# What mathematics background must one have to be conversant in M Theory? **URL:** \ **Category:** Factual Questions\ **Created:** [June 4, 2005, 3:14pm UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884 "2005-06-04T15:14:24Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Smeghead](https://avatars.discourse-cdn.com/v4/letter/s/f1d935/32.png) [@Smeghead](https://boards.straightdope.com/u/Smeghead)\ **Post date:** [June 4, 2005, 10:45pm UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/21 "2005-06-04T22:45:16Z")
> [@E = mc²](#): > > It gets good reviews at amazon, whereas Greene’s book is severely panned by some. (My apologies, **Smeghead**. S’alright. It’s my sister’s book - she just lent it to me. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [June 5, 2005, 12:07am UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/22 "2005-06-05T00:07:17Z")
To elucidate my comments a bit: I’m of the opinion that Witten is somewhat overesteemed as a _mathematical_ physicist. A huge portion of his purportedly mathematical work (including what he won the Fields medal for) boils down to handwaving about what math “should” look like (mostly to make the physics side pretty) and leaving the details for the poor slags in the trenches to work out. Don’t get me wrong. The guy’s a genius no doubt, but he didn’t really do half of the math that has his name attatched to it. ---
**Author:** ![ZebraShaSha](https://avatars.discourse-cdn.com/v4/letter/z/eada6e/32.png) [@ZebraShaSha](https://boards.straightdope.com/u/ZebraShaSha)\ **Post date:** [June 5, 2005, 12:21am UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/23 "2005-06-05T00:21:30Z")
Don’t forgot Riemann geometry! Well, ok, that only is really necessary for General Relativity, but I feel kind of sure that it will, in the end, be worked into M-theory. Now, who wants to tell me the math requirements for quantum loop gravity? Do they even know what math to use yet? ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [June 5, 2005, 1:28am UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/24 "2005-06-05T01:28:37Z")
[http://www.superstringtheory.com/math/index.html](http://www.superstringtheory.com/math/index.html) Beware. This could easily tie you up for a couple of weeks or so. > [@](#): > > Here are some of the topics in mathematics that a person who wants to learn advanced topics in theoretical physics, especially string theory, should become familiar with. > > Real analysis > Complex analysis > Group theory > Differential geometry > Lie groups > Differential forms > Homology > Cohomology > Homotopy > Fiber bundles > Characteristic classes > Index theorems > Supersymmetry and supergravity > K-theory > Noncommutative geometry [http://www.superstringtheory.com/math/index.html](http://www.superstringtheory.com/math/index.html) ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [June 5, 2005, 1:54am UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/25 "2005-06-05T01:54:14Z")
Just to give you an idea of how simple this stuff is here’s a summary of K theory from the above site. > [@](#): > > K-theory > > Cohomology is a powerful mathematical technology for classifying differential forms. In the 1960s, work by Sir Michael Atiyah, Isadore Singer, Alexandre Grothendieck, and Friedrich Hirzebruch generalized coholomogy from differential forms to vector bundles, a subject that is now known as K-theory. > > Witten has argued that K-theory is relevant to string theory for classifying D-brane charges. D-brane objects in string theory carry a type of charge called Ramond-Ramond charge. Ramond-Ramond fields are differential forms, and their charges should be classifed by ordinary cohomology. But gauge fields propagate on D-branes, and gauge fields give rise to vector bundles. This suggests that D-brane charge classification requires a generalization of cohomology to vector bundles – hence K-theory. > > Overview of K-theory Applied to Stringssby Edward Witten > D-branes and K-theory by Edward Witten ---
**Author:** ![Plynck](https://avatars.discourse-cdn.com/v4/letter/p/3e96dc/32.png) [@Plynck](https://boards.straightdope.com/u/Plynck)\ **Post date:** [June 5, 2005, 3:05am UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/26 "2005-06-05T03:05:40Z")
> [@E = mc²](#): > > Imagine an outline of two ripple-shaped Branes, looking more or less like colorless, cruller-shaped clouds. If these two Branes collide, when one Brane’s cruller outcroppings touch the other’s outcroppings, a super gigantic explosion results — a Big Bang. [Homer Simpson] Mmmm… Crullers… [/Homer Simpson] > [@Smeghead](#): > > I’m reading Brian Greene’s book “The Elegant Universe” right now - they made a NOVA documentary about it. So far, it seems quite accessible. Ask again when I’ve finished in a few weeks. 😃 I’m also reading Greene’s book right now as well, about 50 pages into it. I’m not a math guy, and I find it accessible (so far). Some of the analogies are dumbed down a bit, but I don’t mind that; it helps to have real world analogies to some of the concepts. I have no doubt I’ll move on to his next book after this one, and I’ll follow up on the references herein to Kaku’s works. best to all, plynck ---
**Author:** ![Shalmanese](https://avatars.discourse-cdn.com/v4/letter/s/45deac/32.png) [@Shalmanese](https://boards.straightdope.com/u/Shalmanese)\ **Post date:** [June 5, 2005, 5:12am UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/27 "2005-06-05T05:12:42Z")
I found Greene’s elegant universe very well written and worth it for the chapter on General Relativity alone. A lot of his stuff on strings is a bit out of date AFAIK as the field is moving very quickly. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [June 5, 2005, 7:29am UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/28 "2005-06-05T07:29:29Z")
> [@ZebraShaSha](#): > > Don’t forgot Riemann geometry! Well, ok, that only is really necessary for General Relativity, but I feel kind of sure that it will, in the end, be worked into M-theory. > > Now, who wants to tell me the math requirements for quantum loop gravity? Do they even know what math to use yet? Riemannian geometry is a special case of differential geometry. In fact, it’s almost useless for GR since GR assumes a _Lorentzian_ metric. ---
**Author:** ![BarnOwl](https://avatars.discourse-cdn.com/v4/letter/b/e95f7d/32.png) [@BarnOwl](https://boards.straightdope.com/u/BarnOwl)\ **Post date:** [June 5, 2005, 11:40am UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/29 "2005-06-05T11:40:52Z")
Last night, **Mrs. E=mc²** gave me a copy of Greene’s **The Elegant Universe** , so today I’ll be reading it, too. ---
**Author:** ![BarnOwl](https://avatars.discourse-cdn.com/v4/letter/b/e95f7d/32.png) [@BarnOwl](https://boards.straightdope.com/u/BarnOwl)\ **Post date:** [June 13, 2005, 7:10pm UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/30 "2005-06-13T19:10:28Z")
I never offered my heartfelt appreciation to all of you who contributed to this thread, so I’ll do so now: Thank you all, very, very much for taking the trouble to make your contributions. I’m currently enjoying my way through The Elegant Universe, and look forward to reading all the other books that were recommended. I’ll probably never understand M Theory, but I am certainly having a good time exploring it. Thanks again. ---
**Author:** ![sturmhauke](https://avatars.discourse-cdn.com/v4/letter/s/e47c2d/32.png) [@sturmhauke](https://boards.straightdope.com/u/sturmhauke)\ **Post date:** [June 13, 2005, 9:35pm UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/31 "2005-06-13T21:35:29Z")
I used to think I was good at math, but then I read some of these threads and realize I don’t even know what I don’t know. I get the impression that multivariable calculus is just a drop in the bucket of higher mathematics. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [June 13, 2005, 9:38pm UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/32 "2005-06-13T21:38:21Z")
> [@sturmhauke](#): > > I get the impression that multivariable calculus is just a drop in the bucket of higher mathematics. Pretty much. Linear algebra and group theory are both very accessible and will give you a good feel for what higher math is like, so if you’re curious, those are good places to start. ---
**Author:** ![II\_Gyan\_II](https://avatars.discourse-cdn.com/v4/letter/i/bbe5ce/32.png) [@II\_Gyan\_II](https://boards.straightdope.com/u/II_Gyan_II)\ **Post date:** [June 13, 2005, 10:13pm UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/33 "2005-06-13T22:13:59Z")
If you’re serious about it, get a copy of Penrose’s latest book [The Road to Reality](http://www.amazon.com/exec/obidos/tg/detail/-/067945443). He starts from the ‘beginning’ and aims to describe all the laws of physics, including string theory. Penrose doesn’t shy away from the mathematics, which is a point in the book’s favour, IMHO. ---
**Author:** ![II\_Gyan\_II](https://avatars.discourse-cdn.com/v4/letter/i/bbe5ce/32.png) [@II\_Gyan\_II](https://boards.straightdope.com/u/II_Gyan_II)\ **Post date:** [June 13, 2005, 10:17pm UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/34 "2005-06-13T22:17:16Z")
Oops, working [link](http://www.amazon.com/exec/obidos/tg/detail/-/0679454438). ---
**Author:** ![sturmhauke](https://avatars.discourse-cdn.com/v4/letter/s/e47c2d/32.png) [@sturmhauke](https://boards.straightdope.com/u/sturmhauke)\ **Post date:** [June 14, 2005, 5:37am UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/35 "2005-06-14T05:37:41Z")
Heh. I had to take linear algebra for my computer science degree; it kicked my ass. It took me 3 tries to pass the damn thing. They really should call it vector algebra or spatial algebra or something. ---
**Author:** ![Walker\_in\_Eternity](https://avatars.discourse-cdn.com/v4/letter/w/46a35a/32.png) [@Walker\_in\_Eternity](https://boards.straightdope.com/u/Walker_in_Eternity)\ **Post date:** [June 14, 2005, 10:36am UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/36 "2005-06-14T10:36:49Z")
> [@II Gyan II](#): > > If you’re serious about it, get a copy of Penrose’s latest book [The Road to Reality](http://www.amazon.com/exec/obidos/tg/detail/-/067945443). He starts from the ‘beginning’ and aims to describe all the laws of physics, including string theory. Penrose doesn’t shy away from the mathematics, which is a point in the book’s favour, IMHO. I’ll second that, I’m about a third of the way through the book at present, it helps if you have a mathematical background, but he does give very concise descriptions of the mathematical methods. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [June 14, 2005, 6:54pm UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/37 "2005-06-14T18:54:05Z")
> [@sturmhauke](#): > > Heh. I had to take linear algebra for my computer science degree; it kicked my ass. It took me 3 tries to pass the damn thing. They really should call it vector algebra or spatial algebra or something. “vector algebra” would focus on the vectors, which are really incidental. “spatial algebra” would focus on the very limited case of **R** [sup]3[/sup] (maybe **R** [sup]n[/sup]). The subject isn’t vectors or about space. It’s algebras of linear transformations. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [June 14, 2005, 6:55pm UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/38 "2005-06-14T18:55:14Z")
To be fair, most introductory linear algebra courses–especially those in an engineering program–really are about vectors and matrices. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [June 14, 2005, 7:02pm UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/39 "2005-06-14T19:02:32Z")
> [@ultrafilter](#): > > To be fair, most introductory linear algebra courses–especially those in an engineering program–really are about vectors and matrices. I’d say they’re about matrices, which form a (say it with me, now) “linear algebra”. Besides, if we want to rename courses according to what they talk about rather than the field they’re a simple case of, we should call the old high school course “single-variable polynomials over the real (and usually rational) numbers”. ---
**Author:** ![Feydeau](https://avatars.discourse-cdn.com/v4/letter/f/df788c/32.png) [@Feydeau](https://boards.straightdope.com/u/Feydeau)\ **Post date:** [June 14, 2005, 11:57pm UTC](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884/40 "2005-06-14T23:57:44Z")
> [@Mathochist](#): > > “single-variable polynomials over the real (and usually rational) numbers”. Band name? Perhaps not. [Previous page](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884.md?page=1) [Next page](https://boards.straightdope.com/t/what-mathematics-background-must-one-have-to-be-conversant-in-m-theory/306884.md?page=3)