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February 5, 2009

Temptations of Mathematical Structures

Urs Schreiber:

I find that plenty of people are studying plenty of structures with great enthusiasm whose whose true origin and meaning is clearly unknown. I find this eerie, too, but maybe in a different sense: it’s not so hard to just fiddle around with structures and study axiom systems. What is harder is finding out where these naturally live.

When I was a sophomore at Harvard, I took the Mathematical Methods in Physics course. The syllabus in the printed course catalogue contained a long list of interesting topics to be covered, including “Milbert Spaces.”

On the first day of class, the professor gave an overview of what he planned to cover for the semester. When he got to the aformentioned topic, he said

As pure Math, the theory of Milbert Spaces is really fascinating. But, it turns out, what’s relevant to Quantum Mechanics is the theory of Hilbert Spaces. So that’s what we’ll do, instead…

Posted by distler at February 5, 2009 11:46 AM

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Re: Temptations of Mathematical Structures

Humm, lets take the Calabi-Yau manifolds as a modern example.Before they were just being studed for the sake of pure maths but later on they became relevant to string theory and interestingly ideas coming from st became relevant to them as well !
So it is well possible that mathematical structures that don`t look relevant to physics now , will turn out to be relevant in physics.
Will theoretical physics one day become axiomatic ?

Posted by: Serfo on February 8, 2009 8:08 PM | Permalink | Reply to this

Re: Temptations of Mathematical Structures

Out of curiosity, what did the professor think needed to be changed about Hilbert spaces to make them mathematically interesting?

Posted by: D on February 12, 2009 4:21 PM | Permalink | Reply to this

Re: Temptations of Mathematical Structures

In business math, what really matters is Dilbert spaces.

Posted by: John Baez on March 3, 2009 10:51 AM | Permalink | Reply to this

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