Michael Eisermann

Tell me, why are you
Reading this haiku I wrote?
It's a waste of time.

Odds and Ends

All right, so let's suppose you have time to waste.
(After all you have made your way to this page. :-)
In this case you might also find the following links amusing.

Internet, the final frontier – odysseys and oddities

[Mathematical Quotation Server]

The Mathematical Quotation Server is certainly a wonderful waste of time. If you are curious, try a random quotation. Here are two of my favorites:

In mathematics you don't understand things. You just get used to them. (John von Neumann, 1903-1957)

This paper contains much that is new and much that is true. Unfortunately, that which is true is not new and that which is new is not true. (Anonymous Referee's report)

Your browser does not display embedded objects. You can click here to load a random quotation. Random quotation, hm... Less whitty but equally amusing are automatically generated computer science papers. Could you do this with mathematical articles? I doubt it!
[Maths Genealogy Project]

If you are curious about your mathematical ancestors or you want to know about mine, check out the Maths Genealogy Project.

[Petit Nicolas]
[Google inside]

Google is a huge succes in web searching, but how does it work? Unfortunately the information on google's own website on google technology remains little instructive.

[L.Page and S.Brin]

Since I like the subjet, I could not resist to write up a detailed introduction for students: Comment fonctionne Google? For the original article by google's founders L.Page and S.Brin you can have a look at their technical paper: The Anatomy of a Large-Scale Hypertextual Web Search Engine.


Speaking about Google, perhaps we should pause a minute and think about internet privacy.

[Euro-Bill Tracker]

Did you ever wonder how the new Euro coins, introduced in January 2002, mix and spread across Euroland? Well, then the EuroMix Project is worth a visit...

If you find counting coins a strange hobby, then check the Euro-Bill Tracker to peek into an even fancier project, spiced up by the possibility to identify and track individual Euro bills. The original is, of course, the dollar bill tracker Where's George?

From urban legends to global nonsense


If you are interested in urban legends, then Urban Legends or Snopes.com are the sites for you! They offer large collections and lots of links (but don't start reading unless you really have time to waste. – You have been warned.) You might also wish to support one of the most urgent environmental challenges of the 21st century: ban dihydrogen monoxide!


Most us have been taught the water whirl legend: water draining from a bathtub (or sink) rotates one way in the northern hemisphere and the opposite way in the southern hemisphere. "Of course," some nod, "the phenomenon is due to Coriolis force." – "Nonsense," others reply, "Coriolis force is far to weak, other (random) influences are more important at this scale."

So who's right? After all, why should we believe either one when it's so easy to check? Did you ever verify the water whirl legend? Did you check which way water whirls where you live?

[Die Zeit]

The water whirl legend and many other urban legends are also discussed on the webpage Stimmt's? provided by German newspaper Die Zeit. If you read German, it's worth a visit.

If you still have time to waste, then you can indulge in the bible code controversy opposing Doron Witztum's bible code pages and Brendan McKay's scientific refutation.

Since 1994 this debate is hogging resources but, after the dust has settled, it has not been in vain. It nicely illustrates what (mathematics) students should know about pseudoscience.

Topologists' delight

[Andrew Lipson's Lego Thinker]

Andrew Lipson's Homepage displays some spectacular Lego sculptures, like Escher's Relativity or Belvedere. By the way, Andrew holds a PhD in knot theory, so the trefoil knot or the figure eight knot or the Klein bottle are not to be missed.

[Klein Bottle]

If you prefer smooth manifolds, you might consider buying a Klein bottle handcrafted in glass. The site www.kleinbottle.com also features such beautiful gifts as Klein Bottle Hat and matching Mobius Scarf. This proves beyond any doubt that topology has important applications in our everyday lives.

For more recreational geometry take a stroll through the Geometry Junkyard.


This endless movie shows a juggling topologist during his – not so endless – summer holiday. Very relaxing, isn't it?

After a while you will get bored, though, so you may want to animate your own juggling tricks using siteswap notation, see for example JsJuggle or JuggleKrazy. Still fancier, you can juggle braids and even juggle all links, at least theoretically. We thus come full circle back to mathematics again.

[Bremer Knoten]

The way to a topologist's heart is through his stomach.

(Ein Beitrag Bremens zum Jahr der Mathematik: Bremer Knoten!)

Some videos on geometric topology

Blow your mind by turning an immersed 2-sphere inside-out:
watch the Geometry Center's celebrated video on sphere eversion.

Here is a slick 22 seconds movement
but without any explanations:

For comparison:
Eversion is much simpler for the 2-torus!

Numerology and humourology – from profound to profane

Beware, you are about to reach the bottom of the page. Before you leave, why not take some philosophical thoughts with you on your onward journey... For example, a short interview with Sir Michael Atiyah on beauty in mathematics.


Euler's identiy e + 1 = 0 is arguably one of the most beautiful theorems in mathematics. It links the five fundamental mathematical constants 0, 1, i, π, e using the three basic operations of addition, multiplication, and exponentiation.

This statement implicitly also features the first three prime numbers 2, 3, 5: among the five constants, three are rational or algebraic, whereas two are transcendental. Notice that 2 is a very odd prime. It is currently the smallest known prime.

[taxi 1729]

Of course, some numbers are more interesting than others, as illustrated by Hardy's famous anecdote:
I remember once going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. "No", he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two [positive] cubes in two different ways."


Compared to that, despite being the answer to life, the universe, and everything, 42 seems rather uninteresting.
The first impression, however, is misleading:

Theorem. Each natural number is interesting.

[Laurel and Hardy]

By way of contrast, there must be uncountably many uninteresting real numbers, but no one has ever seen one: whenever you focus on one, it ends up being interesting.

This is open to debate, though: teaching experience suggests that non-sensical exercises and calculator experiments make students believe that all numbers are equally uninteresting and essentially random.

[Math Monster]

Are mathematicians really evil monsters who want to inflict quadratic equations on a younger generation as a means of corrupting their immortal souls? Maybe so, but it's not the quadratic equation's fault!

[Mathematical Kangaroo]

Let's end with something much more positive: Since 1991 the Mathematical Kangaroo is popularizing mathematics among school children of all ages. It has become an international competition with more than 30 participating countries, see the original French site Le Kangourou des Mathématiques or Känguru der Mathematik in Germany or Math Kangaroo in the US. Each year, the Kangaroo is a maths festival in the best sportive tradition of popular marathons. Try it, it's fun!

© Michael Eisermann last modified on Wednesday 27/02/2013 www.igt.uni-stuttgart.de/eiserm
Disclaimer: The information on this website is provided by the author and has not been reviewed or approved by the University of Stuttgart. It is distributed in the hope that it will be useful, but it is provided without any warranty whatsoever, without even the implied warranty of fitness for any particular purpose. The author is not responsible for the content of external webpages. So, as always, be critical of what you see and read on the internet. Well, I assume that I am preaching to the converted: Who on earth reads disclaimers and footnotes in the first place?