## The Real Mathematics Podcast

And next, the Real Mathematics Podcast. Also with some complex numbers in it.

The integer of the week is 59… for this 59th episode of the Real Mathematics Podcast.

And we start with Julius Approximate.

"Let n be a natural number, let f be an almost everywhere continuous function from the extended real domain to itself, and let I stand for the Lebesgue integral over t from x to x zero of f prime function of t squared, function squared, not t, over the square root of n log f function of t, plus one, one outside the log, inside the square root, times two, outside the square root, outside the fraction."

And that was Julius Approximate, answering the question "Why aren't there more mathematics podcasts?" Another part of the answer is, unlike physicists who can always blow stuff up, mathematicians have a subject whose appeal is not intuitively obvious.

Next a promotional clip from the Lot Society of Graduate Students.

"So, you want to get to that conference, but you don't have the money? The department is poor, the head thinks it was you who defecated on the hood of his new car, the meeting's on the slopes of Mauna Kea and no-one believes it would be work, not leisure? All common problems for graduate students. We can't always help you, but we have a probabilistic remedy: the Lot Society of Graduate Students being the 'we' of this sentence. Pay us a dollar a month — surely something you can afford — and you can enter our raffle once a year. The winner will be paid, out of the dues, a stipend to attend a conference of his or her choice: conference fee, travel, accommodation, even a sandwich allowance. It could be you, and it could be the conference which changes your life, for better or for worse, but usually for the better. Remember, when gastric and/or mental irregularities get you in trouble with the dept head — the Lot Society of Graduate Students may be your only hope."

And that was who it was.

We do not have a puzzle this week.

We do not have exciting education-related news, visions, hallucinations or interviews this week either.

We also do not have breathless news stories about "applied mathematics", where exploding things play a part so big there's no mention of any mathematics beyond shallow hand-waving.

This has been the recitation of the three things there is not, not this week, last week or next week, not ever. This is the Real Mathematics Podcast.

Our mathematician of the week is Klaus Stengun… a male human, from Poland. Doctorate in 1930, retired in 1977. Seventeen papers on differential equations. Much work among the trivial ones. Did not name a lemma, did not name a theorem, did not name a conjecture or a proposition, did not name a field of study. Per our unisex policy, the show notes include three pictures: in formal wear, in swimwear, and in the nude. We thank Ms. Sczcarywerykgb of the former Polish Ministry of Public Security for their help in acquiring these pictures, lovely pictures.

Next a promotional clip from the Society Against Teabagging.

"Hello. Used tea bags smell bad, clutter the coffee room, and are an eyesore. Plus tea is inferior in its invigorative potency when compared to coffee or amphetamines, which leave no such aftereffects. This is the Society Against Teabagging — outlaw tea, inlaw amphetamines and other stimulants of similar or greater efficiency is our slogan! Rise or otherwise assume a position indicating great determination, academical people and associated others of the world is our other slogan!"

Now, another installment of our very useful series, "The Mathematician's Guide to Practical Life".

"The toilet."

"The following axioms are commonly assumed among the non-mathematical people."

"One. Outside the toilet, the zipper of the overpants is kept up, and the dress is kept buttoned in the lower parts. On which you should wear, see our episode on Dressing. The act of up-zippering (and similarly dress-buttoning) is extraneous, given that eventually the zipper will be pulled down for defecation or some other pants removal operation, but this is an axiom of practical life, not a result of any logical evaluation of work-minimizing benefit. Not keeping your zipper up outside the toilet is classified as rude, but it is not a social suicide. The zipper, if down, can be pulled up in company without causing any further offense."

"Two. Interpersonal co-ordination for maximization of efficiency in personal waste expulsion is not appreciated. One should not offer advice, no matter how well-meaning, without it being clearly solicited first. One should also, in case of a problem in this field, not seek to consult a book or a person in the adjacent stall, but instead rely on one's own ingenuity and prior experience. Only when physical harm seems likely and immediate, or when an infinite loop has been reached, should one voice a call for help. After such help has been received, a mutual vow of silence about the matter is common; one formula is Q: 'Let's agree this didn't happen and never speak of this again.' A: 'Let's agree what never happened?'"

"Three. While toilet paper is not 'dirty' in its natural state, one should remember it is often considered so by association. Yes, this is a very annoying and illogical axiom. Toilet paper should not be used to wrap presents, to replace spousal pillow-cases, or to write letters on. Uses to which toilet paper may be put but which cannot be mentioned in polite conversation are its uses as underwear substitute, emergency sock or stocking, and coffee break or airport emergency dry snack. The last of these is called "the lunch roll". Toilet paper is not a polite subject of formal or informal conversation."

"This has been three important practical tips for… the toilet. In our next installment, the orgasm."

Very useful tips, those. The next promotional clip is from the Travel Society of Dr. Reinhardt Durchfall.

"Dr. Alois Reinhardt Heinrich Durchfall was one of East Germany's most brilliant mathematicians, but due to practical details outside his influence he did not travel much outside the borders of East Germany. Due to practical details within his influence, agoraphobia and fear of moving things mostly, he did not travel much within the borders of East Germany. Despite all this he had a great desire to travel, and to see places: departments of mathematics mostly, since other places are profoundly trivial to a practicing mathematician. Dr. Durchfall tragically passed away in 1988 in a pencil-related accident, and never traveled outside the Leonid-Brezhnev University of Honecker, Bezirk Karl-Marx-Stadt. His dream seemed as dead as he himself was."

"Now, however, thanks to a generous donation from his grandson, the hygienics magnate Martin 'Total' Durchfall of Durchfall Tuch und Badeanzug GmbH, the Travel Society of Dr. R. Durchfall is finally making that dream a reality. We are currently seeking mathematics departments all around the world that would be willing to house and possibly exhibit the embalmed remains of Dr. Durchfall in a suitably dignified and academic a manner, possibly in a lecture hall of small to medium size. If you are interested and also in a position to decide about these things, please contact us. The world must know mathematicians take care of their own."

A worthy cause, that, and I do not say that because Durchfall was my thesis advisor's thesis advisor, because he was not.

Our mathematical name segment for this week is Cauchy — as in Cauchy's integral theorem, and in the name of Cauchy, another famous French mathematician. Cauchy, pronounced K-O-SH-I, with "K" as in "sky", "O" as in "sole", "SH" as in "shoe", and "I" as in "see". On the scale of pronouncing difficulty "Cauchy" is rated 4.0, very difficult, slightly below the average difficulty of French names.

Let us repeat that for emphasis: K-O-SH-I.

K-O-SH-I.

And finally, in our series "Understanding the Size of Numbers", recommended for graduate students, we have a moment of silence which is exactly n minutes long, n determined by the equation \(n^2 - n(50+50i) + 2500i = 0\) , not the complex root.

The end. Our podcast will return next Thursday, it being a weekday 4 modulo 7, which is the weekday in which a new episode of the Real Mathematics podcast is released. With some complex numbers in it.

Imagine this as read in a Monty Python voice. I know I did. Oh, and$$\int_x^{x_0} \frac{2f'(t)^2}{\sqrt{n \log f(t) + 1}}\,dt$$

and that's nice compared to what a pure-audio expression of a half-page string of integral inequalities would be like. Might indeed explain why I haven't found a podcast with *real* mathematics in it. (Really, some library with too much free time should offer an "audio thesis copy" service for busy graduate students — you don't get paper copies of the thesis you want to see, but hours of a monotonous voice going "hence phi prime prime theta plus phi prime theta squared plus phi prime prime prime theta cubed plus two phi prime theta —")