The grandfather -1 was very happy for the birth of his grandson. Actually it was not only him but also the entire numbers kingdom. This number was the last number expected to come in the lineage of numbers to complete and seal all of the sets and operations. They knew this from the signs foretold in the previous books of wisdom.
Holding the grandson in his arms, the grandfather -1 fell into a silence, which veiled a mental journey to his painful beginning in life. When he was born, he was not accepted by the numbers on the grounds that every number should be useful for counting things, and "-1 of something" did not make sense in this regard. To persist on their nonchalance, the numbers even resisted the establishment of certain operations such as 5-7, since they led to uncountable results. Actually, such operations and the resultant numbers were going to be the children of -1, but other numbers did not know that at the time. More precisely, they did not want to know. It had taken them years to accept -1 to their kingdom.
When -1 was officially admitted and counted as a legitimate number, numbers kingdom grew to include all integers, both positive and negative. With that, the subtraction operation became the mirror image of summation, and so the "theory of everything" was established as the summation operation.
Their acceptance to the numbers kingdom was not as painful as the emergence of -1. They were rational because you could part something into however many units, and their size would be expressed by the ratio of two integers.
As a mirror image of this operation was established the multiplication. Multiplication was a shortcut for summation, but it led to a devastating question in the minds of the scientist numbers. It was common practice to multiply any two integers to obtain another one. But, instead of going from the ingredients to the result, if you do the opposite, what happens? For example, instead of multiplying 2 by 1 to obtain 2, what happens if you ask "what is the number which gives 2 when multiplied by itself?". Although they did not know the answer, they named it: root of 2.
Scientist numbers worked for long decades to figure out the answer. They were even able to visually see it on the hypotenuse when they plotted a right triangle with perpendicular edges of length 1. But when it came to writing the number itself, there was no avail. No two integers or no ratio of integers, i.e. rational numbers, fit the bill. They were able to approximate a number, but they could not really pinpoint it. The more they continued the approximation process, the more decimal digits they produced for the root of 2. Thus the throne of summation as the theory of everything was shaken.
One day, one of them suggested that such irrational behavior was present with many more numbers. In fact there were infinitely many of them. During the same time frame, they also figured out that the most prominent number Saint pi, i.e. the ratio of the circumference of a circle to its diameter, was also behaving the same way. Later on, they were shocked by the finding that the number used for approximating the area under the 1/x curve, known as Saint e, was also extending two infinity in the decimals.
Thus, the numbers kingdom came up with the idea of irrational numbers, i.e. numbers that cannot be expressed as the ratio of two integers. With this expansion, summation was again crowned as "the theory of everything", since subtraction was a mirror image of it, multiplication was a fast version of it, and division was the mirror image of multiplication, hence another form of summation.
Unfortunately, the years of happiness did not last long among the scientist numbers. When the scientist numbers extended the root operation to negative numbers, again summation found itself at the verge of losing its crown. They could not come up with a single number known to them that would give negative numbers when multiplied by itself.
Eventually the numbers realized that this was a new kind of number, just like negative integers and the irrational numbers once were. They did not know what it was, but they predicted its existence. All this happened before the birth of -1's grandson. When the birth of that number took place, the honor of naming it was given to none other than -1.
-1 was a scientist himself. He knew that although he was the grandfather of this new number, the young one was the expected number to resolve all the troubles of the numbers kingdom, including the mesmerizing theory of everything. Drawing on the wisdom of ages, -1 named this newborn as i. A name consisting of a line and a dot, that is 1 and 0, that is everything and nothing, juxtaposed in the essence of a single being. By virtue of this dichotomy, all numbers discovered before i were combined under the umbrella "real", and those associated with i under "imaginary", since the latter were only perceived by imagination.
Right from its birth, i was surrounded by Saint pi, Saint e and of course his grandfather -1. i grew as a number of God. Although mortal like all others, i did not fear being multiplied by 0, because i knew by heart that 0 was nothing other than union with all existence. This idea was revolutionary, and as with everything revolutionary, it was unacceptable at first. But that didn't matter, because pi, e and -1 were not only caregivers of i but also loyal comrades. If something was unacceptable to masses but reasonable at the same time, it had to be proven once and for all.
The long awaited revelation came around when numbers were considered not as one-dimensional but two dimensional entities. That is, instead of being just real or just imaginary, what if they carried both components? What if numbers could be transformed through these components so that a given number could become positive, negative, or imaginary, or a combination of them?
This idea of continuous transformation led to the usual suspects that were at the foundation of trigonometry; namely sines and cosines. Sine of an angle was equal to the cosine of another angle, and these functions displayed an elegant dance over a circle of unit radius.
At the time, it was already known that these functions embodied in a triangle were indestructible by the flames of derivatives, so they represented the concept of change in the most concise form. But what if sine and cosine were to be summed up with their mirror image? They would certainly taste death in the infinite depths of 0. But that was exactly what was argued by i. 0 was a continuous journey, not an end.
This notion of eternity sparked the union of Saint pi, Saint e, i, grandfather -1, cosine and sine. Together, they established a laboratory where they could fire the greatest derivatives, spin the fastest transformations and perform the finest divisions. They named this facility as The Complex Lab.
This was exactly what i had been arguing all along. 0 was an endless journey, not an end; it was a union with all numbers, not a death.
