All scientists should have their PhDs in integers. Every mistake is inconsequential until the error scales up to the curve at the end of the number, when it turns out that yes, actually, the fault lies with you.
One of the nice things about education – at least for the higher levels, or what there is of it – is that it forces you to spend time in contexts that you can’t solve. In many science classrooms, students learn about complex mathematical problems that they’ll never have to handle in their real-world jobs.
Read the story of the solution to one of the longest algorithms in the world, and not only does the acceptance that you can’t solve the problem not apply, it puts you in an even more difficult position.
The key is to understand the scientific reason for the solution. When you do, you start seeing that most problems are not solved just by measuring and solving. These algorithms deal with randomness and states that other people believe exist. They can’t explain them simply by saying that the world is in constant motion.
Every failure of an algorithm is due to a different, explicit reason. Imagine having two different algorithms for the same control in the same geometry world. You may imagine that the one that you prefer is true, but will clearly change in case it requires a continuous motion of pendulums in another system. Therefore, the second algorithm is just an error.
So be careful about that first algorithm: it is your mistake.
Also, don’t be a dick. An average number of errors is a very small number. Put your finger on the scale, and find out which ones apply to which set of problems. When you can see the red column under your algorithm, or the middle column under the other algorithm, then you know to commit a common error in those cases. You should always treat an error as a mistake, no matter how tiny its apparent importance. And keep the bell curve from getting lost in the shuffle.
It’s enough to teach a sensible mathematician something, and frankly, that sense of self-preservation can be quite a thrilling thing to begin with.