If you like this kind of story, I highly recommend putting Quanta (https://www.quantamagazine.org/) on your radar and avoiding most of the tabloid-science articles in Wired.
I personally know several IMO winners who started studying Math when they were 3~4 years old and it's been part of their life.
Seeing a real-world example of this fantasy come true is fascinating. The article was also surprisingly well-written; most mention of higher mathematics in the media is oversimplified to death, but this was an honest and yet approachable presentation of the Rota conjecture (now theorem).
By the way, here's another result on chromatic polynomials (proved first by I don't know, but re-discovered by my combinatorics class):
Define a "gluing" operation by taking two graphs and connecting them along a common vertex.
The chromatic polynomial, h(x), of the new graph, is the product of the chromatic polynomials of the subgraphs over x: h(x) = f(x)*g(x) / x.
[1]: https://www.cs.elte.hu/blobs/diplomamunkak/mat/2009/hubai_ta...
I think fixating q as the number of possible ways to color the end points of the deleted edge leads to the wrong result.
https://www.quantamagazine.org/a-path-less-taken-to-the-peak...
> Correction June 27, 2017: The original version of this article included an error in the calculation of the chromatic polynomial of a rectangle.
I notice that really talented people, always have talented parents. Rarely do I read stories about poor blue collar parents producing science wiz. It leads me to believe that genetics play a much bigger role in our intelligence than nurture.
Children with genius parents usually expose their children to high level content very early into their childhood. They also pass on a way of thinking and intuition of their subjects that a non-expert in the field won't have.
I noticed that too but my parents weren't talented in an intellectual sense. In fact, they were fairly ordinary and one was a high school drop out. I was brought up believing that science is for eggheads and worse people who spent too much time studying were socially inept and justly shunned.
Fast forward a few years. I went to university in my mid twenties and study computer science and take as many hard, ball-busting science classes I could. I noticed that a lot of the people there had already had patents who had careers in science, particularly physicians and engineers. I'd say that's very important to grow up with mentors and resources to teach you how to learn in the first place (my life has improved by orders of magnitude since I learned how to grok). Almost everyone I know who performed well in these classes put in more time studying and they struggled just as much as anyone else.
Genetics plays a role in success in science and math but socialization also plays a profound role. Maybe I just have an axe to grind but the myth of science and math being reserved for rarified genius over the curious and dedicated does a lot more harm then good.
Would be interesting to see if the children of talented parents that are put up for adoption and raised by average parents are as successful. Or vice versa, talented parents raising children of average parents.
But to your point, Steve Jobs is an example of that. He had blue collar adoptive parents, but his birth parents were PhD level people.
I am not gonna put my foot in my mouth again and say this is proof of anything, but it is interesting to me.
Rare. But when it happens, it rocks the Earth. [1]
[1] Richard Feynman
This is incorrect. Two different graphs may have the same chromatic polynomial. For example, all trees of N vertices have the same chromatic polynomial: x(x-1)^(N-1)
> This is incorrect. Two different graphs may have the same chromatic polynomial. For example, all trees of N vertices have the same chromatic polynomial: x(x-1)^(N-1)
As soverytired (https://news.ycombinator.com/item?id=14697626) points out, you're refuting the claim that the graphs have distinct chromatic polynomials. To say that a graph has a unique chromatic polynomial means that it has only one, not that no other graph has the same one. (For example, (almost?) everyone has a unique biological mother.)
