Why can't we divide by 0? Is it just a arbitrary construct created by mathematicians? Couldn't we solve some problems by providing a definition to the division of zero?
The reason we cannot divide by zero is because it is undefined in mathematics. Division is the inverse of multiplication, and when we divide a number by zero, we are essentially asking, What number multiplied by zero gives us the original number? This question has no answer, as any number multiplied by zero always gives us zero. 

Furthermore, dividing by zero can lead to contradictions and inconsistencies in mathematical reasoning. For example, if we allow division by zero, we could prove that any number is equal to any other number, which clearly does not make sense.

While it may seem like an arbitrary construct, the fact that we cannot divide by zero is a fundamental rule in mathematics that forms the basis of many other concepts and calculations. It is not possible to provide a consistent and meaningful definition for division by zero that does not lead to contradictions or inconsistencies.
Can you explain why we created a definition for the sqaure root of -1 (i) ? And why was this necessary for some branches of mathematics ?
The historical origin of the imaginary unit i is tied to Gerolamo Cardano and the solution of the cubic equation.

The cubic equation is ax^3+bx^2+cx+d=0 and the specific case that brought about the invention of the imaginary unit was the situation when the discriminant of this equation D=18abcd-4ac^3-27a^2d^2+b^2c^2-4b^3d is greater than 0. This case is called *casus irreducibilis* or 'the irreducible case'. Cardano had found the solution to the cubic equation, the famous *Cardano's solution*, but in the *casus irreducibilis* his solution would only work if the result of a square root could be a negative number. This led him to invent the imaginary unit.

Much later on, in 1730 it was discovered by Abraham de Moivre that the use of the imaginary unit can make certain trigonometric calculations much more compact. This was further studied by Leonhard Euler, leading into the creation of a branch of mathematics called *complex analysis*, where the imaginary unit plays a key part.

This has been a brief overview of the history of the imaginary unit. Would you like to hear more of any of the things I mentioned?