> Possessions meant little to Erdős; most of his belongings would fit in a suitcase, as dictated by his itinerant lifestyle. Awards and other earnings were generally donated to people in need and various worthy causes. He spent most of his life traveling between scientific conferences, universities and the homes of colleagues all over the world. He earned enough in stipends from universities as a guest lecturer, and from various mathematical awards, to fund his travels and basic needs; money left over he used to fund cash prizes for proofs of "Erdős problems" (see below). He would typically show up at a colleague's doorstep and announce "my brain is open", staying long enough to collaborate on a few papers before moving on a few days later. In many cases, he would ask the current collaborator about whom to visit next.
You can't have Erdős if you don't also have the dozens of mathemeticians with homes, families, and patient and forgiving spouses who tolerated and supported him so that he could focus on his work. Mathematicians as a profession can't really exist as an order of traveling monks, nor do most of them even want to.
I would have guessed mathematicians were, on average, supernerds with less life responsibilities than average people.
About the first part, I don't think mathematicians specifically get so many life responsibilities - I think most people do most of their "learning" in their 20s, and most of the execution of that learning in their 30s and onwards. Research mathematicians are a bit different in that, like most academics, their serious intellectual work which pushes the frontier and gets them career credit is of the same kind of learning/intellectual work.
E.g. compare to programmers- most will learn to program in their 20s, pick up a few languages/technologies, then spend a big chunk of their career with those.
This makes mathematics an outlier scientific field, so if your explanation is "life responsibilities", you have to explain why mathematicians have more life responsibilities than others.
So my money is on some brain development thing. Not that I have any better argument than "what else could it be?".
> In a study of nearly 2,000 famous scientists throughout history, he found that mathematicians were the youngest when they made their first important contribution. The average age at which they accomplished something important enough to land in history books was 27.3. By contrast, biologists were 29.4 years old, physicists were 29.7, and chemists were 30.5.
>mathematicians make their best research contributions (which he defined as the ones mentioned most often by historians and biographers in reference books) at what many might consider doddering old age: 38.8. That age is very similar to those he found in other sciences: 40.5 in biology, 38.2 in physics, and 38.0 in chemistry
Math is also a bit unusual compared to most of other disciplines in that math dissertations are often written very quickly and you don't need months or years of studies/experiments to support a thesis. That could easily explain the 2 year gap between mathematicians and biologists noted above.
My, now less certain views, were based on some article I read years ago where the peak ages for various fields were listed, and were quite further spread out. I especially remember that historians peak in their 60s!
Like someone says in your article "This myth, if you wish to call it a myth, is so prevalent that it's quite probable that there's some truth to it", but I'm now far less certain and flippant about. Thanks again!
I bet when you're old enough that you can see firsthand how perceptions of the same events change over time, you get a hell of a lot better at recognizing that in history.
There are also confirmation and sample biases involved. Everyone hears about Terence Tao because Terence Tao's story is remarkable. All the 38-year-old mathematicians who are making those research contributions are normal, and hence their stories aren't interesting.
until age 17 i had no more than 2-4 hours of second and third language classes. (english from first grade, french from 7th) even including homework that just barely approaches 1 hour a day of language learning.
my own efforts resulted in grades ranging from B to D and my english skills after 10 years of that were less than mediocre.
my english only improved through immersion for a year in the united stated during grade 11. after that one year i reached near fluency (except probably for a much smaller vocabulary)
at age 21 i was able to learn dutch through 3 months of immersion alone (no classes). of course i have reached far from fluency, but i learned enough to be able to read and speak, to allow me to continue practicing and learning without classes.
children only then have no choice to learn if they live in the country where the second language is spoken. in fact it may well be that the second language becomes their first and they learn their own parents language as a second language.
When I was 6 years old I decided to take Chinese/Mandarin lessons for a few months. If I compare my progress then to my colleague in his 20s who is learning Chinese in the same way - one hour a day, 2 times a week with an instructor - he certainly is learning much faster than I did. After 6 months he has already surpassed my level and is have basic reading/writing skills, which I never achieved.
I also had German courses from age 8-10 with a similar schedule. After that 2 year period I still could not have anything but the most elementary conversation in German, despite getting very high grades in that class.
On the other hand, I decided to become fully fluent in English in my late teens, and after intense self-directed practice and a few years in an English-speaking environment, no one is able to tell that I am not a native speaker.
I think it's a natural part of the human psyche. If you read about the Mongols or the Comanche or some other horse-nomadic culture, the one thing you learn is that they are really really good at horse archery. As in: virtually every adult male Mongol or Comanche could accurately perform archery from horseback, at full gallop, while hanging from the horse sideways to shield their body and firing arrows from underneath the horse's chin. How is that possible? Well, if you grow up as a Mongol boy, once you reach the stage in life where a Western kid might get a skateboard or a guitar or whatever, you have horses and bows, and all the older kids can already do that stuff.
For example, I noticed that in high school if I really liked a subject I would just sponge it all up, no need for spaced repetition and I could be focused for hours.
In college, I started to feel the need for spaced repetitions but yet be focused for hours.
Now, if I get to do something I really enjoy intellectually, I can get 30-45 minutes of focus. Then rest and spaced repetition. Last time I tried to push 3 hours of study, I not just forget most of the content but it affected my mood so badly.
Somewhat, I see the same pattern with physical activities. I could run have hard workouts back to back in high school while now it is so easy to overtrain and rock my hormones that I need to be really careful.
This is with learning pretty much anything. Adults typically just have less time than their younger counter parts.
If a child is learning a second/third language, they'll be way less interested than somebody that has to learn it to because they're doing it out of genuine interest or for a job.
There is another important aspect: learning your second or third foreign language (or subsequent ones) is easier than the first one. I think studies or comparisons which neglect to take that into account are flawed. Adults (at least outside the US) are likely to be learning their second foreign language, not their first, hence should do relatively well, in spite of a (possible) age handicap.
Well, at least didn’t help me much
1 hour a day is seen as a really dedicated adult language learner. If you only did activities that involve languages for 1 hour a day as a kid you would almost certainly flunk school and be way behind your peers.
Adults can simply run away into their native language when things get too frustrating. Kids have no where to run to, there is no choice to not learn and no choice to give up.