Does getting an undergrad degree in astronomy and physics, and then a math PhD from UIUC, really count as "blooms late"? Sounds like a fairly standard career path to me.
You're correct: Wired has hyped the original title of the article in Quanta Magazine: "A Path Less Taken to the Peak of the Math World". Any time you see the words "Math Genius" you should assume hyperbole.
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.
"and the truly great ones are dead before they're 40 so all old mathematicians must be worthless" I've heard that one, too. Doesn't make it beneficial to the field.
I would just like to express my gratitude to [Kevin Hartnett](https://www.wired.com/author/kevin-hartnett/) for making an enjoyable article that I could almost follow as a quantitatively minded programmer / non-mathematician. It makes sense saying that graphs are somehow a form of matroid. Even without knowing what a matroid is, I get a sense of the importance of spatial relationships.
I majored in math in undergrad, and I always daydreamed about solving difficult mathematical problems despite a lack of formal training. I even had a teacher that I had to "pretend to understand".
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.
That's neat! If you redundantly add an extra vertex (in its own component) whenever you glue, then you actually get h(x) = f(x)g(x). I wonder if there's some natural way of defining a multiplication of connected graphs so that you get equality on the nose?
As another user pointed out, why should be the chromatic polynomial of rectangle with deleted edge be: q^4 - 3q^3 + 2q^2 and not q * (q - 1)^3. A counter example: when q=2, we have two ways to color the rectangle with a deleted edge. Am I missing something?
I think fixating q as the number of possible ways to color the end points of the deleted edge leads to the wrong result.
This article was "reprinted" from the original at Quanta Magazine. The original article has the correct answer of q(q-1)^3. (It was probably corrected after Wired "reprinted" it.)
> his father taught statistics and his mother became one of the first professors of Russian literature in South Korea
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 think exposure has a lot to do with it along with aptitude.
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.
Why does it lead you to believe that? If they have talented parents, wouldn't the parents raise them in a way to encourage their talents to blossom?
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.
It's the nature vs nurture thing. It mostly boils down to 'a bit of both' and if you are really lucky in either department then you can still very well manage to succeed.
> "Every one of these graphs has a unique chromatic polynomial"
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)
I think they're trying to say that the graph uniquely determines the polynomial, rather than that the polynomial determines the graph. Or at least, that's how I read it. But I agree it's a bit ambiguous.
> > "Every one of these graphs has a unique chromatic polynomial"
> 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.)
