Fourier Analysis Quotes

We spend the last several weeks in my Real Analysis course on Fourier Series, which I had never seen in undergraduate. So I spent a fair amount of time in an undergraduate text book trying to learn how to do it. But that is neither here nor there, because the rest of the class understood most of it, so our professor felt comfortable making a couple extra comments about the work we are doing. I have collected four quotes from one class- all of which my professor spoke in a dead pan voice which he used to give the rest of his lecture.

“If you consider Fourier Analysis useful, then these theorems are useful.”

Because who wouldn’t find Fourier analysis useful?!

“Real Analysis: Calculus in a form a calculus student can’t recognize”

True that!

We were taking the Fourier transform and as you may know pi appears at fairly regular intervals. And as it appears we hear,

“It always amazes me when these things happen, Where did pi come from?”

Our professor pauses to look around the classroom, as though he might see the pi symbol zoom into the room through one of the open windows (!), then continues with his lecture.

And finally, one of my favorite quotes from that class for the whole year, after finishing a proof with a flourish he pontificates,

“All of mathematics is related!”    “…except maybe combinatorics.”

So there you have it, if you are a combinatorics lover, then you are not related to anyone. Have a lovely week!

Cipher

Cipher is one of the many names for the zero symbol. Now, of course, it now also means a code or encryption. I would like to draw your attention to this very cute poem about the double meaning of 0 and it’s name, “cipher”.

You O my O, but I O thee,
O O no O, but O O for me,
O let not my O a mere O go,
But O my O I O thee so.

Which translates into:

You sigh for my cipher, but I sigh for thee,
Oh, sigh for no cipher, but Oh sigh for me.
Oh let not my sigh for a mere cipher go,
But sigh for my sigh, for I sigh for thee so.

Origin Unknown

Idyllic Galileo

Back in the Renaissance scientists were allowed to be such poets!  The breath of study was more liberal arts degree than pre-med.  Which is to say, the romantic mathematician is much more my style than not.  And so it is not at all surprising, but beautifully eloquent all the same, that I like to return to these poet mathematicians to hear their devout praise.  In the words of Galileo:

“The human intellect does understand some propositions perfectly, and thus in these it has as much absolute certainty as Nature itself has.  Of such are the mathematical sciences alone; that is, geometry and arithmetic, in which the Divine intellect indeed knows infinitely more propositions, since it knows them all.  But with regard to those few which the human intellect does understand, I believe that its knowledge equals the Divine in objective certainty.”

G. Galileo, Dialogue Concerning Two World Systems,
transl. S. Drake, California Univeristy Press,
Berkeley (1953)