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My experience in academia has taught me the following: Any slowdown in productivity among mathematicians as they age is more a result of increased administrativ

My experience in academia has taught me the following: Any slowdown in productivity among mathematicians as they age is more a result of increased administrative duties, childcare, or loss of interest than it is cognitive decline. The slowdown is real, but the commonly suggested reason (biological aging) is not quite right. You can look up cognitive decline studies and see that it really doesn't hit in full force until the 60s and 70s, with lots of heterogeneity. I've seen plenty of sharp 70-year-old academics doing great work (though I can't remember someone at 80 who I thought was still going full steam).

RC_ITR 4y ago
There's also an argument to be made about bias - the younger you are the less you 'know,' which can lead to more experimentation and creative solutions to problems. There's also the 'hunger' argument that dovetails with yours - are younger people just more incented to 'prove' themselves? (since, as you imply, most older people realize a supportive family makes them happier than a well-regarded publication does) An interesting question to address is 'Is the status quo just fine? Will any solutions to this just make more academics die as virgins or can we actually improve the output of older academics?' (cue: a joke about Newton)
- SiempreViernes 4y ago
  Not sure how Newtons later career that sees him going undercover to prowl seedy London bars to hunt coin forgers has anything to do with virginity?
  - RC_ITR 4y ago
    Huh, the more you know. I was just making the tired 'Newton died a virgin joke' but thanks for the history of his life.
whimsicalism 4y ago
I think it is way too common to look at studies of the median person and then generalize to older. Major discoveries are made by top, top people - it seems not unlikely that past a certain age most people cannot remain top. The same is true with chess, which does not have the same administrative duties problem.
- hervature 4y ago
  But I think the OP has a point that falling out of the top has nothing to do with cognitive ability. For instance, many researchers become known for certain contributions and then eventually expected to remain in that field. If the landscape changes (say neural networks become the hot topic) then your research might fall in prestige but the level/complexity/quality does not. There are things beyond their control to prevent quick pivots let alone large pivots. A biologist cannot start doing NLP stuff. Then there is the problem of your graduate students who are doing other things and so the momentum to switch is very real.
  - whimsicalism 4y ago
    Hm. If someone in their 20s is able to make a major discovery for a problem they only heard of when they were 18, that is maximum 12 years of that line of research, which could certainly be replicated by someone older. you also see people in their 20s make big contributions to many disparate fields, like Tao.
    - hervature 4y ago
      I think you are misunderstanding me. I'm saying that having time in the field is the exact problem. If you have established a pipeline of graduate students and you have 5 of them at various stages of completion. It's difficult to convince new students to join you in a new endeavor because no one in your group does that. Keep in mind, your role as a professor is to take on students. You would also face pressures from your current students to stay in the forefront of your field as that is what they are banking on getting advised from you. If you're 20 years old, you don't care about any of that, you just switch fields.
- spekcular 4y ago
  I think there are a lot of relevant dis-analogies between math and chess. A chess match at the professional level is a grueling, multi-hour contest, while math research is a lot more chill. Also, the time limit matters a lot in chess. Anyway, you can look at the pages of Annals of Math and Inventiones and see that there is a good mix of ages.
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KineticLensman 4y ago
In my experience as a 60 year old, I can recognise cognitive decline in myself compared with younger me. Examples include finding it hard to remember language constructs and APIs, and taking longer to navigate window systems and hierarchical menus. I suspect there are maths equivalents that would impact problem solving performance. This is in addition to changes in lifestyle and life perspectives that have changed the way I prioritise my tasks and interests.

RC_ITR 4y ago

There's also an argument to be made about bias - the younger you are the less you 'know,' which can lead to more experimentation and creative solutions to problems. There's also the 'hunger' argument that dovetails with yours - are younger people just more incented to 'prove' themselves? (since, as you imply, most older people realize a supportive family makes them happier than a well-regarded publication does) An interesting question to address is 'Is the status quo just fine? Will any solutions to this just make more academics die as virgins or can we actually improve the output of older academics?' (cue: a joke about Newton)

SiempreViernes 4y ago
Not sure how Newtons later career that sees him going undercover to prowl seedy London bars to hunt coin forgers has anything to do with virginity?
- RC_ITR 4y ago
  Huh, the more you know. I was just making the tired 'Newton died a virgin joke' but thanks for the history of his life.

whimsicalism 4y ago

I think it is way too common to look at studies of the median person and then generalize to older. Major discoveries are made by top, top people - it seems not unlikely that past a certain age most people cannot remain top. The same is true with chess, which does not have the same administrative duties problem.

hervature 4y ago
But I think the OP has a point that falling out of the top has nothing to do with cognitive ability. For instance, many researchers become known for certain contributions and then eventually expected to remain in that field. If the landscape changes (say neural networks become the hot topic) then your research might fall in prestige but the level/complexity/quality does not. There are things beyond their control to prevent quick pivots let alone large pivots. A biologist cannot start doing NLP stuff. Then there is the problem of your graduate students who are doing other things and so the momentum to switch is very real.
- whimsicalism 4y ago
  Hm. If someone in their 20s is able to make a major discovery for a problem they only heard of when they were 18, that is maximum 12 years of that line of research, which could certainly be replicated by someone older. you also see people in their 20s make big contributions to many disparate fields, like Tao.
  - hervature 4y ago
    I think you are misunderstanding me. I'm saying that having time in the field is the exact problem. If you have established a pipeline of graduate students and you have 5 of them at various stages of completion. It's difficult to convince new students to join you in a new endeavor because no one in your group does that. Keep in mind, your role as a professor is to take on students. You would also face pressures from your current students to stay in the forefront of your field as that is what they are banking on getting advised from you. If you're 20 years old, you don't care about any of that, you just switch fields.
spekcular 4y ago
I think there are a lot of relevant dis-analogies between math and chess. A chess match at the professional level is a grueling, multi-hour contest, while math research is a lot more chill. Also, the time limit matters a lot in chess. Anyway, you can look at the pages of Annals of Math and Inventiones and see that there is a good mix of ages.

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KineticLensman 4y ago

In my experience as a 60 year old, I can recognise cognitive decline in myself compared with younger me. Examples include finding it hard to remember language constructs and APIs, and taking longer to navigate window systems and hierarchical menus. I suspect there are maths equivalents that would impact problem solving performance. This is in addition to changes in lifestyle and life perspectives that have changed the way I prioritise my tasks and interests.