Some years ago... Ok, ok, let's start over:
Many years ago, when I was a Physics student in college, I happened to learn one of the most valuable lessons I've ever learned in life.
The last year of my BS in Physics I decided to take some courses in Mathematics. Of course I had studied a lot of Maths in Physics, but we did not use to be as rigorous as mathematicians are.
I met this Professor, who taught Abstract Algebra. Knowing that I had almost finished my studies in Physics, he called me to his office one day.
«Here,» he said, «I have this problem I want you to solve. Just remember: do not look through books for the solution. You should be able to find it just with what we've learned in class.»
Funny as it seemed to me at first, I eventually thought it was something every student in his course would go through. So I went for it.
For the next two weeks, I tried every possible way to solve the problem. I used brute force, I broke down the problem into smaller ones and worked through every piece of it, I looked at the problem from different angles, etc. But I didn't succeed at all.
Exhausted, I finally went to his office. I unfolded a pile of papers in front of him, showing every single reasoning I had tried.
«I couldn't...» I started babbling.
He didn't even glance at the papers on his desk. He just looked at me, condescendingly, and said:
Many years ago, when I was a Physics student in college, I happened to learn one of the most valuable lessons I've ever learned in life.
The last year of my BS in Physics I decided to take some courses in Mathematics. Of course I had studied a lot of Maths in Physics, but we did not use to be as rigorous as mathematicians are.
I met this Professor, who taught Abstract Algebra. Knowing that I had almost finished my studies in Physics, he called me to his office one day.
«Here,» he said, «I have this problem I want you to solve. Just remember: do not look through books for the solution. You should be able to find it just with what we've learned in class.»
Funny as it seemed to me at first, I eventually thought it was something every student in his course would go through. So I went for it.
For the next two weeks, I tried every possible way to solve the problem. I used brute force, I broke down the problem into smaller ones and worked through every piece of it, I looked at the problem from different angles, etc. But I didn't succeed at all.
Exhausted, I finally went to his office. I unfolded a pile of papers in front of him, showing every single reasoning I had tried.
«I couldn't...» I started babbling.
He didn't even glance at the papers on his desk. He just looked at me, condescendingly, and said:
«You know? In Maths, we always check if the problem has a solution before even trying to solve it.»
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