"subgraphs are all the graphs you can make by deleting an edge or contracting vertices."
That doesn't sound right to me.
A Path Less Taken to the Peak of the Math World
41–50 of 51 posts
Re: A Path Less Taken to the Peak of the Math World
#42tl;dr wish they could just get to the point
Are you one of the people who like Blinkist and think everything has to be distilled into dot points?
Re: A Path Less Taken to the Peak of the Math World
#43It seems like not THAT much of a stretch. Undergrad in Physics at the top school in Korea, followed by a masters in Math. But I still like the story.
Make that double major in astronomy and physics plus unofficial personal instruction by a Fields medalist.
Re: A Path Less Taken to the Peak of the Math World
#44On a slight tangent, I find it interesting the contrast the author paints between poetry and math. Perhaps it was unintentional, but it saddens me to hear or read people discuss math as if it were some polar opposite of the arts (or in this article, poetry). Math, physics, biology, the 'hard' sciences, all have so much more in common with the arts than we give credit. Is a math proof not poetic in its own right? Does…
""" When mathematicians describe equations as beautiful, they are not lying. Brain scans show that their minds respond to beautiful equations in the same way other people respond to great paintings or masterful music. The finding could bring neuroscientists closer to understanding the neural basis of beauty, a concept that is surprisingly hard to define. In the study, researchers led by Semir Zeki of University Colle…
>The scientists found that the more beautiful an equation was to the mathematician, the more activity his or her brain showed in an area called the A1 field of the medial orbitofrontal cortex.
From the sound of that, "beauty" evokes a reward response in the part of the brain (medial orbitofrontal cortex) responsible for processing reinforcement learning signals. This is pretty interesting, since it says that the brain can process a reward signal for a very abstract property that probably has very little correlation with direct sensory rewards.
Re: A Path Less Taken to the Peak of the Math World
#45Earlier quoted context omitted.
Well he says this, "he decided to regard it as a barren pursuit of one logically necessary statement piled atop another" This indicates that he views a certain type of worthlessness in math. Then he can justify not being good at math, and distance himself from the pursuit of math on its own grounds. Of course his perception of him not being good at math and actually not being good at math are two different things. Ph…
I think there's a bigger problem the article is getting at, that people are kind of missing or downplaying, which is the culture around math skill acquisition and ability. It's obvious this guy had a love of math and ability in it, from his majors and subsequent events. But it's also actually not that unreasonable for him to start second-guessing himself when he struggled with math earlier in life. I do think there's…
Very much agreed. I've definitely encountered the attitude that my high-school grades or my undergrad GPA define me. And by "define me", I mean that my undergrad GPA of 3.45, higher in just my CS+math courses, is considered a little on the low side to be applying for STEM grad-school. My GPA was sufficient to graduate with Latin honors, but it's low for STEM? Come on.
Yes, we definitely treat STEM as a competition to see who can be the closest to "perfect" at set tasks and classwork, rather than as an exploration (or even exploitation) of structures and spaces through strictly logical reasoning.
Re: A Path Less Taken to the Peak of the Math World
#46Earlier quoted context omitted.
Actually Ed Witten was not a total newbie to advanced Math before grad school.From his commemorative lecture: At about age 11, I was presented with some relatively advanced math books. My father is a theoretical physicist and he introduced me to calculus. For a while, math was my passion. My parents, however, were reluctant to push me too far, too fast with math (as they saw it) and so it was a long time after that b…
That he learned calculus when he was younger doesn't really explain how he so easily transitioned into mathematical physics after a liberal arts education. Calculus is relatively basic compared to grad level work in that area.
Calculus at 11 and never having been challenged for a while at school implies he self studied some courses that he is not explicitly mentioning.
Re: A Path Less Taken to the Peak of the Math World
#47On a slight tangent, I find it interesting the contrast the author paints between poetry and math. Perhaps it was unintentional, but it saddens me to hear or read people discuss math as if it were some polar opposite of the arts (or in this article, poetry). Math, physics, biology, the 'hard' sciences, all have so much more in common with the arts than we give credit. Is a math proof not poetic in its own right? Does…
Quite a few of our conversations with my ex (who is an artist) revolved around the contrast between mathematics and the arts. We realized quite early on that mathematics is actually quite artistic and could have easily been considered one of the arts, if it weren't for its inescapable rules and structure. High level mathematics takes just as much creativity as any of the arts.
I don't think this necessarily negates it being one of the arts. They very act of choosing which rules to induce a particular structure is the art itself, no? (since the space of possible rules is infinite)
Re: A Path Less Taken to the Peak of the Math World
#48On a slight tangent, I find it interesting the contrast the author paints between poetry and math. Perhaps it was unintentional, but it saddens me to hear or read people discuss math as if it were some polar opposite of the arts (or in this article, poetry). Math, physics, biology, the 'hard' sciences, all have so much more in common with the arts than we give credit. Is a math proof not poetic in its own right? Does…
Completely agree about the sadness in the contrast they paint between the sciences and the arts. send an email to this username at cerebralinguist.net - I have something for you that's not quite ready for public consumption yet.
Re: A Path Less Taken to the Peak of the Math World
#49Earlier quoted context omitted.
That he learned calculus when he was younger doesn't really explain how he so easily transitioned into mathematical physics after a liberal arts education. Calculus is relatively basic compared to grad level work in that area.
Calculus at 11 and never having been challenged for a while at school implies he self studied some courses that he is not explicitly mentioning.
>and so it was a long time after that before I was exposed to any math that was really more advanced than basic calculus.
This suggests calculus was all he knew before at least college (for some value of "a long time").
Re: A Path Less Taken to the Peak of the Math World
#50Earlier quoted context omitted.
Calculus at 11 and never having been challenged for a while at school implies he self studied some courses that he is not explicitly mentioning.
>and so it was a long time after that before I was exposed to any math that was really more advanced than basic calculus. This suggests calculus was all he knew before at least college (for some value of "a long time").
I wound not be surprised if he is the product of a Math Circle:a nice place to stretch one's mathematical abilities while retaining the bragging rights of never having formally studied math in college.