Imagine sitting at your desk with three items:
1. Yesterday's newspaper: You've already read it; you remember every word. 2. A screen of static noise: pure random flicker from a TV with no signal. 3. A Rubik's cube you've never solved: You can't solve it yet, but you sense there's an elegant hidden pattern.
Which of the three feels 'interesting'?
Almost everyone picks the Rubik's cube. The newspaper is too simple (already known), the static is too complex (pure randomness), and only the cube sits at the edge of 'about to be understood.' This pull toward something—the urge to dig into it—is what we call curiosity or interestingness.
For a long time, 'interesting' seemed like a subjective, emotional experience. But in May 2026, AI pioneer Jürgen Schmidhuber and his team published a landmark paper: 'Interestingness as an Inductive Heuristic for Future Compression Progress.'
They used rigorous mathematics to prove a striking conclusion: 'interestingness' is a computable quantity, and it is the best predictor of future progress.
The Mathematical Definition of Interestingness
Feynman once said: 'The essence of understanding is simplification.' In computer science, this is called data compression.
The paper's core logic: if you can compress a piece of data, it means you've understood its regularities.
- Newspaper: already compressed to its limit; nothing left to extract, so it's 'boring.'
- Static: no patterns at all, incompressible, so also 'boring.'
- Interesting things: things where you perceive that 'with a bit more study, I can dramatically simplify this.'
- It sniffs through massive data streams.
- When it detects that some domain's (say, quantum mechanics') patterns are being rapidly simplified by it, its interestingness metric spikes.
- It then spontaneously invests more compute into conquering that domain.
Interestingness = the first derivative of learning progress. In other words, when something feels interesting, your brain is essentially experiencing the pleasure of a 'surge in compression rate.'
Key Finding: Interestingness Predicts the Future
The paper's hardest-hitting result is that this feeling isn't just momentary—it is forward-looking. Using Kolmogorov complexity, the researchers showed:
1. The 'strike while the iron is hot' effect: Mathematically, if you've just discovered a new pattern in some domain (compressed some data), you are highly likely to soon discover more patterns in the same direction. 2. The 'stagnation penalty': If you've spent a long time studying something without achieving new 'compression,' exponential decay suggests it's probably genuinely not for you (either too hard, or pure noise). You should decisively move on to the next 'interesting' target.
Why This Matters for AGI
For AI, this paper provides a navigation system for autonomous evolution.
Previously, we had to tell AI: 'go learn math,' 'go write code.' AI was a passive executor. Now, with this 'interestingness formula,' AI can decide for itself what to do:
Summary
'Interestingness' is not some emotional byproduct of the brain—it is nature's most elegant shortcut.
When a book, a hard problem, or a new model feels extremely 'interesting,' your intuition is using mathematical law to tell you: 'Hey, look here! Truth is lined up here waiting to be compressed—don't walk away!'
Just as Feynman preferred exploring amid uncertainty to gaining false certainty, this paper tells us: 'interestingness' is the beam guiding us through uncertainty toward the deepest understanding.
The essence of intelligence is seeking out complexity that can be simplified. That is the ultimate wisdom of the 2026 'mathematics of curiosity.'