Fishing for a presentation idea

NRS

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Hello all. I'm a math major attending a "math in history, art and philosophy" class as an elective. For that class, we have to give a presentation on a topic of our choice. As many of the people in the room aren't math majors or had much exposure to the subject, I was thinking about giving a presentation on proofs. Perhaps why they are so important, maybe give an example of an example which appears true but isn't (Gauss's overestimation conjecture or something). But I would like to finish off the presentation with a relatively non-trivial but elementary proof. I really can't think of anything, any suggestions would be nice.
 
Well GH Hardy considered Euclid's proof of the infinitude of primes as one of the most beautiful proofs. The proof that the square root of 2 is an irrational is pretty elegant. Cantor's diaganolization proof is cool. The proof (by Oresme????) that the harmonic series diverges is quite simple. None are difficult. None is trivial.

But I think "Euclid's proof of the infinitude of primes" is most elegant and understandable proof among all those......
 
Hello all. I'm a math major attending a "math in history, art and philosophy" class as an elective. For that class, we have to give a presentation on a topic of our choice. As many of the people in the room aren't math majors or had much exposure to the subject, I was thinking about giving a presentation on proofs. Perhaps why they are so important, maybe give an example of an example which appears true but isn't (Gauss's overestimation conjecture or something). But I would like to finish off the presentation with a relatively non-trivial but elementary proof. I really can't think of anything, any suggestions would be nice.

If you are looking for a subject which covers mathematical history, art and (a little bit) philosophy then have a look here:

http://en.wikipedia.org/wiki/Catenary

For additional information see Hairer / Wanner, Analysis by Its History, Springer, New York, 1997, page 136 ff
(probably there exists a newer edition)
 
One good book to read would be: "One, Two, Three .....Infinity" by George Gammow.
 
Hello all. I'm a math major attending a "math in history, art and philosophy" class as an elective. For that class, we have to give a presentation on a topic of our choice
You can find a whole variety of possible modern topics in Reuben Hersh's ​What is Mathrematics Really?
 
Hey, thanks a lot for all of the feedback. This presentation is nothing huge, I simply plan to maybe state a little bit of history of mathematical thought, and then talk about proof and its development a bit. Perhaps I will show the development from the "Behold!" proof of the Pythagorean theorem to a simple congruence proof.

I agree that the proof of the infinitude of primes is gorgeous, and for some reason I didn't think of that. Perhaps I will wrap up with that. Thanks a lot, I wasn't expecting all of this input. :D
 
HAHA, that would be an interesting little twist as well.
 
Euclid alone has looked on Beauty bare
by Edna St. Vincent Millay

Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.

O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.
 
Don't forget to weave in Edna St. Vincent Millay's line that "Euclid alone has seen beauty bare."

Edit: Thanks Subhotosh Khan for correcting my memory. It is always nice when a line scans properly.

I have to admit - I did not catch your lapse in memory. I just faintly remembered this poem from my early days of struggle with geometry. Recovered and shared it with the help of Wiki... (what a wonderful thing)
 
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