# The Innovator's Paradox

One of my favorite problem-solving techniques from math is the innovator's paradox.

Inventor's paradox.A more ambitious plan may have more chances of success. In math, this means generalization and induction.

It comes from a book called *How to Solve It *by mathematician George Pólya (known for the Pólya conjecture, Pólya inequality, and more).

Imagine solving the sum of a sequence of integers `1 + 2 + 3 + ... + 999 + 1,000`

(without a calculator). You could probably brute for the solution, but it's a lot simpler to figure out a generalized pattern for the sequence to solve that. In this case, you can pair up the numbers `(1 + 1000) + (2 + 999) + ... = n * (n + 1)/2`

where `n=1000`

.

Solving the general case is usually easier (and smarter) in programming as well. It's not just tied to math and computer science, but it also seems to hold true when it comes to taking different types of risk – e.g., a startup attacking a potentially massive market (vs. a constrained one).