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A Path Less Taken to the Peak of the Math World

quantamagazine.org

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Re: A Path Less Taken to the Peak of the Math World

#31

Post by vlasev »

ajc-sorin wrote: post #17

On 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.

Re: A Path Less Taken to the Peak of the Math World

#32

Post by kafkaesq »

bjl wrote: post #24
kafkaesq wrote: post #15

Earlier quoted context omitted.

Can someone explain how someone who has decided to distance himself from math can major in PHYSICS?! The pure math world (and certain rarified branches of physics and CS) are quite different from the "measurement-based" sciences. If anything they're almost more similar to endeavors like musical composition (or even poetry) than any "lab-based" science. Particularly when it comes to the fetishization of "genius", "pur…

This is completely off. At the college level physics is almost completely math. Linear Algebra, Functional Analysis, and Abstract Algebra aren't exactly 'measurement-based' subjects.

At the college level physics is almost completely math.

It's not the formulas; it's how you look at them. And what they "mean" to you.

Linear Algebra, Functional Analysis, and Abstract Algebra aren't exactly 'measurement-based' subjects.

Right; but those are just the ABCs, is it were.

Physicists and astronomers, by and large, are interested in a broad range of mathematical subjects -- but generally as tools, just enough therein to make sense of what's coming out of their particle detectors and their telescopes.

Pure mathematicians, meanwhile, are into things like the Langlands program, or Inter-universal Teichmüller theory. And they constructions they consider aren't the mere means to some end, grounded in the prospect of obtaining some better understanding of the physical world. They are, rather, the end goal in itself.

Or if you will, the "music".

Re: A Path Less Taken to the Peak of the Math World

#33

Post by [deleted] »

Pamar wrote: post #2

I think that the author is trying too hard to create sensationalism by stressing how the person in the article had decided that "math was not for him", by saying stuff like: After that bad math test in elementary school, Huh says he adopted a defensive attitude toward the subject: He didn’t think he was good at math, so he decided to regard it as a barren pursuit of one logically necessary statement piled atop anothe…

[deleted]

Re: A Path Less Taken to the Peak of the Math World

#34

Post by travmatt »

ajc-sorin wrote: post #17

On 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 College London asked 16 mathematicians to rate 60 equations on a scale ranging from "ugly" to "beautiful." Two weeks later, the mathematicians viewed the same equations and rated them again while lying inside a functional magnetic resonance imaging (fMRI) scanner. 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.

"""

https://www.scientificamerican.com/article/equations-are-art...

Re: A Path Less Taken to the Peak of the Math World

#35

Post by bigger_cheese »

xyzzyz wrote: post #18
lumberjack wrote: post #4

I have noticed this in many mathematicians: they will start explaining you something that you are completely unable to grasp, being completely ignorant of the specifics of the field. However they will insist in their pursuit and the polite thing to do is to try to understand some general idea as best as you can, and they don't really expect you to understand everything that they are telling you. This has happened to…

Mathematicians know mathematics is hard, and hardly ever expect you to fully understand they're saying, as you cannot compact in a handful of sentences something that took you hours, days or weeks to fully grasp. It doesn't mean that it's a waste of time: in an otherwise incomprehensible monologue you might find a nugget of knowledge that will stay with you, and will form a foundation on which the future understandin…

I feel the same way. I'm an engineer not a mathematician but I've always thought if I can't sit down and explain the problem I'm working on in a way that makes sense to a layperson then I don't understand the problem well enough It can be a useful way to quantify your own knowledge as well.

Re: A Path Less Taken to the Peak of the Math World

#36

Post by Retra »

rocqua wrote: post #28
bjl wrote: post #24

Earlier quoted context omitted.

This is completely off. At the college level physics is almost completely math. Linear Algebra, Functional Analysis, and Abstract Algebra aren't exactly 'measurement-based' subjects.

As a math student with lots of physics friends. Physics and math are very different. One way to explain this might be that physics isn't about doing math, but using math to do computations. Meanwhile, math is about abstract ideas and rigorous proofs. Physics doesn't care about wondering if an integral is a well-defined concept, nor does it care about the real numbers being uncountable. Similarly, maths looks at the f…

Physicists definitely do care about those things, they can just put off figuring them out because they are useful in the meantime.

Just like mathematicians can turn the results of 'unsolved problems' into axioms and go on with their lives.

Re: A Path Less Taken to the Peak of the Math World

#37

Post by kem »

kenjackson wrote: post #7
Pamar wrote: post #2

I think that the author is trying too hard to create sensationalism by stressing how the person in the article had decided that "math was not for him", by saying stuff like: After that bad math test in elementary school, Huh says he adopted a defensive attitude toward the subject: He didn’t think he was good at math, so he decided to regard it as a barren pursuit of one logically necessary statement piled atop anothe…

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 this idea that if you're good at math and have something to offer in it, it will show early on regardless of life circumstances or mentors or role models or whatever, that if it's not immediately obvious that you're a mathematical genius you should forget about it.

"Realizing a test you took in elementary school needn't define you" is actually a nontrivial thing to overcome in today's society, maybe even especially in STEM circles.

Sometimes I wish STEM culture was more focused on sharing the joys of STEM and trying to be as open-minded and inclusive as possible, instead of brandishing it as a competitive tool.

Re: A Path Less Taken to the Peak of the Math World

#38

Post by sn9 »

ekm2 wrote: post #30
shas3 wrote: post #6

Ed Witten, arguably one of the greatest mathematicians/physicists/mathematical physicists alive majored in liberal arts, worked for Nation and New Republic, enrolled in the economics PhD program at UW-Madison, before he switched to math!

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.

Re: A Path Less Taken to the Peak of the Math World

#39

Post by eutectic »

This is a fantastic example of how to do math/science journalism right. It's not afraid to get into the technical details, but everything is explained so that someone without much math background can understand.

The human interest stuff is also great; just enough to give you a full picture without the padded-out feeling that a lot of long-form journalism has. Great all around!

Re: A Path Less Taken to the Peak of the Math World

#40

Post by nl »

kafkaesq wrote: post #32
bjl wrote: post #24

Earlier quoted context omitted.

This is completely off. At the college level physics is almost completely math. Linear Algebra, Functional Analysis, and Abstract Algebra aren't exactly 'measurement-based' subjects.

At the college level physics is almost completely math. It's not the formulas; it's how you look at them. And what they "mean" to you. Linear Algebra, Functional Analysis, and Abstract Algebra aren't exactly 'measurement-based' subjects. Right; but those are just the ABCs, is it were. Physicists and astronomers, by and large, are interested in a broad range of mathematical subjects -- but generally as tools , just en…

I suspect the Math test the subject failed during elementary school wasn't on Langlands.
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