"Mathematics is the form in which we express our understanding of nature; but it is not the content of that understanding"When I solve a mathematics problem, I do use models and formulas to solve a problem. But that is definitely not the first step I take. Before thinking about which formulas to use, I glance at the problem and then instantly know how to approach this problem. I never knew how this works, but I knew this is the way it works for me. So if I was asked for "intuition or mathematical?" question, I will immediately answer, "intuition."
Whenever people think about science, they easily deduce logical thinking. However, the creativity brings forward. If you look back on the new scientific discoveries, often it is first unaccepted by that scientific community because it seems totally out of logical sense. The logic follows after the intuition in the scientific discoveries and people value too much of "what is making sense" does not have a flexible mind to accept some wacky rules or properties that nature created.
I personally always feel the intuition is the first step for the thinking. However, the main problem is how to build that instinct. I don't think I can get any of these math intuition unless I have done hundreds of repetitive calculations. But at same time, some people do same amount of work but still have a difficult time having that intuition. Can the intuition can be trained or is it just a certain talent?? I wished the article touched more on this issue.
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