Primes and Platypuses: two prototypical archetypes for innovation

Here's a simple model of two types of new things.

Prime numbers are famously hard to find but have an incredibly simple algorithm. Any number that is only divisible by 1 and itself is prime.

The platypus breaks beyond existing categorization. Not a mammal or a bird, the platypus both lactates and lays eggs.

Some innovations are like prime numbers. There's a known unknown path that can be incredibly difficult to transverse but still follows a well understood algorithm.

Think: Moore's law, Jensen Huang at Nvidia, or Toyota's Kaizen model.

A platypus by contrast upends old categories and creates a new model. Such innovators can come out of left field.

Think: Steve Jobs creating the personal computer or smart phone or Airbnb refactoring hotels.