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 a well structured musical composition not engage with our most innate neurology on a microscopic level?
What's sad to me is that we seem to silo people into one of the two camps, which is like locking someone in a room in search of a key that's in the room next door. Businesses do this too - how many engineers get brought on to learn marketing? How many chefs learn the chemistry which serves as a foundation for every recipe they cook?
I say this as a former political-science-major-turned-accountant. I loved tax policy, but struggled to understand the law and treatment of certain issues, so I switched to accounting and found that the same logical, rational work that goes into formulating a political argument can be applied to rationalize control processes or budgeting in businesses. I've tried to un-learn my bias against people who majored in the "soft" sciences and strive to make more of an effort to understand how they think and what drives them.
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.
>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.
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)
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.
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 another. As a teenager he took to poetry instead, viewing it as a realm of true creative expression.
But then...
By the time he enrolled at Seoul National University in 2002, he had concluded that he couldn’t make a living as a poet, so he decided to become a science journalist instead. He majored in astronomy and physics, in perhaps an unconscious nod to his latent analytic abilities.
Can someone explain how someone who has decided to distance himself from math can major in PHYSICS?!
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", "pure talent" and all that -- and especially when it comes to the character model (myth, really) of the lone genius who locks himself in an attic for N years and not only solves some major problem but totally reimagines the field, front to back.
I mean - at least in terms of the culture of pure mathematics, that's the image one can easily fall into the habit of having about one's self, if one attempts to do mathematics. Such that if you were to switch to physics, astronomy, or CS... you actually would feel like you were "leaving math".
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 formulae in physics and thinks those things are way to complicated.
Our lin-alg course is joined physics and maths. The older physicists complain about all the proofs needed there. Mathematicians lament the lack of rigor in the same course.
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.
Having majored in mathematics and music, and taken only undergraduate physics courses I would say my personal experience agrees with kafkaesq. I often thought maths was closer to English literature & composition classes or music composition classes than to my physics classes. For me, maths was definition focused like the difference between lightning and lightning bolt, big picture focused like writing a thesis argument or a composition, and detail focused similar to understanding how the structure of a sentence altered the affect of that sentence or detail focused when manipulating melodic lines or harmonies and rhythm within one measure of music (ie get through a harmonic progression to another key while still maintaining the set of rules/laws/constraints I had created for myself for a specific piece).
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. Physics uses math, but not for maths sake. And in reality, I'm sure he was more than competent in math, so the level of math required for undergrad physics was not a problem.
It was only, through his journalism, did he let down his guard enough to enjoy math for maths sake -- and realize that a test you took in elementary school needn't define you.
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.
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.
Can someone explain how someone who has decided to distance himself from math can major in PHYSICS?!
Exactly that. At my university first-year physics students would effectively take the same courses as mathematics students and Mathematical Methods in Physics on top of that.
There is, in my experience, a difference between the courses required of mathematics majors and the courses that students who might want to be mathematicians are expected to take.
This is true, but becomes a lot less relevant when you're playing in Huh's league. It's not that easy to make a move even from theoretical high-energy physics to pure mathematics. You can read about some interesting success stories in Quanta, but I think most people who try this end up leaving academia. There's a large cultural gap they have to cross, and most will never integrate enough to survive the job market.
This just shows how writers like to sensationalize people and real life events. It is obvious that this guy was a math person who didn't know what trajectory to take. He was not good in math for his own standards, which are certainly much higher than for the rest of the population.
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 me various times, first time I was not even an undergrad yet.
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 understanding will rest.
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.
Conversation would be so much more lively if the general population knew the basic results and definitions of maths. :p
I'd wax poetic about most reals being uncomputable, but good luck explaining cantor's diagonal theorem, measure theory, why we need measure theory, what a real number is, why we need real numbers, how sqrt(2) isn't rational, how numbers can be transcendental, what a limit is.
There is so much background needed for maths. People feel like they don't have the talent to get it, whereas really it's a matter of putting in the time to get comfortable with the basics.
TL;DR it's not about a HS dropout who learned math in a non-regular way, but about someone much smarter than average, who just didn't like 'bleeding edge math' but was okay with most of the stuff many people would consider 'hard math'
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 before I was exposed to
any math that was really more advanced than basic cal
culus. I am not sure in hindsight whether their attitude was
best or not. However, the result was that for a number of years the math I was exposed to did not seem
fundamentally new and challenging. It is hard to know to what extent this was a factor, but
at any rate for a number
of years my interest in math flagged.
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.
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.
His mathematical talent is his greatest ability. But the ability to willingly switch fields to find what you're good at (or enjoy) is also important, and something most of us either don't have the nerve or engine to do.
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!
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 a well structured musical composition not engage with our most innate neurology on a microscopic level?
What's sad to me is that we seem to silo people into one of the two camps, which is like locking someone in a room in search of a key that's in the room next door. Businesses do this too - how many engineers get brought on to learn marketing? How many chefs learn the chemistry which serves as a foundation for every recipe they cook?
I say this as a former political-science-major-turned-accountant. I loved tax policy, but struggled to understand the law and treatment of certain issues, so I switched to accounting and found that the same logical, rational work that goes into formulating a political argument can be applied to rationalize control processes or budgeting in businesses. I've tried to un-learn my bias against people who majored in the "soft" sciences and strive to make more of an effort to understand how they think and what drives them.