs to know how to do solo research. That’s the foundation upon which the entire metagame is built.