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The answer may be related to the early age at which mathematicians seem to peak.

Another factor is the rate of change in technology. Mere experience may be an obstacle there. When you start knowing nothing and pick a technology to learn, you naturally tend to pick the newest one. Whereas for an old person, learning new technologies is something you do out of duty as much as eagerness. An old person learning new technologies is keeping current. A young person learning the same new technology is learning to build stuff, which is much more exciting.

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> The answer may be related to the early age at which mathematicians seem to peak.

I may have been searching badly, but I couldn't really find anything to support this idea, at least in terms of a cognitive deficit. The following was the best discussion about mathematicians and age that I found:

http://sps.nus.edu.sg/~limchuwe/articles/youth.html

Bullet points:

- Mean age of best contribution by mathematicians is 38.8 (based on counting references to research by historians and biographers). This is roughly the same for other SET researchers.

- The Fields Medal cannot be awarded to mathematicians over the age of 40, which skews the mean age of mathematicians receiving their field's most prestigious award.

- As mathematicians get older, they take on more administrative work, have families, etc., which reduces the time and energy they have to devote to research. (I'm reminded of how Andrew Wiles basically shut out the world while proving Fermat's Last Theorem.)

- Rapid expansion of the field meant an increasing proportion of mathematicians were young, thus more discoveries were by young people.

- Math is a field where someone can make a great contribution without having acquired a large body of knowledge.

- Young math prodigies get a disproportionate share of attention.

The Fields Medal cannot be awarded to mathematicians over the age of 40.

Say what?

Geez, you're right. Wikipedia:

The Medal also has an age limit: a recipient's 40th birthday must not occur before 1 January of the year in which the Fields Medal is awarded. As a result some great mathematicians have missed it by having done their best work (or having had their work recognized) too late in life.

Clearly someone needs to endow a better math prize. You know, one that is for the best math, not the best math by a specific sort of person.

That would be the Abel prize. Although I wouldn't call it a better or worse prize. The two awards simply have different goals they want to recognize. Abel is more of lifetime achievement award and Fields is more of a recognition of brilliant younger mathematicians and an encouragement to go on to greater things.

I disagree with everything you say on multiple points.

Firstly, Mathematicians don't peak at an early age this is just one of the many nonsense Hardy spouted. And I say this as a non mathematician < 25 who just enjoys the history of science - I have no horses in that race.

There are many examples of people who not only contributed work at a late age > 30 (some near or over 40) but did so while being outside of the academic community - George Green, Faraday (physics) and Grassman. Then there are those such as Weirstrass who started late or those who produced an amazing work later, some in addition to earlier success e.g. Poisson, Bayes, Fourier or Hamilton whose quaternions came quite late. And then there were the Eulers who were just none stop greatness.

Nextly, although maths is a subject where some topics require very little background knowledge the vast majority of these low hanging fruit (knowledge wise) are gone. It was much easier to sketch out the core of an algebra while still in jail and have it be new and profound 200 years ago than it is today. As the amount of knowledge increases I expect the mean age of precocious contributions to increase. Knowledge and even experience will increasingly become a hard minimum.

Finally, you imply that only young people want to build things and have enthusiasm. I think an eagerness to learn and build great works is something you never lose. At least I hope so, otherwise growing old sounds like a very miserable prospect to me. And while the examples of old fellows not keeping up abound, I think this is simply a philosophical state that can be consciously guarded against.

Fair enough but as you said the young person is "learning to build stuff". There is an advantage in this in that they have a beginners mind and may well come up with a new and better way of doing things. But that is probably one in a hundred. In my experience (and this is an observation not a grouch) a lot of them just end up making a brilliant mess that only becomes apparent when the project gets to a certain size. Not all of them, mind you, some are so good so young that they manage to accumulate experience and judgement faster than anybody else. But there are simply not enough of them to go around. In the meantime someone who has learned about this stuff the hard way (and has the capability to reflect on it) can lend some guidance that can so that we get the brilliance without the mess. One more thing - building architects often do their greatest work in their 60s. Software is not that dissimilar in that its about design and complexity. If I were starting out I would like the idea that I am entering a field where I have the potential to improve with age like that. Norvig's "Teach Yourself Programming in Ten Years" hints that its possible that that may be the case but its not recognized by the industry.

I am not sure one can really say that there is an age where a mathematician peek. They do generally make their great works young, but that if often because it takes many, many years for the world to realize that the work they are making is a big deal (solving famous, difficult problems are one exception). In addition at some point they are going to end up more and more involved with the politics side of mathematics (organizing and presenting research, holding conferences, getting grants, etc) which means there is less and less time to do actual research.

When it comes to learning about new technology, I can associate with the difficult of learning something new now than it was in my teens. I started programming in the early 90s in Basic and C (available in India back then), which was more exciting then, than learning Scala now which on occasion feels like a chore.

However the argument can be made that we need experienced folks to evangelize what is good and productive in the current context and the more of them the merrier.

The in-ability or lack of desire to learn something new is a determent to the individual and should apply equally to all professions. It does not adequately answer the question, Given the choice of 2 programmer equally skilled in new technology X why is there a preference for the 21 yr old over the 45 yr old?

While the economic arguments (lack of family responsibility resulting in the ability to work long hours and lower cost including benefits and pay) apply in the case of start ups they do not address the industry as a whole.

Peaking at an would be an excellent reason, it implies that the experience gained from practice is not sufficiently relevant, which I cannot immediately judge and is possibly correct in the context of technology. I am inclined to think that it is more related to the inability of those responsible for hiring to realize ability outside of their own limitations.

I always thought that your essay on not being able to recognize a better programming language outside of the one you knew (forget the title), is more generally applicable.

There is a correlation between attitude and age. But this is actually a question of attitude rather than age per se.

If I couldn't get a job programming I'd do it for free. Heck, I'm working on a startup so I basically am doing it for free. It's the thrill of making something other people find useful.

From the people I know and have worked with, the older the programmer, the less likely that attitude has survived.

Someone still has to build the new technology that the young folks learn.

"The answer may be related to the early age at which mathematicians seem to peak."

An extraordinarily small percentage of mathematicians ever make any significant contribution to the realm of knowledge, as is true in most fields. It is unfortunate that such a small sampling is then used to judge the pursuit as a whole.

They are the exception. Further, it's just as possible that those very, very few would have led long lives of contributions, but the early success corrupted and waylaid their focus.

We see the same sort of observations in the field of software engineering where a remarkably small samping of Torvalds and Carmacks are used as a baseline, when they're anything but. With all due respect, the technology behind most startups -- many of the YC examples included -- almost qualifies as purile. There are remarkably few that represent any depth or significance, although granted there are some great fundamental ideas and some excellent dedication.

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