Are Mathematical Breakthroughs Limited to Youth?

[moe darklight]

I just started reading GH Hardy's |A Mathematician's Apology;| a book that will probably scare and depress the crap out of me, because I have a horrible fear of growing old.

Anyway, I just finished reading the CP Snow foreword (which takes up a good third of the book), whose following comment struck me right in the phobia:

[...] I do not know an instance of a major mathematical advance initiated by a man past the age of 50.

Clearly I don't plan to ever be a mathematician, but since mathematics is one of those few professions that truly stretch an individual's mental abilities (in areas of logic, creativity, problem solving, etc.) to their fullest, I figure a mathematician's abilities as he or she ages are highly indicative of the effects of aging on the brain.

So is this true?

I've looked around and noticed that most important mathematicians and physicists "boomed" around the age of 23-35. This is regardless of whether they were child prodigies (like Newton or Gauss) and got a "head start" or not; the 20's are the magical number it seems.

Surely there must be exceptions to the rule. Are there any examples of mathematicians or physicists who made their major contributions late in their life?

What about the brain's ability to acquire new skills as it ages? are there any who began their careers later in life?

Do I need therapy? ... I am seriously mortified of becoming senile, and I'm only 20. Or maybe it's because I'm 20; I find it horribly depressing to think that this is as good as It gets, and that in 10 years I'll begin a slow and inevitable decay.

I mean, if a great thinker like GH Hardy felt his mental faculties were performing at less than optimal levels in his 50's and 60's, what hope is there for me to not be a complete vegetable by the time I'm that age.

I'd like to think that it's possible to acquire new skills and keep leading a productive creative life well until the end.

O God. I'm 21 thursday.

 

[Evo]

You think at the age of 31 you will "begin a slow and inevitable decay"? Not unless senility starts at an unusually young age in your family. Then it's not age you have to worry about.

 

[tgt]

The main reason is that you don't have as much energy to do stuff in general. Hence you find it much harder to do something as unnatural (from a biological perspective) as mathematics.

 

[rootX]

Maybe, you will get a better meaning for "greatness"/"life" when you reach 31/50

You clearly don't have it right now lol

 

[Astronuc]

Do I need therapy? ... I am seriously mortified of becoming senile, and I'm only 20. Or maybe it's because I'm 20; I find it horribly depressing to think that this is as good as It gets, and that in 10 years I'll begin a slow and inevitable decay.

I mean, if a great thinker like GH Hardy felt his mental faculties were performing at less than optimal levels in his 50's and 60's, what hope is there for me to not be a complete vegetable by the time I'm that age.

I'd like to think that it's possible to acquire new skills and keep leading a productive creative life well until the end.

One does not need therapy. One simply needs to stop worrying about it. Don't worry about the end, just enjoy the journey.


My grandfather was a voracious reader, and he read a book a day and keep up with current events and world affairs. His mind was sharp even at 100. He only started to deteriorate physically around 102, and his mental deterioration only set in at 103, when he started getting recurrent illnesses.

 

[mgb_phys]

Paul Erdos

 

[Crosson]

http://www-history.mcs.st-andrews.ac.uk/Biographies/Weierstrass.html" is a a 19th century mathematician whose is considered to be one of the founders of the rigorous theory of mathematical analysis. He published the work that made him famous only after many years as an instructor at a high school.

Although he was not a mathematician, Immanuel Kant is considered to be one of the greatest philosophers of all time, and his groundbreaking work was written when he was over age 50.

Paul Erdos

Erdos hated getting old, and he primarily combated the mental effects of the aging process by taking amphetamines (the street drug known as speed). Any account of Erdos's life includes all kinds of humorous idosyncrasities of his, many of which are related to age e.g. he would say "John is dead" to mean that John no longer does mathematics, and he would say "John has left" to mean that John had passed away.

IMHO, I think that Erdos is not a good role model for aspiring mathematicians. But I think that Hardy is even worse! My recommendation is to stop reading the mathematician's apology, since all it does is unnecessarily and without justification promote an elitist and selfish stereotype of a great mathematician. If you look at the true greats from the distant past through the 19th century: Archimedes, Newton, Euler, Gauss, Laplace, Lagrange, Poincare, these men all expressed the importance of the root connection between physics and mathematics. Yes, they were in awe of pure mathematics (mostly number theory), but all of them did great work in fields that would now be considered applied. Hardy wants to smugly dismiss that tradition by appealing towards the ego of modern mathematicians, assuring them of their own superiority for being pure.

About his attitudes towards age, my opinion is that Hardy was a very frustrated person both professionally (it has been said that his greatest contribution to mathematics was to discover Ramnnujan) and personally (Hardy himself said that his collaboration with Ramanujan was the "one romantic encounter of my life"). IMO, his "apology" is just an expression of his personal jealousy, spite, guilt, and frustration, and I consider it terribly unfortunate that generations of mathematicians have been intoxicated by the elitist world view Hardy offers.

 

[moe darklight]

My grandfather was a voracious reader, and he read a book a day and keep up with current events and world affairs. His mind was sharp even at 100. He only started to deteriorate physically around 102, and his mental deterioration only set in at 103, when he started getting recurrent illnesses.

wow how old did he live to? it is amazing sometimes that while some people in their 60's are completely destroyed, others in their 80's or even 90's are perfectly fine.

maybe it is somewhat of an irrational fear... but not completely. I don't know... it's not the fact of growing old itself that scares me; it's the idea of decay. it sounds stupid but when I was a kid I was obsessed with the idea that I would some day run out of ideas. I remember every few months I would have these depressive episodes and I would freak out at my parents convinced that I've run out of original ideas.
Anyway I don't want to come off as a complete nutcase

IMHO, I think that Erdos is not a good role model for aspiring mathematicians. But I think that Hardy is even worse! My recommendation is to stop reading the mathematician's apology, since all it does is unnecessarily and without justification promote an elitist and selfish stereotype of a great mathematician. If you look at the true greats from the distant past through the 19th century: Archimedes, Newton, Euler, Gauss, Laplace, Lagrange, Poincare, these men all expressed the importance of the root connection between physics and mathematics. Yes, they were in awe of pure mathematics (mostly number theory), but all of them did great work in fields that would now be considered applied. Hardy wants to smugly dismiss that tradition by appealing towards the ego of modern mathematicians, assuring them of their own superiority for being pure.

About his attitudes towards age, my opinion is that Hardy was a very frustrated both professionally (it has been said that his greatest contribution to mathematics was to discover Ramnnujan) and personally (Hardy himself said that his collaboration with Ramanujan was the "one romantic encounter of my life"). IMO, his "apology" is just an expression of his personal jealousy, spite, guilt, and frustration, and I consider it terribly unfortunate that generations of mathematicians have been intoxicated by the elitist world view Hardy offers.

hm... he doesn't come off as terribly elitist or arrogant to me. He does come off as proud, but I don't see anything wrong with pride. Pride is a good thing; why is society so down on pride lately? His point that "great work is not done by humble men" is honest and true, but unfortunately easy to misinterpret and might come off as elitist when I don't think it's meant to be take as such. Either way, I'm interested in all points of view, and I don't think his is to be dismissed just because of some character flaws (some serious character flaws it seems at times).

... OK, so we have one example so far.

 

[mal4mac]

Faraday was the first to use the word 'field' in 1845, he used it then in a purely descriptive sense to describe the space surrounding a magnet. During the first half of the 1850s, he developed arguments for the reality of the field, which by 1851 he defined in terms of lines of force. He was 54 in 1845. Of course he wasn't a mathematician, but I think he was reasonably creative :-)

 

[George Jones]

But I think that Hardy is even worse! My recommendation is to stop reading the mathematician's apology, since all it does is unnecessarily and without justification promote an elitist and selfish stereotype of a great mathematician.

What a great book! One of my favourites! I encourage anyone who wants to learn what it means to be creative at the highest level to read this wonderful book.

(it has been said that his greatest contribution to mathematics was to discover Ramnnujan)

Completely unfair, and intentionally misleading.

and personally (Hardy himself said that his collaboration with Ramanujan was the "one romantic encounter of my life").

Hardy did not mean:

"romance: sentimental or idealized love",

he meant,

"romance: a feeling of excitement or adventure (the romance of travel)".

Hardy had high standards, and he applied these high standards to himself. According to these high standards, his discovery of Ramanujan was his only adventure that deserved to be called a "romance". This does not mean that he led an otherwise uneventful life.

IMO, his "apology" is just an expression of his personal jealousy, spite, guilt, and frustration, and I consider it terribly unfortunate that generations of mathematicians have been intoxicated by the elitist world view Hardy offers.

Hardy, elitist? Of course! Why shouldn't he be? Research mathematics is a competitive sport, and Hardy was one of the best mathematicians of his generation.

I am astounded that someone could write such a venomous diatribe about Hardy and his great literary work.

 

[Astronuc]

wow how old did he live to?

He died at 103.5, and as I recall, it was 1 hr into the new year, 2003.

maybe it is somewhat of an irrational fear... but not completely. I don't know... it's not the fact of growing old itself that scares me; it's the idea of decay. it sounds stupid but when I was a kid I was obsessed with the idea that I would some day run out of ideas. I remember every few months I would have these depressive episodes and I would freak out at my parents convinced that I've run out of original ideas.

Anyway I don't want to come off as a complete nutcase

It's probably not that uncommon to worry about such things. Best to learn not to worry, but the enjoy life and accomplish what one can.

. . . He does come off as proud, but I don't see anything wrong with pride. Pride is a good thing; why is society so down on pride lately? His point that "great work is not done by humble men" is honest and true, but unfortunately easy to misinterpret and might come off as elitist when I don't think it's meant to be take as such. Either way, I'm interested in all points of view, and I don't think his is to be dismissed just because of some character flaws (some serious character flaws it seems at times).

Pride is fine, as in pride of what accomplishes. I prefer to leave it as self-satisfaction.

I find that many get carried away with pride, and in some cases it devolves into self-absorption.

I prefer to live without 'pride' with respect to myself (from my studies of Buddha and ध्यान (dhyāna), Tao, K'ung Fu-tzu), but I don't mind feeling proud of others and expressing it.

 

[Gokul43201]

(it has been said that his greatest contribution to mathematics was to discover Ramnnujan)

That was said by Hardy himself, in one of his humble moments - he may have really meant it, but I can't imagine most mathematicians would agree. In any case, that by itself says little about the quality of Hardy.

There was a joke, early last century, about England having 3 great mathematicians at the time: Hardy, Littlewood and Hardy-Littlewood.

 

[OrbitalPower]

I thought that maybe Whitehead was maybe older because he was Russell's teacher before Principia Mathematica, but I just looked it up and Russell must have been in his 20s when that was written, and Whitehead in his 30s.

So, I'm out of suggestions.

 

[rootX]

I prefer to live without 'pride' with respect to myself (from my studies of Buddha and ध्यान (dhyāna), Tao, K'ung Fu-tzu), but I don't mind feeling proud of others and expressing it.

Learning same from Budda, Tao and, K'ung Fu-tzu.

I still have 80 yrs.

 

[wildman]

As I have said already in another thread, I knew a lady who retired as an unknown legal secretary at the age of 65. When she died at 102, the governor of the State of Washington, two US Senators and the mayor of Seattle attended her memorial. Also, a high school was named after her as well as an annual film festival. Shows that many people are not over at 65.

 

[wildman]

Also, as we watch the Olympics, keep in mind that no great athletes are above the age of 50 either (I would have said 40, but Torres in the Olympics proved me wrong), but that hardly means that 50 year olds are washed up. There are plenty of people who compete very well into their 70s or 80s. And often the difference between the best 60 year old is just seconds compared to the best 20 year old.

It is also interesting how people age at different rates. Part of it is how one takes care of ones self (smokers go a lot earlier on the average than non smokers for example -- just ask any doctor), but a lot of it is just luck.

 

[Howers]

There is no doubt that once we pass the age of 30, our mental abilities decline. However, nothing serious happens until about the age of 60. Keep in mind a lot of this also has to due with substances that damage the brain, like alcohol and pollutants, which at that age have accumulated for some time.

I believe Archimedes, one of the greatest mathematicians of all time, was productive well into old age. Euler sounds like another example, who worked until he was very old. I don't personally know the quality of the work at old age, so that might be something you'd want to look into. Also, I didn't know Newton was a prodigy... how do you know this? Guass yes, Newton? Hmm. I believe Newton was an average student too, not shining until Campbridge.

 

[tribdog]

I don't think mental abilities decline after 30. They definitely change, but that is not necessarily a bad thing. there is a reason for the "wise old man" stereotype.

 

[tribdog]

There are great mathematicians older than 50. the only reason it seems like you only hear about the young ones. the reason is simply because the young ones think they are invincible and they take on the jobs that supposedly can't be done. When they succeed it becomes news. Older mathematicians could probably solve the same problems, but they aren't as willing to devote their time to something that they may fail at.

 

[koolmodee]

Andrew Wiles was 42 when he proved Fermat's Last Theorem.

 

[moe darklight]

He died at 103.5, and as I recall, it was 1 hr into the new year, 2003.

It's probably not that uncommon to worry about such things. Best to learn not to worry, but the enjoy life and accomplish what one can.

That's amazing to have lived straight through the 20th century. I mean, he witnessed everything from the popularization of cars and airplanes to the internet, eh.

And yea, there's no point in worrying I guess... either way it's not something I can control so might as well not waste time worrying about it.

Pride is fine, as in pride of what accomplishes. I prefer to leave it as self-satisfaction.

I find that many get carried away with pride, and in some cases it devolves into self-absorption.

I prefer to live without 'pride' with respect to myself (from my studies of Buddha and ध्यान (dhyāna), Tao, K'ung Fu-tzu), but I don't mind feeling proud of others and expressing it.

Well yea as long as one doesn't get carried away... to me the relationship between pride and self-absorption/arrogance is tantamount to the relationship between passion and anger; one can turn into the other or arise from equal circumstances, but one is healthy and constructive while the other is destructive. So in that sense, I see pride as healthy.

For the most part, people who are arrogant are not sincerely particularly proud of themselves, and thus feel the need to undermine others' accomplishments or character. I personally find this type of people funny; the holier-than-thou voice is great for short stories or little comedy essays.

Stephen Colbert is great at it

Also, I didn't know Newton was a prodigy... how do you know this? Guass yes, Newton? Hmm. I believe Newton was an average student too, not shining until Campbridge.

oops you're right. My bad. I don't know why I was under that impression. Probably from the stories about him spending a lot of his time avoiding doing work at home and making experiments or building devices... but this only shows that he was curious and creative from a young age, not a mathematical prodigy.

 

[Defennder]

Andrew Wiles was 42 when he proved Fermat's Last Theorem.

He worked on it for seven years, which means he was in his mid-thirties when he started on it seriously. But it seems like he had been trying to prove it all his life, if you read his biography online. He only devised a proper strategy for tackling the problem when he began his 7-year work.