Hacker News Reader

Comment by hughdbrown | Hacker News Reader

I don't know why this would qualify as simple.

Compare it with the proof by contradiction that the square root of 2 is rational:

$$\sqrt{2} = \frac{a}{b} 2 {b^2} = {a^2} {b^2} and {a^2} have an even number of factors of 2 Therefore 2 {b^2} has an odd number of factors of 2 and cannot equal {a^2}. $$

I can explain this to a ten year old. The irrationality of pi proof has too many non-obvious steps and claims.

[Hacker News can't render math?]

View on HN

It's simple for a proof that pi is irrational. It isn't simple as √2, but the number itself is quite a lot more complex -- even defining pi to mathematical precision takes more work than the whole of your irrationality proof!

It's simpler than other proofs. Yes, it relies on real analysis (differential and integral calculus), including calculus of transcendental functions. But a high school calculus student could follow the proof, if they take some faith in infinitesimals.

Okay, then think of it from a strictly quantitative viewpoint. Euclid's proof of the irrationality of root two was known circa 300 BCE. Mathematicians would have to wait until 1670-ish for the math to be invented to understand the proof of the irrationality of pi.

You can say it's obvious today to a high school calculus student, but the elapsed time between understanding of the two proofs is about two millennia.

Simple to confirm, much harder to generate. What to strive for!

agreed. i think they were doing the math equivalent of code-golf to cram this proof onto a single page.

As a mathematician, I find this proof reasonably written. Yes, not everything is spelled out, but the proof was published by the AMS for mathematician, and imo it can be expected that those know how to fill the gaps.

As a grammatician (wanker!), I find you shy of:

  * λ: [reasonably] well [written] - the lambda, written in stern red Biro, in your double spaced manuscript, indicates you missed out a word.  Reasonably is an adjective that requires a comparative (reasonably ... what).

  * [imo]: sp - imo is an abbreviation so why not use some capital letters?  You are a mathematician: you deploy many alphabets routinely so why piss around with the Roman one?  I doubt you muddle your h and H. 

  * Final clause: expected meaning can be derived but why make it hard?

For goodness sake: I get you are a mathematician but there is no reason to dribble on the page.

"Reasonably" is an adverb. "Reasonable" is the adjective.

A grammarian would know that. Not to mention their nephew in the fifth grade.

Also, "grammatitian" is an irregular word used by people who don't know about "grammarian" and "grammatist", likely because they don't read books and can't be bothered to use a dictionary.

> From Alexander the grammarian, [I learned] to refrain from fault-finding, and not in a reproachful way to chide those who uttered any barbarous or solecistic or strange-sounding expression; but dexterously to introduce the very expression which ought to have been used, and in the way of answer or giving confirmation, or joining in an inquiry about the thing itself, not about the word, or by some other fit suggestion.

Honestly, this approach also sounds like it has the potential to be insufferable, though I've seen it done skillfully. But I guess it must have been better than the prevailing norm for Marcus Arelius to cherish the wisdom. Maybe to Marcus it was more about the humility therein than about playing the role of a grammar tutor.

If your conversation partner is made to feel like a human on equal footing with you, then you can just mention the mistake candidly without any condescension implied or perceived. Maybe don't try it in settings where you would risk accidentally embarrassing someone.

Bugger, I missed out the emoticons.

Reply on news.ycombinator.com