Mathematical Superintelligence as a Path to Human Simulation

What’s the point of solving math using AI? What do we gain from this besides the pleasure of pure academic pursuit?

My guess is that it has implications for an entirely different abstraction level that spans a broader area than individual academic disciplines. Solving mathematical superintelligence will unlock the scaffolding to support simulations of the human world¹.

Examples of cellular automata

Cellular automata, coined by John von Neumann, provide a simple yet useful simulation of how individual entities can interact with one another on a microscopic scale to create unexpected behaviors that form at the macroscopic level. Chris Langton became interested in this idea and coined the term Artificial Life. Playing John Conway’s Game of Life, you feel the same excitement that Langton felt - that consciousness is emerging from these simple, binary, digital bits.

Yet human beings should not be this simple.

Even math cannot explain certain phenomena like the three-body problem in a nice close looped form. If that’s the case, how could math explain and predict human behavior? Humans couldn’t possibly be reduced to a collection of mathematical equations...right?

I would posit that we are precisely heading towards a future of formalizing the observations that are easy but tedious to capture. One of them being human behavior. The math we are attempting to solve using AI today is quite convoluted. However, there are low-hanging observations that should be able to be captured with the technology today, one of them being human behavior. If we have millions of virtual, PhD-level mathematicians, the labor problem of doing so is solved.

Jimmy Ba and the broader xAI team posed the Galileo question, in which they ask themselves whether AI today is intelligent enough to the point where, if it were sent back to a time when geocentric ideas were abundant and widely accepted, it would figure out that our solar system is actually a heliocentric one.

In my opinion, if the AI model were solely dependent on interactions with other humans, the model may not be able to figure this out. But if the model could observe the planetary movements, it would only be a matter of time before it figured out that we are orbiting the sun.

Similar to this, human behavior can be captured in an algorithm from observations. Kahneman and Tversky’s Prospect Theory is mathematically based. Game theory is a mathematically based approach to optimization across different scenarios that humans may come across. Algorithmic trading is an attempt to gauge the current state of the market and make bets accordingly. Bob Mercer has famously said that Renaissance Technologies’ success rate is about 50.75%, reflecting the difficulty of making the right call on the movement of the market. But if we have perfect information and understand the behavior of each individual, formalizing this microscopic behavior can help calculate a more accurate macroscopic behavior of the world.

A fully simulated future of mankind is what I envision as the ultimate unlock. AI would be fed new information and be constantly updated to understand the current state of the world and its expected trajectory.

A key roadblock that would be solved along the way would be the task of managing a massive collection of individual agents².

By doing so, we could simulate what a country of agents can achieve collectively. Perhaps we initialize the state as a communist or a capitalist society. Maybe we throw in an anomaly by incorporating Reflexivity. We can see which method of incentives (gulag vs. societal rehabilitation) works best. The scaffolding to support this would be similar to the scaffolding of math in requiring the right interventions for corrections³.

So what’s the point of solving math using AI? It may be the first step toward simulating ourselves.

1. Thank you to Christian Szegedy for seeding many of the ideas here. Cristopher Moore’s interview on MLST provided additional inspiration.

2. There could be a scenario where we formalize human behaviors first before formalizing the expected behavior of agents. But based on today’s trend of humans managing multiple agents and their respective subagents, the likely scenario would be the formalization of agent behavior first.

3. Imagine a Bridgewater-esque conversation in everyday life (setting aside how tiring it could hypothetically be). As you form sentences, they’re transformed into a formal representation. Naturally, human logic will not be completely bulletproof. Contradictions will exist, as well as inconsistencies in opinions expressed in previous conversations. These will need to be accounted for as well. But formalizing is the first step in correcting this, and agents are well-suited to be subjects of this experiment.