Problem of a slow thinker

Question

I am a graduate student of mathematics. I often feel frustrated due to my inability of solving sums or thinking of a sum as fast as my peers can do.

Let me clarify.

I have noticed whenever I sit to discuss sums or mathematical problems with others or confront a new question in a classroom, I need more time to understand, think and solve a sum than my peers. It’s not that I am unable or afraid of solving hard problems. Of course I love confronting tough problems and can solve many of them.

The problem is about speed. I just can’t solve them or think of them in a speed others of my age can or expected to be. Rather I am much slower than them. The same goes on for understanding a sum, it takes more time for me to understand and visualize a sum, perhaps in the meantime others already have started thinking about its solution. Consequently I had face a tough time in viva or while giving a seminar and someone ask a question. Most of the time the answers came to me after it’s over.

As a result I often doubt myself whether I should be in mathematics or not. Unfortunately I love mathematics.

However it makes me frustrated. Isn’t there value for a slow thinker in mathematics?

Still I don’t know how to be a fast thinker like the usual maths people out there. Is there any way to be as fast as them?

Please help me.

Answer 1

During my postdoc at the University of Chicago I shared an office with Tom Wolff. He was already famous, at that early point in his tragically short career, for this.

I was amused at the time by how he didn't seem at all brilliant in social/mathematical interactions, if anything almost the opposite. If you asked him a question on a topic he wasn't prepared for the only thing he ever said was "uh...". But sometimes he'd have an answer the next day, and when that happened it was worth the wait.

Answer 2

We are all individuals and each of us is unique and has his/her own talents.

Being slow or fast is not an issue unless it keeps you from being successful in your studies.

As you indicated, you love mathematics.

Well, you need to make mathematics love you too if you want to live together for a long time.

One indication of success in graduate school is your grades in mathematics classes. If you are making $As$ and $Bs$ you are fine and I would not worry at all.

If your grades are not good then you need to manage your time better and seek ways to improve your grades.

Answer 3

There is one story I once read in a book about meditation, but I think it applies to your concern. This is how it goes (from my poor memory, in my own words):

Once there was a little boy who was all the pride of his parents. He was handsome, extraodinarily kind and empathetic and he always surprised his parents with his bright ideas.

One day he was about to be sent to school. At first he appeared to be very happy to learn new things. When it came to the first math lessons, the teacher taught all the pupils the number "1" and how to write it onto the blackboard. Our little boy was delighted to hear about this exquisite concept of the number "1". He wrote it down onto the blackboard very eagerly, over and over again.

But then, after the first week, the teacher decided it was time to go on and teach the children number "2". But, alas, our little boy didn't feel all that well about this sudden change and refused to write down "2" onto the blackboard. He resumed writing the "1", repeatedly.

The teacher was tolerant and gave the boy the time he needed, but after several weeks, when all the other pupils had learned already almost all the numbers up to "10", the teacher got worried about the boy lagging behind so much, and so he informed the parents about the state of affairs.

The parents were concerned severely because they simply couldn't understand how their smart little boy could have turned into such a learning-resistant pupil. They talked with him about it, but he insisted that he had not yet been able to learn how to write "1" correctly. After all, it appeared to the parents that their son was already writing it perfectly. Why was he so stubborn?

Half a year later the boy was still writing "1" when all the other pupils had already learned summation. The parents were almost hopeless and thought about sending him to a school for disabled children.

But then suddenly one day, the boy ran to his teacher, highly elated, and told him: "Teacher, Sir, now I know how to write 1 correctly". The boy took him by the hand and drew him to the blackboard. Then he took the chalk and wrote "1".

And the blackboard broke in two.

Answer 4

Of course, speed is a very desirable skill to have, but in research mathematics what matters most (in my humble opinion) is the depth of one's ideas rather than the speed. Anyways, I will just recite one of my favorite quotes by Alexander Grothendieck (see here for example).

Since then I’ve had the chance, in the world of mathematics that bid me welcome, to meet quite a number of people, both among my “elders” and among young people in my general age group, who were much more brilliant, much more “gifted” than I was. I admired the facility with which they picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle — while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things that I had to learn (so I was assured), things I felt incapable of understanding the essentials or following through to the end. Indeed, there was little about me that identified the kind of bright student who wins at prestigious competitions or assimilates, almost by sleight of hand, the most forbidding subjects. In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of 30 or 35 years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birth-right, as it was mine: the capacity to be alone.

Alexander Grothendieck

Answer 5

Well, apart from many other considerations, there are sectors of mathematics and collateral where slow-thinking is much beneficial. One example for all is programming.