Goldbach’s Conjecture, by Punya Mishra

Goldbach, a mathematician, serious and stern
Many years ago noticed a pattern
He wrote, to Euler, the math genius
Here is something, he said, to excite us!

I have seen, he scribbled, with my imagination
That every even digit
(except two, which doesn’t fit)
Can be broken into a partition
Of two primes which add
To the original even digit
(Now, Euler, don’t fidget!)
But isn’t that totally rad!

Now since that day this simple thesis
Remains just that, a hypothesis
Forcing number lovers to lose their slumber
As they try to prove, primes in pairs can add up to any even number.

(Two is the exception, as we said before
Which is, come to think of it, a bit of a bore).

The Goldbach Variations
A Prussian by the name of Christian Goldbach
As a mathematician no mean hack
Once noticed in numbers a hidden structure
Which he set out as a conjecture
That every number in the number zoo
As long as it was larger than 2
Could be expressed as the sum
Of three primes, wasn’t that rum?

Not having a proof, he thought it better
To write it up and send it to the great Euler, in a letter
Euler took what Goldbach had wrought
Played with it, making it elegant and taut
By suggesting that one should see
Every even as the sum of two primes not three!
Adding the caveat that this was true
of all even numbers greater than 2.

It is of course no surprise
That a question should arise
Should the one who first saw
A version of this numerical law
(That would be Goldbach whose song
Turned out, in essence to be wrong)
Should he be the one to receive the credit
Or should it be the one who did the final edit.

Euler was more famous, the deck was stacked
in his favour, rather than lesser known Goldbach
Would this be the conjecture of Euler
Of Goldbach’s name would he be the spoiler

But as it happens the workings of history
Often remains, to us mere mortals, a mystery
History does not really care
If the attribution is truly fair

Thus it is surprising to anyone who looks
In most standard textbooks
Or sits in mathematical lectures
On hitherto unproven mathematical conjectures
That Euler today receives none of the credit
Though, clearly one can say that he did it.
The idiosyncrasies of life and citation you can blame
For this becoming Goldbach’s significant claim to fame.

About history and credit you may quaff
It was Goldbach who had the last laugh.
More so since this conjecture has remained just that
A conjecture! Unproven, which is nothing to scoff at.

The Mathematical i
The negative numbers were full of dismay
We have no roots, they were heard to say
What, they went on, would be the fruit
of trying to find our square root?

Matters seem to be getting out of hand
Since the negatives have taken a stand,
On the fact that positives have two roots, while they have none
They plead, would it have killed anybody to give us just one?
The square roots of 4 are + and – 2! As for -4? How unfair,
He has none! None at all. Do the math gods even care?

This lack of roots, our value does undermine
Is it some sinister plan, ‘cos we’re on the left of the number-line?
Among the more irrational negatives, one even heard cries
It is time, they said, it is time, to radicalize!!

Hearing this non-stop (somewhat justified) negativity
The mathematicians approached the problem with levity
And suggested a solution, kinda cute and fun
Lets rename, they said, the square root of minus 1!

In essence lets re-define the problem away, on the sly
by just calling this number (whatever it may be) i.
i times itself would be one with an negative sign
Every negative could now say, a square root is mine!
This simple move would provide the number -36
With two roots, + & – 6i, what an awesome fix!

The positives grumbled, what could be dumber
Than this silly imaginary number
But it was too late, much too late you see
To bottle this rather strange mathematical genie
i was now a part of the the symbolic gentry
Finding lots of use in, of all places, trigonometry.

With time i began its muscles to flex
extending the plane, making it complex!
In fact, hanging out with the likes of e and Pi
i got bolder, no longer no longer hesitant and shy.
And combined to form equations bold and profound
That even today, do not cease to astound.

Consider for a moment the equation
e to the power Pi i plus 1
It was Euler who first saw, how these variable react
To come up with a beautiful mathematical fact,
To total up to, (surprise) the number zero.
Could we have done it without our little imaginary hero?
Even today Euler’s insight keeps math-lovers in thrall
One equation to rule them all.

So if you want to perceive the value of this little guy
I guess you have to just develop your mathematical i.
It may also help you remember how often we forget to see
The significance, to human life, of the imaginary.

Mathematical Groove
Doesn’t it just race your heart to see
These games with numbers and infinity.
How can one stay aloof
From the elegance of a proof
Time to groove on mathematics and beauty.

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