Does intuition matter in solving problems?

Does intuition matter in studying science or solving problems in general? I’ve been trying to arrive at a conclusion to this question since I was in high school. I summarize my personal thoughts as follows, which, as a disclaimer, are not meant to be rigorously justified.

Why did I care about intuition?

During my high-school life, I had several friends who did maths very well, partly due to their hard work and on the other hand because of their inborn talent in dealing with abstract ideas. But soon I realized that I had missed something. When we did some hard problems together, they could easily “guess” an efficient way of solving the maths. To emphasize, I meant, they really just made guesses without rigorous logical reasoning and most of the time the guess turned out to be indeed correct. This couldn’t be by pure luck and there must be some magic in their mind. So I started to think: does someone have better intuition than others?

Is intuition simply a guess?

Intuition is totally different from pure guessing. Guessing is just like gambling and there is certainly no promise to whether the said answer is right or not. But in my opinion, giving an answer by intuition does involve logical reasoning but even we ourselves don’t know our minds are doing such work. You may be thinking how it is even possible. But do we really fully understand how our brain works? If you ask a sophisticated musician who can play the song after listening to it once only, I bet he or she can’t answer you in a scientifically logical way and simply tells you that it’s due to experience. So the next natural question is: does intuition have something to do with experience?

Does an experienced person have better intuition?

I believe experience can be a factor that affects one’s intuition. I always do certain kinds of maths using a lot more time than solving other types of questions. The reason is that most of the time I start working on the problem in an incorrect way and I’ll say that I have bad intuition in this area. Perhaps it’s due to my lack of in-depth domain knowledge and insufficient experience in tackling similar problems.

Does experience solely lead us to better intuition? I think not. There’s still something more. Some managers in a large company have been working for many years but they still always make “guesses” incorrectly, such as giving a wrong direction for kicking off a project. Why do they have bad intuition despite their years of experience? I think this is because they lack the ability to put fragments together. Some people are good at connecting things together. We may know the same ideas but there are just someone who can put the seemingly irrelevant ideas together to arrive at something different, which I’ll call it talent.

So to briefly wrap up my thoughts, intuition is not any magic but rather is kind of a combination of experience and talent. Wait, do I still miss something?

Can good intuition be developed?

Experience can be accumulated over time but it seems not to be the case for talent. In other words, can we develop our talent to lead us to better intuition? My answer is no because talent is inborn and you can never become talented in an area in any way. BUT, we can develop a better way to think. In the past, I always struggled to know the finest details of any maths or science problems without trying to get known of the full picture, perhaps due to my personality and also perhaps owing to the style of Asian education which urges you to dig into every detail or otherwise your marks will be deducted.

In recent years, when I study some theories, I feel better to have a high-level understanding first as well as the relevant history. Knowing the motivation and the big picture of the theories does guide me to solve problems in a better direction. I don’t mean that technical details are not important. But to me, it’s much better to get the picture first and fill the details afterwards. This thinking style helps me to have a better intuition.

Is talent that important?

In the past, I always thought that my friends who did maths well were just talented, allowing them to have good intuition and giving me an excuse not to work hard because I’m just not talented. But as I summarize my thoughts, I realize that good intuition is not simply an inborn ability, but is indeed reflecting the time and effort you have devoted to gaining the experience and strengthening your skills as well.