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A triplet tree forms one of the most beautiful structures in math

quantamagazine.org

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Re: A triplet tree forms one of the most beautiful structures in math

#11

Post by roenxi »

_a_a_a_ wrote: post #3
ykonstant wrote: post #2

The related concepts of Lagrange and Markov spectra have intrigued me since my student years; nowadays I study them using geometric methods in homogeneous dynamics, a strategy with roots in the 50s and 60s starting with W.Schmidt and brought to prominence by Dani, Margulis, Kazhdan and others. I had the good fortune to be invited for lectures at Tata by Dani and Yale by Margulis, and I hope one day to reciprocate the…

I've never been able to perceive the beauty that others such as yourself can see. Genuine question, where do you see the beauty? All I see in your link is a wall of equations, although I have a maths background it's all abstract and I can't get anything out of it.

I'm not sure about most people, but it is quite pretty how we start with (1, 1, 1) and x^2 + y^2 + z^2 = 3xyz which is all nice and simple then ... kaboom. Suddenly there are patterns everywhere. Not just similar patterns either, but a big range of things. Setting numbers to constants gets other known sequences like Fibonacci numbers, meaningful patterns when permuting, meaningful patterns when ordering, links to trees, links to irrational numbers, links to linear transforms. And all this is going on while many basic-sounding properties are apparently hard to analyse.

There is a lot going on for summing 3 squares. It is fun and unexpected. All the weirder because they don't seem to have linked all this to pi, e or i yet in an obvious way looking at the wiki page.

Re: A triplet tree forms one of the most beautiful structures in math

#12

Post by dabeddabed »

ykonstant wrote: post #2

The related concepts of Lagrange and Markov spectra have intrigued me since my student years; nowadays I study them using geometric methods in homogeneous dynamics, a strategy with roots in the 50s and 60s starting with W.Schmidt and brought to prominence by Dani, Margulis, Kazhdan and others. I had the good fortune to be invited for lectures at Tata by Dani and Yale by Margulis, and I hope one day to reciprocate the…

What would you add on the article about the Markov spectrum? Wikipedia can be edited by anyone

Re: A triplet tree forms one of the most beautiful structures in math

#13

Post by kstrauser »

_a_a_a_ wrote: post #8
ykonstant wrote: post #6

Earlier quoted context omitted.

You could say the same thing about music notation; the beauty is not in the notation, but the objects the equations describe. In order to perceive the beauty, you have to study the objects, not the notation.

Others (mathematicians) can peer through the notation to the thing beneath. That's extremely difficult for me to do, and once I've done it I can see something interesting, but beautiful? No, that tree is intriguing but beautiful to me it ain't.

I’ve stumbled across bits of program code I’d call beautiful: simple, understandable, clearly correct, and… elegant. Win I find them, I experience the same feelings as when seeing a beautiful painting. My wife’s like “why are you smiling and laughing at words on the screen”, but it’s not the words, it’s what they’re saying and how they’re saying it.

That must be what a mathematician feels when they see a beautiful proof, or formula, or relation.

Re: A triplet tree forms one of the most beautiful structures in math

#15

Post by [deleted] »

keithalewis wrote: post #5
_a_a_a_ wrote: post #3

Earlier quoted context omitted.

I've never been able to perceive the beauty that others such as yourself can see. Genuine question, where do you see the beauty? All I see in your link is a wall of equations, although I have a maths background it's all abstract and I can't get anything out of it.

Give not that which is holy unto the dogs, neither cast ye your pearls before swine, lest they trample them under their feet, and turn again and rend you.

[deleted]

Re: A triplet tree forms one of the most beautiful structures in math

#16

Post by ykonstant »

dabeddabed wrote: post #12
ykonstant wrote: post #2

The related concepts of Lagrange and Markov spectra have intrigued me since my student years; nowadays I study them using geometric methods in homogeneous dynamics, a strategy with roots in the 50s and 60s starting with W.Schmidt and brought to prominence by Dani, Margulis, Kazhdan and others. I had the good fortune to be invited for lectures at Tata by Dani and Yale by Margulis, and I hope one day to reciprocate the…

What would you add on the article about the Markov spectrum? Wikipedia can be edited by anyone

Motivation, historical context, landmark results, open problems.

> Wikipedia can be edited by anyone

Tried once; never again.

Re: A triplet tree forms one of the most beautiful structures in math

#17

Post by keithalewis »

_a_a_a_ wrote: post #9
keithalewis wrote: post #5

Earlier quoted context omitted.

Give not that which is holy unto the dogs, neither cast ye your pearls before swine, lest they trample them under their feet, and turn again and rend you.

That doth not illuminate, nor does it reveal.

When the student is ready the Buddha appears.

It also takes a mighty big dog to weigh a ton.

Re: A triplet tree forms one of the most beautiful structures in math

#18

Post by dabeddabed »

ykonstant wrote: post #16
dabeddabed wrote: post #12

Earlier quoted context omitted.

What would you add on the article about the Markov spectrum? Wikipedia can be edited by anyone

Motivation, historical context, landmark results, open problems. > Wikipedia can be edited by anyone Tried once; never again.

I see, sad those potential edits will be missed from appearing in the article, still could I ask you anyways to expand about "landmark results, open problems" ?
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