After 16 years devoted to mathematics you start to see a lot of misconceptions about the learning process. For me, one of the most toxic misconceptions regards the Eureka effect. Apparently, people tend to think that some things, which changed the course of humanity, came out of nowhere.
For instance, historians like to tell people about Isaac Newton’s discovery of the law of universal gravitation. We are told that it was just a random apple falling on the head of a genius, who was enjoying a nice afternoon under a gentle shade, and BOOM: immediately after that, Sir Newton had a concise explanation for gravity.
The most famous example is probably the one to give birth to the Eureka effect term as we know it: the Greek polymath Archimedes is believed to have essentially created hydrostatics while he was bathing in a tub.
The movie industry is probably the main responsible for propagating this misconception that great ideas are just revelations. The problem with movies, for example, is that to keep high levels of audience engagement they show only a few portions of the hard work involved, or sometimes cut it out completely. The result is a dangerous over-simplification of all processes of learning and researching. On one hand, I kind of understand the decision. As a mathematician, I can say that the task of solving a problem is full of frustration and boredom (like almost everything in life, actually). So, a truly accurate movie would carry over all those feelings onto the screen.
On the other hand, the way those stories are told hides tons of hours and effort used in solving these problems by humans. They give the false sensation that either you are a genius and things come to you as revelations with no effort needed or you cannot do great things in the world. Neither of those impressions are correct.
All the great ideas and tools humanity has developed so far came after really hard work. Even those groundbreaking ideas, like Theory of Relativity , required years of dedication to be fully understood, to be digested and recorded in a clear way. Moreover, even completely new ideas rely on, to some extent, previous work, which took time to be done.
The take-home message here is the following one: don’t fall into the trap that things can be done easily or that you need to be a genius to make your contribution to the world. Even the greatest minds of all time struggled at some point as they looked for the truth. The path is full of ups and downs, this you can take for granted. Making scientific progress can be boring and painful in many ways, but at the end of the day (or week, or month, or year, or decade!), the feeling of discovering or understanding something new is priceless. Believe me when I say that the process of learning, even if it demands so much effort, is one of the most beautiful things I have ever seen.