does every algebraic concept theoretically have an equivalent geometric concept?

Question

I had a student ask what the relationship of algebra and geometry is.

does every algebraic concept theoretically have an equivalent geometric concept, even if it's impossible to draw/picture/visualize such as infinite dimensions?

for example, $x^n$ is the equivalent to 'volume' of the n-dimensional figure with dimensions whose length is $x.$

Answer 1

The answer is no.

For example can you graph the function defined by $$f(x) =1 \text { if x is rational }$$ and $$f(x) =-1 \text { if x is irrational }$$

Could you graphically show that $$x^4-1= (x^2-1)(x^2+1)$$ or the binomial coefficient is $$ \frac {n!}{r!(n-r)!}?$$