Can every math problem be visualised?

Question

Basically, title.

Can everything in mathematics be represented graphically one way or another?

Answer 1

It is very hard to visualize things as they go to higher dimensions . For example consider $\Bbb{R}P^n$(the real projective space). For, $n=1$ this is just the circle but as $n$ value increases it becomes very difficult to visualize it. So questions involving $\Bbb{R}P^n$ become very difficult to visualize.

For that matter consider the Poincare conjecture in higher dimensions . It is nearly impossible to visualize it because it goes to such higher dimensions.

Edit: Since you are not familiar with these spaces I will give you a more easier example. Consider $S^1$ this is your normal circle , $S^2$ your sphere, But for $S^3$ we have issues. Because you know that $S^1$ lies in $\Bbb{R}^2$, $S^2$ lies in $\Bbb{R}^3$ . But $S^3$?? This lies in $\Bbb{R}^4$. Since it is difficult to visualize $\Bbb{R}^4$ it is difficult to visualize $S^3$.

Answer 2

Not true. If everything could be represented visually the science called geometry, not mathematics.