“At heart, mathematical thinking is little more than formalized common sense. It always has been. Which means it is something we can all do.”

— Keith Devlin

How Today’s Pros Solve Math Problems

If you have some time to spend pondering big ideas, dig into Devlin’s entire series of posts about what real-world mathematics looks like and the implications for math education:

And a related series on K–12 school math:

“Make no mistake about it, acquiring that modern-day mathematical skillset definitely requires spending time carrying out the various procedures. Your child or children will still spend time ‘doing math’ in the way you remember.

“But whereas the focus used to be on mastering the skills with the goal of carrying out the procedures accurately — something that, thanks to the learning capacity of the human brain, could be achieved without deep, conceptual understanding — the focus today is on that conceptual understanding.

“That is a very different goal, and quite frankly a much more difficult one to reach.”

— Keith Devlin

All The Mathematical Methods I Learned in My University Math Degree Became Obsolete in My Lifetime