September 30, 2012 6:24 PM Subscribe

Are some areas of maths inherently central and others as more peripheral?
Or is any sense of centrality just a human experience, a cultural artifact arising from:
what has had greater application,
what has been studied more,
what produces a greater sense of the sublime in the human mind?
Are some parts of mathematics inherently a more fundamental description of what is going on in the universe, or is it as silly (or correct?) to talk about maths that way as it would be to talk that way about a classical ballet?

**Is there an objective way of classifying whether some branches of mathematics are inheritently more central and others less so? Assuming that's not something we really have a solid grasp on, what are the current ideas about this?**

Long ago, my housemate way studying knot theory and topology.

I wasn't, and my only contact with it was what he told me. At the time, I percieved it as beautiful and a triumph, but in the way a ship in a bottle is a beautiful triumph,

that so much care and effort was invested to perfect something utterly frivolous.

Of course I was wrong on the useless, topology and knot theory are both tremendously useful.

So the importance of topology and knot theory were validated in terms of human application, but does that hint at a deeper relevance, that these theories are at the core of how the big engine works?

**My friend J will complain this is such a second year university mathematics student conversation.*

but I have never been a second year maths student,

I wasn't in the hot tub that night you and your classmates dropped acid and broke it all down.

(and did you resolve the mysteries that night or did you end up downloading goatse over a 14k modem?)

So I'm primed to be easily impressed, I have the wide ears open eyed gape of your 14 year old nephew.

(Just because you've told the kiki/bouba story in your best Vilayanur Ramachandran voice a couple of dozen times doesn't make it a cheap shot to blow my mind with it when you tell it to me for the first time.)
posted by compound eye to Science & Nature (6 answers total) 9 users marked this as a favorite

Long ago, my housemate way studying knot theory and topology.

I wasn't, and my only contact with it was what he told me. At the time, I percieved it as beautiful and a triumph, but in the way a ship in a bottle is a beautiful triumph,

that so much care and effort was invested to perfect something utterly frivolous.

Of course I was wrong on the useless, topology and knot theory are both tremendously useful.

So the importance of topology and knot theory were validated in terms of human application, but does that hint at a deeper relevance, that these theories are at the core of how the big engine works?

but I have never been a second year maths student,

I wasn't in the hot tub that night you and your classmates dropped acid and broke it all down.

(and did you resolve the mysteries that night or did you end up downloading goatse over a 14k modem?)

So I'm primed to be easily impressed, I have the wide ears open eyed gape of your 14 year old nephew.

(Just because you've told the kiki/bouba story in your best Vilayanur Ramachandran voice a couple of dozen times doesn't make it a cheap shot to blow my mind with it when you tell it to me for the first time.)

Probably not. But if it was going to be anything, it would probably be Group Theory.

posted by Chocolate Pickle at 11:54 PM on September 30, 2012

thank you for making sensible attempts to answer an unanswerable question :)

posted by compound eye at 4:15 AM on October 1, 2012

posted by compound eye at 4:15 AM on October 1, 2012

The Tao Te Ching

posted by zengargoyle at 4:52 AM on October 1, 2012

Tao gives birth to one,Set Theory always seemed to be the bottom of "turtles all the way down" to me. You've got nothing and then something and then otherthing and then anotherthing that isn't the something or the otherthing and blammo you now have everything. The division and differentiation of one thing from another and others is what makes it possible for the existence of more than nothing.

One gives birth to two,

Two gives birth to three,

Three gives birth to ten thousand beings.

Ten thousand beings carry yin on their backs and embrace yang in their front,

Blending these two vital breaths to attain harmony.

-- from chapter 42, E. Chen (tr.)

posted by zengargoyle at 4:52 AM on October 1, 2012

Another vote here for set theory, and more broadly, mathematical logic. You might also take a look at Wikipedia's article on the foundations of mathematics.

posted by Johnny Assay at 5:25 AM on October 1, 2012

posted by Johnny Assay at 5:25 AM on October 1, 2012

This page of Bill Thurston's statements seems to have some bearing on your question.

posted by flug at 12:25 PM on October 1, 2012

posted by flug at 12:25 PM on October 1, 2012

This thread is closed to new comments.

Speaking as a physicist, the farther down you get into the 'basic building blocks of matter!' the more esoteric your mathematics becomes. The brain is built to handle the things it encountered as it evolved - one of these, three of those, more caribou in that herd than in that one, logs pick up speed as they roll downhill... so that's the stuff that has the 'basic' math. Quantum mechanics, string theory, gravity-as-deformation-of-spacetime, that stuff feels very tangential to the human mind... but actually it's what underlies all of the rest of it, from a physical point of view. And we don't yet even have a good mathematical model that pulls it all together.

posted by Lady Li at 11:49 PM on September 30, 2012