Wandering

David Louapre explains what we lose when we use AI to get a direct route to solving a problem and why wandering around a problem helps us with an analogy to Civilization game.

In Civilization, you explore a map hidden by a fog of war. Maybe you just wanted to reach a new city, but along the way you find rivers, valuable resources, other places worth visiting.

Searching for a proof can work like that. You solve a problem…and discover things you weren’t looking for.

These discoveries matter as much as the original problem. Because a failed attempt can suggest a new question, or a method invented for one problem can help with another.

Initially, you only wanted to reach one city, but you end up knowing more of the world.

Now imagine an AI-oracle tell you :

“Looking for the red city? Here it is. You’re welcome. (And btw I checked it in LEAN)”

Sure, that is useful information. But the map between you and the city is still dark.

Ok then suppose the AI also gives you a direct route to it, and you can check every step.

That’s a real achievement…but you may still know very little about the surrounding terrain, or how to find a route to the next city.

The AI-route can be correct and straight, but without teaching you much about the map.

The concern of mathematicians makes sense to me because the exploration actually does useful work. You develop methods, notice connections and learn which questions are worth asking.

Of course, the pleasure of wandering is part of it ! Let’s not deny it !

But the value is also in what the wandering produces.