⚠️ New challenges arise every day. At work, in life, for us and for other people around us, everywhere. Solving a specific problem can be easy for one individual and yet very hard for another, it all has to do with the parameters of the problem and its solver.
Imagine you encounter a challenge, perhaps within the realm of engineering. In my experience, the hardest problems are often the most interesting ones. While it might be tempting to go for an apparent, straightforward solution, it's exactly in those situations where an alternative remedy is apparent and there is no fear of failure, that the appeal of facing a difficult problem becomes irresistible.
⏳ Deep down, the solver is aware of the fact that the time investment in that problem can be a rewarding experience because of the new things and ideas that come as a byproduct of the process. "Beautiful" problems, for me, are the ones that have the highest returns. An example of a “bad” problem for me would be the exact opposite: spending time on something that you feel that, even if it gets solved, won’t make a difference to anyone, not even yourself.
Elon Musk said something along these lines: "Engineers excel at solving problems that may not necessarily need solving." I would fully agree if the quote ended like this: “unless the time investment on the problem-solving makes more sense than the problem itself!”
☝️ Engineering is forgiving, math is not
In engineering, we play with accuracy: we have accurate and not so accurate solutions to a problem. Depending on the accuracy needed, the complexity of the problem can increase exponentially, which makes solving it almost impossible.
The good thing is that experienced engineers know the limit of their methods and their accuracy. This is not straightforward, and many years of experience are necessary to get a good understanding of this. But, at least, you can count on other more experienced engineers, books and the internet as good weapons.
🫀 The same happens with life problems. There are defined problems that we can face with logic, and then there are others that require emotions or a blend of logic and emotions. It is often the case that a solution to a problem can work for just one individual alone. It’s all so subjective… Suddenly engineering problems seem easier to tackle!
Whilst life and engineering problems may have accurate, inaccurate, logical, subjective answers, mathematics is the exact opposite. In this sphere there are no opinions, no subjectiveness, no inaccuracies, and answers are either true or false.
🎯 Once a conjecture is proven true or false, this is it. It’s an absolute truth. Difficult math problems can stay unresolved for hundreds or thousands of years. That is the case, for example, of “Fermat’s last theorem”, that stayed unresolved for 356 years, only to be solved by Andrew Wiles back in 1993. For anyone who hasn’t read the book with the overmentioned title by Simon Singh, I highly recommend it.
💡 A fascinating story
What I like in the case of Dr. Wiles is the absolute sheer determination to solve a very simple problem, as far as describing it, and the path he chose to do it.
