An essay by Brendan Caldwell made the rounds arguing against games like Vampire Survivors that automate a key verb without changing what the player sees. Reading it, I couldn't help but see parallels to research mathematics. How different is watching an LLM connect lemmas while you vaguely steer it from watching a pixelated vampire hunter throw axes while you vaguely steer it?
Vampire Survivors moves agency from aiming/firing to choosing a walk direction and upgrades. In Caldwell's words: "Self-playing games take microdecisions away from you in favour of macrodecisions."
Idle games and the second derivative
Cookie Clicker (2013) helped create the idle genre: currency accumulates automatically; the player spends on upgrades that change the rate. Skill moves from the first derivative of score to the second. Vampire Survivors is, for Caldwell, an uncomfortable hybrid that teases first-derivative control while really being about the second.
Mathematics
Today mathematicians are trained to make progress directly—a higher first derivative of mathematical progress. Watching LLMs contribute to that derivative is a serious change. Where supervising LLMs is more efficient than doing the work directly, the change "kind of sucks" in exactly the Vampire Survivors way.
As Terence Tao and collaborators have argued, solving problems is not the only point of mathematics as a human activity. Still, mathematical progress isn't only for mathematicians. If AI can solve open problems—even "badly"—and help apply solutions to science, pressure to continue will be strong. We could see a bifurcation: knowledge understood by research mathematicians versus a larger body of formally verified facts applied to natural phenomena—inverting the historical pure/applied relationship.
Macrodecisions matter
In games, macrodecisions can be fun. Cookie Clicker's achievements cover 72 orders of magnitude of cookie production; how many orders of magnitude of mathematical progress for science are out there? Could applied mathematics move 10× or 100× faster?
Direction matters as much as magnitude. There may be effectively infinite possible mathematical progress and only finite applied progress practically accessible to humans. Then macrodecisions about what to work on are all we have—and mathematicians are best placed to make them.
Despite legitimate concerns, the authors entreat the mathematical community to be yokefellows shaping the world with orders of magnitude more applied math—even if its foundation is messy by historical standards. For every layer AI automates, there remains a layer above where someone decides what's best for humans.
Originally published on Reinvent Science.