A Stanford mathematician spent forty years watching one brilliant student after another crash into hard problems.
Not because they weren’t smart.
But because no one had ever taught them what to actually do “before” they started solving.
His name was George Pólya.
In 1945, he published “How to Solve It”. The book sold over a million copies and has never gone out of print.
Even Marvin Minsky, who built the first neural network, said that everyone should read it.
Yet most people still haven’t heard of it.
What Pólya kept seeing was the same failure pattern, again and again:
The moment a difficult problem appears, students get anxious and immediately start calculating.
Not because calculating is the right first step, but because doing somethingfeels much more comfortable than sitting with “I don’t know.”
They end up working hard in completely the wrong direction.
The step he found most neglected was this: Truly understand the problem first.
Not just skim it. Not just think “this looks familiar.”
His test was simple but ruthless: Can you restate the problem in your own words without looking at the original?
If you can’t, you don’t actually understand it yet.
Most people skip this step entirely. They jump straight into execution and then get stuck on a problem they never truly grasped.
Pólya outlined four steps for solving problems. But in real life, the two that matter most are usually the first and the last:
1. Understand the problem deeply
2. Devise a plan (if you’re stuck, try solving a simpler version first and bring the insight back)
3. Carry out the plan
4. Look back — verify, generalize, and reflect
The people who get truly good at this aren’t the ones who practice more.
They’re the ones who’ve learned to slow down when every instinct is screaming at them to just start calculating — especially at the beginning, and again at the end.
What struck me most after reading this:
We assume hard problems are difficult because they are.
Most of the time, it’s simply because we never took the time to truly understand them.
The Two Different Paths: We are about to find out which path we are on. As I said in my last note, from my conversations with a number of world leaders in a number of countries, and as seems obvious to me, there will either be a) a U.S. win over Iran, which will require taking control over the Strait of Hormuz and assuring that Iran's nuclear program is dead—i.e., defanging Iran, or b) a U.S. loss, which is the result if these things don't happen.
Most senior policy makers I speak with believe that we are likely headed down the b) path and that will be made clear soon. It needs to be made clear soon because continuing on the current path or being more forceful will cause sharp increases in oil and gasoline prices and great difficulties during the high travel season, bad political consequences for President Trump, and difficulties in his upcoming meeting with President Xi in China. So, we should have that verdict soon.
The perception that the b) path is most likely is already leading to a view that the United States will not be a reliable protector against possible opponents like Russia in Europe and/or China in Asia, and that is already leading to actions being taken that are sensible in light of that belief, like leaders paying "tribute" visits to China. As explained before, this set of circumstances is likely to have some analogous consequences to Great Britain losing the Suez Canal in 1956. By the way, this is also happening at a time when China is earning huge amounts of money through its very strong exports—so much money that it is difficult for those Chinese earning the money to know what to do with it. This is making China a very important player in world capital markets as well as world trade. In other words, these events are making China geopolitically and financially stronger.