# Problem from A Beautiful Mind

1. Aug 27, 2009

### Dragonfall

Problem from "A Beautiful Mind"

In the movie when he first walks in to teach that ad cal class, this is the problem he wrote on the board (verbatim):

$$V=\{F:\mathbb{R}^3\backslash X\rightarrow \mathbb{R}^3:\nabla\times F=0\}$$

$$W=\{F=\nabla g\}$$

$$\dim (V/W)=?$$

What's X?

2. Aug 27, 2009

### Fabius2

Re: Problem from "A Beautiful Mind"

V/W is the first deRham cohomology group of the space R^3\X, where X is presumably some subset of R^3.

3. Aug 27, 2009

### Freddy_Turnip

Re: Problem from "A Beautiful Mind"

Just finished reading the biog. A good read. Can't help with the above math though.

4. Aug 27, 2009

### Dragonfall

Re: Problem from "A Beautiful Mind"

Can't solve it without X.

5. Dec 23, 2010

### icystrike

Re: Problem from "A Beautiful Mind"

Dim(v/w) = 8 instead of question mark.

inverse cohomology problem to find a manifold M with a 8-dimensional fundamental group.

6. Dec 23, 2010

### AlephZero

Re: Problem from "A Beautiful Mind"

$$\times$$ is the vector cross-product.

$$\nabla\times$$ is the vector calculus "curl" operator.

7. Dec 23, 2010

### disregardthat

Re: Problem from "A Beautiful Mind"

In that case, what does $$\mathbb{R}^3 \slash \times$$ signify?

8. Dec 23, 2010

### Kevin_Axion

Re: Problem from "A Beautiful Mind"

Firstly the person is right in saying $$\times$$ is the x but that is not what the person is referring to, they are asking what the $$X$$ means in $$X\rightarrow \mathbb{R}^{3}$$. But I believe the person is right in saying it is the first deRham cohomology group.

9. Dec 24, 2010

### Edgardo

Re: Problem from "A Beautiful Mind"

Material on the Nash problem: