
A Path Less Taken to the Peak of the Math World - bkudria
https://www.quantamagazine.org/a-path-less-taken-to-the-peak-of-the-math-world-20170627/
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ajc-sorin
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.

~~~
travmatt
"""

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...](https://www.scientificamerican.com/article/equations-are-art-inside-a-
mathematicians-brain/)

~~~
eli_gottlieb
>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.

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Pamar
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?!

~~~
HarryHirsch
_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.

~~~
auntienomen
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.

~~~
coliveira
Talking daily to a world-class professional mathematician for two years will
do a lot to help in this respect.

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lumberjack
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.

~~~
xyzzyz
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.

~~~
kmill
I'm surprised how often someone's told me something incomprehensible, but then
years later I realize what they meant.

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k__
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'

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shas3
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!

~~~
ekm2
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._

[https://www.sns.ias.edu/ckfinder/userfiles/files/Comemorativ...](https://www.sns.ias.edu/ckfinder/userfiles/files/ComemorativeLecturePopular\(1\).pdf)

~~~
sn9
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.

~~~
ekm2
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.

~~~
sn9
>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").

~~~
ekm2
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.

~~~
sn9
I wouldn't either, but there's really no evidence to suggest that.

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mathattack
It 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.

~~~
lookACamel
Make that double major in astronomy and physics plus unofficial personal
instruction by a Fields medalist.

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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!

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ouid
"subgraphs are all the graphs you can make by deleting an edge or contracting
vertices."

That doesn't sound right to me.

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rm2040
tl;dr wish they could just get to the point

~~~
willbw
Are you one of the people who like Blinkist and think everything has to be
distilled into dot points?

