How I found God through Algebra (An original Math story)

Still, the first engineer insisted that he wanted to derive it on his own because, as he put it, he was got be just as smart if not smarter than Cardano.

I thought this was an interesting challenge, sort of like a Facebook test “Your friend scored 140 in IQ test. Can you beat him?” I decided to try. Not that I thought I was smarter than Cardano, but I thought back in the 16th century they didn’t even have logs yet, let along trig. So I thought I should be able to derive this formula after graduating from a decent college with the degree in engineering.

Thus, I came home, pulled out a piece of paper and wrote down this equation…

The solution of this equation would be the real roots x1, x2 and x3 such than

First of all, I simplified it as much as possible by making the following substitution…

As a result the equation became much better looking.

So far was so good.
Then I thought, let’s see what the partial solutions would look like if the middle root was 0 or two high or low roots were equal.

This is the case of the Zero.

This is the solution in case of two low roots

And this is the case of two high roots

Also, I certainly was tracking what in these cases the C coefficient would be in terms of B coefficient

I decided to plot the roots on the graph. This way, I could see where the root laid in relation to each other.

As you can see, in order to make the plot more readable, I normalized the roots by dividing them by the common divisor
and plotted them on the graph. The yellow line here represents the root locus for C coefficient.

When I plotted the points, it appeared that the roots laid on the same sinusoid, but they only were shifted by a phase.

Thus, I assumed the solution being in the following form.

It was easy to find the coefficients A1, A3 and A3 from private solutions. They turned out to be…

Next I had to find some sort of a correspondence between the angles α1, α2, α3
Thus I assumed…

After long and arduous calculations, of which I spare you, I came up with this dependency.

This gave me some hope before I dived into the last part… that is the correspondence between

Yet, when I wrote the expression out it seemed pretty hopeless.

I was going deeper and deeper into the uncharted territory and, honestly, had absolutely no clue of where I was going and what exactly I was expecting to find out. Although I was moving within an algebraic derivation, I felt I was moving instinctively, more like amoeba, than a conscious human being.

To make a long story short after many rewrites and much boring tinkering... it came out looking like this…

At this point I was absolutely exhausted, mentally and spiritually. Looking at this clumsy expression I was panicking that it would never converge to anything descent, anything reasonable, anything a normal person can put his finger on.

I just wanted to drop the whole thing as another failure. Oh, well… not the first one and not the last one.

Yet deep down inside I knew this wasn't just any failure. This was the big one, the major one, to which I gave it my all and still couldn't do it. That I couldn't match what Cardano did even though I had 5 centuries head start.
Then suddenly chill ran down my spine. I looked at the expression on the right and I couldn't believe my eyes. It was an expression for

This yielded a very simple correspondence between the C coefficient and the angle alpha 2. So my assumption on trigonometric solution held up.

Some of you might be interested what I've got in the end? Whether I actually go the answer…See for yourself.

Pretty, isn't it? Well, for me anyway.

And you know what, it really changed my life. I got promoted, I met some new and exciting people, I even got somewhat famous.

No. I am pulling your leg. I didn’t become famous, I didn't get promoted, didn't get to meet new and exciting people, and I didn't begin speaking tongues or at least English without an accent.

Did it make me a better person? No. I don't think so either. Internally something did change, though.

It's not that I started believing in an angry bearded man up in the sky.

or think that dinosaurs lived in Nova's ARK.

Yet that perfect order, in which the Universe appears to be existing, made me believe that something or somebody out there has actually made it. At least, if I want to make myself believe into a superior being, this is the easiest way to approach it.