You can expend precious energy chasing the holy grail of 100% certainty, or you can choose to settle for 95%, or 70%, or even 20% certainty.
When I was a graduate student, I worked for months to prove the main mathematical result in my dissertation. I struggled with this proof. I churned out pages of chicken scratch calculations. I manipulated equations in my head while I ate, showered, vacuumed, and exercised. I had math dreams.
Finally, I thought I’d nailed it. It was a large and hairy beast that sprawled over many pages. I showed it to my adviser and declared, “I’m 95% sure it’s correct.”
He raised his eyebrows. “Well, you’d better be 100% sure,” he replied.
That’s when I realized that he wasn’t planning to check it himself. He was just going to trust me. And then I started to worry. What if there was an error in my proof? What if the central result in my dissertation turned out to be wrong? Could they take away my PhD? And if I got a job based on work I’d done in my dissertation, could they fire me? Would my career be ruined?
I checked my proof carefully many times. But I still couldn’t be 100% sure it was right. I knew there could be a glitch in my logic that I simply wasn’t smart enough to pick up on, no matter how many times I checked. After all, how many times had I turned in math homework – confident that my answers were correct – only to find out later that there was a major flaw in one of my solutions? And the stakes were much higher here. I asked a classmate – someone a lot smarter than me – to check my proof, and he thought it was correct. But I knew it wasn’t his dissertation or his responsibility, so I couldn’t completely trust his assurances.