Originally, it was a question on Quora that prompted this and got me thinking. The person asked if “math geniuses” struggled with math problems. Hmmm well first let’s answer that question.
Struggling is actually relative to the one solving the math problem. So, if you are asking if a math genius struggles with some of the problems that are difficult in basic classes up through calculus, then probably not. If, however, you are asking if such gifted individuals work through problems of their own without always knowing every step beforehand, then yes.
I provided the picture to exemplify my meaning here because it can be difficult to imagine problems that “geniuses” would find challenging, even for me with a math degree. While the first problem is hopefully easy for those reading through this, a student experiencing math for the first time can have a hard time putting together that one quantity plus another quantity gives a third quantity.
As a tutor and teacher, I have worked with students from the ground up, so to speak. It’s actually really cool watching little ones light up as they make connections and discover patterns. Getting there can be a struggle, though, and we all went through it at one point or another. In fact, the same struggle sticks with us all the way through our discovery and practice of mathematics.
There are problems out there that remain unsolved despite these brilliant mathematicians working together to arrive at a solution to benefit all of mankind. I would say that qualifies as a struggle since they haven’t been able to determine an adequate answer. But this is not a bad thing!
One of my personal education mentors asked me a question that has forever changed the way I approach math both as a student and teacher. Does struggling have to be a bad thing? While at first, of course I was opposed to ever having a student I was pouring myself into go through any distress in their attempts mostly due to the already negative association many people have with math, I came to understand that this is how individuals grow.
No matter how many times I explain a concept to someone, it will always seem easy when I do it because I already know how to perform the calculation or derivation. Until that person realizes for his or her self, they cannot repeat the process on a new problem. The struggle leads to discovery. Working through examples and then problems on their own helps foster both independence as well as appreciation for the effort needed to become a capable mathematician in their own right.
Granted, I don’t mean locking someone in a room and leaving them to their own devices. No, no. What I mean is a guided study that is equal parts help and discovery so that every student can feel that they understand the subject matter.
If you’re like me, then this revelation is one that does not come easy and can lead to a good deal of strife in terms of concern not only for your own progress but those you are responsible for. Hence, one of my favorite quotes from one of the greatest minds that has ever lived.
The famous math genius and physicist himself, Albert Einstein said not to let your struggles get you down because he was sure he had a much harder problem that he was trying to solve. Hard to get more authoritative than that!
Hopefully this not only answers your question but also serves as a springboard for any discouraged students looking toward the future for a little hope.
As always, thank you for letting me a part of your journey through math!