In Apology and the
Ramanujan readings, we learned a lot about the lives of the mathematicians
Hardy and Ramanujan, respectively. While
this information presented the lives of the mathematicians not strictly in
terms of their work, the thing I took away from the readings was highlighted by
the third article. Is math really a
young person’s game?
The
Ellenberg article assumes that everyone knows mathematical discoveries are the
work of the young and accomplished is a moment of epiphany. I would tend to agree with the second part of
that assumption, but I never even considered the first part. I always thought mathematicians spent years
of their life working in secrecy and locked up in a room, much like Wiles,
whittling away at some new theorem, and presented their findings when they were
around 40 years old. But Hardy says “the
years between eighteen and twenty-five are the critical years in a
mathematician’s career.” So
hypothetically, I would have to come up with something brilliant either before
I finished my undergraduate math major or graduate school for math. Personally, I think that’s an unrealistic expectation
for math students. But Hardy’s statement
was mentioned about 70 years ago. More
recently, the Ellenberg article says that “today one doesn't find
mathematicians who revolutionize their field – even once – before the age of 22,” and that young probably means under 50. The only reason the earliest “prime-time age” has been
pushed back is because there is more math to learn.
I don't think we can really say when someone is past their potential as an academic. To me, that's like saying that person can no longer create unique connections within their subject area, just because they are past a certain age. I know the age range is not definitive, but it still bothers me that society has constructed an age range for when someone is going to be the most brilliant. Are the math
prime years just something people extrapolated from the information about past
brilliant mathematicians? Do those prime
years exist in other fields or even at all?
We label prime years in athletics; is it fair to label the prime years
in academics?
When looking at prime years of education, what you learn in elementary school lays a lot of the foundations for further learning. There are prime ages where you are suppose to learn certain skills. After those ages it becomes very difficult to learn basic skills. For example in our literature class we are told almost if a student doesn’t learn to read by the end of 3rd grade, their reading levels in adulthood will be significantly lower. This can be a cause of why some high students are still reading at an elementary school lever. Also there are the students who go to emersion schools, and why certain elementary schools have foreign languages. These students have an easier time picking up the language at an earlier age than say a middle school student or adult. Our brains when we are younger are more fluid and it is easier to learn and adjust to concepts. Applying this to mathematics, I would say that there may be an age but like you touched on it would have to be older. Certain skill sets would possibly have to be met to continue excelling at knowledge. It is also pointed out in education that everyone learns at different rates so these are just the general time frames there are always exceptions.
ReplyDeleteI think you made an excellent observation of the overarching theme of the readings by highlighting the question of age, which is likely the key to understanding the progress of progress itself.
ReplyDeleteWhy is it that great advancements in the field of mathematics are - or at least appear - to have come mainly from young and exceptionally brilliant mathematicians, and why is that no longer the case?
Course the obvious answer to the latter part of this question is that mathematics itself is so much more advanced that the only way for anyone to make groundbreaking discoveries is to undergo years and years of study just to understand the modern state of their field. A perhaps less obvious answer (that I will expand on later) might be that some aspect of our cultural evolution is making it harder for our younger mathematic minds to be able to make such discoveries. But why in the past does it seem that there is an age limit on mathematical brilliance? What, if anything, about a younger person (who is less experienced and more naive) would facilitate such discoveries?
I believe the answer lies in Poincare's assertion that deduction alone is not enough, and it is only the coalition of logic and intuition/creativity that allows one to see those possibilities. As we age, we tend to more heavily rely on strict rules and guided absolutes, and most people tend to become far less likely to stray outside the lines/be creative. So if creativity is indeed such a momentous aspect of discovery, it would make sense then that after a certain [relative] age, individuals in the field of mathematics - which requires extremes of both logic and intuition - would have a harder time making those discoveries.
So, too, it might be that, in this day and age where math students spend so much of their years learning rigid absolute rules, the young - who are normally very gifted in creativity - are stifled in their ability to think outside of that box of learning; thus it would follow that only those who held fast to their "childlike" nature and creativity through to old age would be able to make groundbreaking discoveries in the field of mathematics.