Punya+Mishra


 * 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).

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?
 * The Goldbach Variations**

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 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?
 * The Mathematical //i//**

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, + & – 6//i,// 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.

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.
 * Mathematical Groove**

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