How has the idea of the existence of extra space dimensions ingrained?

Moving along the familiar four dimensions of the multidimensional universe…

Back in the 20s of the last century, the mathematician Theodor Kaluza and the physicist Oskar Klein noticed that adding another dimension to our four-dimensional space-time makes it possible to move forward in building a unified theory of the fundamental interactions known at that time: the gravitational and electromagnetic interactions. They assumed that the additional, the fifth dimension is folded into a circle so that the corresponding coordinate can vary from zero to the length of the circle’s circumference. A very small radius of the circle would explain the fact that the extra dimension could not be seen by us. Afterwords, a quantity of schemes have been devised in which there are several extra dimensions that, in addition, can be large or even infinite while remaining almost invisible without special experiments.

Extra dimensions  of the space-time are not visible

Actually, why should it be exactly three spatial dimensions — this number is not that special.

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