schele

Question#

• Before answering this question, we should first ask ourselves, what is genius?

  A genius is a person who is exceptionally intelligent.

  • Without a doubt, we can think of many associated identities from the term [genius], such as numerous awards, high IQ, good at math, and winning the highest awards in certain fields, etc. These people seem to be naturally talented and more capable than most people...
  • After a series of associations and enumerations, we can directly summarize a concise definition, according to Wikipedia and various dictionaries, that a genius is someone who is naturally very intelligent. But if we think carefully, we will find that in the previous explanation, we do not know what [intelligent] means, nor do we know what [very intelligent] means.
  • When we use [intelligent], we often treat it as a kind of praise, a praise for someone's success in something. It is often confused with adjectives like [successful], and it seems that we have never used and understood it. So, is [intelligent] actually a synonym for [successful]? Let's recall some other uses of it. Sometimes we use testing methods to quantify a person's level of [intelligence], but this also has a problem: what we are actually measuring is [success], not intelligence.
  • This is very puzzling and disheartening because it leads us to a fact: being successful means being intelligent, and not being successful means not being intelligent or not being intelligent enough. [Intelligence] is measured, not an innate characteristic. Without measurement, there is no [intelligence]. It is a subjectively constructed definition.

  Physics no longer exists! Intelligence no longer exists!

• Could it be that there are actually no geniuses at all, and it's just because those people are successful that they are considered geniuses?
  • I believe that some sensitive readers, after reading the above discussion, may have a feeling of doubt, or some intelligent and imaginative readers may have already noticed some unspeakable questions. Although intelligence is considered a subjectively constructed definition at this point, for those "intelligent" people, their success is a definite fact. So when we want to describe their ability to succeed in the "test," if we use [intelligence] to describe their [success], according to the previous statement, it is difficult to accurately describe this ability. So, what is this ability?

  You can try to use your thinking ability and think about it. The answer is hidden in your thinking or in this blog.

Enlightening Conversation#

• "I understand you. I also experienced this collective anxiety and exam-oriented torture in my sophomore year of high school. At that time, I could only constantly fight against those irrational fears, without even a chance to take a breath and think. Yes, I couldn't even have a cup of coffee."
• "No matter how hard I tried, I couldn't catch up with those people who could get good grades just by studying casually. They could even spend most of their free time playing games. I have doubted more than once whether they are time travelers or people who can predict the future and know the answers to exams. But they are geniuses, just like you."
• "No, my friend, I learned something in my career of studying mathematics, and that is that there is no such thing as a genius who can solve all problems. What do you think we rely on when we think about the answers to our questions?"
• "A flash of inspiration? I heard that mathematicians are like that."
• "No, (takes a sip of coffee) that is a description of looking back after solving the problem. In our thinking process, a flash of inspiration is not recognized. It's like the feeling you get when you read descriptions about love and the feeling you get when you actually experience love are not the same. Think about it again, the answer should be more essential."
• "Basic mathematical knowledge and logical knowledge, past experience, excellent reasoning and calculation abilities? The ability to think of things that seem unrelated and unimaginable to ordinary people."
• "Exactly, the key is association. Do you know about the Abel Prize and the Fields Medal?"
• "I've heard of them. Aren't they like the Nobel Prize in mathematics? I remember they are specifically awarded to those mathematical geniuses."
• "Do you know Andrew Wiles?"
• "Do I look like I know?"
• "You can look up his biography. You will find that he is not outstanding, even obscure. Compared to those who have won many Olympic gold medals and awards along the way, why is he the one who proved Fermat's Last Theorem?"
• "Because he could think of how to solve it?"
• "To be precise, it is because of his unique association in this regard. Being a genius is not important, what matters is the ability to solve problems through association. At least in mathematical research, this is the case."

A New Kind of Intelligence#

• You can find many examples in the mathematics community that are similar to Andrew Wiles, such as Perelman, Hugo Duminil-Copin, etc. This inspires us that association is the key.

  Perelman is even a dropout who writes poetry.

• At this point, we can answer the question in the title using a new, more reasonable definition of intelligence: when faced with a problem, being able to think of a solution is intelligence.
  • Congratulations, we have obtained a suitable answer, and it seems to be closer to the essence of our thinking. From here, we can draw a few simple conclusions:
    • When we examine whether a person is intelligent, we are examining whether they can have an inclination for association to solve problems appropriately.
    • Geniuses still exist, but now we can describe them more clearly: using innate conditions and a small amount of shared progress, they become intelligent, which means they are geniuses.
      • It emphasizes the combination of innate conditions and the environment, allowing some people to develop a certain kind of association that is worth attention outside of school education.
    • The process is no longer important; we value the result more. If you can do it, you are intelligent; if you can't, you are not.
  • Then, a new question arises: is it that if you can't think of it, you are not [intelligent]? Can this kind of [intelligence] be quantitatively compared?
  • Yes, if we define [intelligence] in this way, we can say that someone is not intelligent, but only in this particular question, they cannot think of the association to solve this problem. We cannot compare who is more intelligent than others under this definition of intelligence. It lacks practical significance under this definition. Therefore, IQ tests cannot reveal who is more intelligent, nor can exams. It only depends on whether you can think of it, whether the association of the test taker can adapt to the test. We are only selecting people who are more inclined to associate in a specific direction.
• At this point, we have clarified the answer. Being successful means being intelligent, but it is only a fitting appearance. True intelligence lies in association. However, whether one can think of the solution to this problem does not mean that they cannot solve other challenges. We cannot deny and give unequal judgments in all cases.

Final Thoughts#

• "Are there any other definitions of intelligence? Just looking at the result without considering the process is too cruel. Shouldn't we add some fair factors to it? Otherwise, those who memorize exam templates will be the same as those who come up with solutions on their own."
• "Then how do you define 'coming up with solutions on their own'? However, we can indeed have more definitions, which inspire us to have such a definition."
• "What do you mean?"
• "When faced with a problem that one cannot figure out, the amount of time spent solving the problem constitutes the answer to the problem."
• "Ah?"
• "For a problem that is more difficult for oneself but easier for others, if one can solve it before others, we can say that they are 'intelligent' in this case."
• "Isn't that just comforting oneself?"
• "No, if you can do it, you are intelligent, and more intelligent than others."