SVM optimization problem with constraint

I am studying SVM from Andrew ng machine learning notes. I don't fully understand the optimization problem for svm that is stated in the notes. So we have optimization problem

$$\max_{\gamma, w, b}\gamma$$ s.t. : $$y^{(i)}(w^Tx^{(i)}+b)\geq\gamma, i=1,\dots m,\\||w||=1.$$

I get a little bit confused here, as i don't see why we should need this first constraint. Isn't it enough only to maximize $$\gamma$$ and in that case we already have the maximal margin hyperplane where observations are at least $$\gamma$$ away from the decision boundry (because $$\gamma$$ is already defined this way)?

I think I don't understand something simple here. If you have any explanation for this I would appreciate it very much.

(because $$\gamma$$ is already defined this way)?
But how does the optimization problem know that $$\gamma$$ is defined in such way ? if you remove that constraint, your optimization problem becomes:
$$\max_{\gamma, b, w} \gamma \\ s.t. : ||w|| = 1$$
The optimization problem will just indefinitely increase $$\gamma$$, as is not restricted in any way. You have to enforce the way gamma is defined so that the optimization problem has solutions that respect that definition.