How Hard is Your Maths?

In Brainiac: Science Abuse, there is a wonderful category called How Hard is Your Thing? (see [1]). Thaila Zucchi makes seemingly hard things undergo some of the ultimate stress tests: Can they stand the heat of thermite? The abrasion of an angle grinder? The impact of a ton of bricks?

There were several occasions in the history of mathematics when mathematicians had to answer to the question: how hard is your maths?

The Ivory Tower

To me, mathematics is an ivory tower.
An ivory tower, vast, complex, and beautiful.
With its doors wide open.
At each level, helping hands are offered,
However, the steps are steep
And there is no elevator.
No-one can carry you up.
You need to take the steps by yourself.
If you climb just a little
The view will be spectacular.

What’s on Your Napkin?

Either nature or my brain or both do a wonderful job of clustering related things for me so that I often feel coming along many related things within a short time. Recently, I read Stuart L. Pimm‘s wonderful The World According to Pimm: a Scientist Audits the Earth. It contains the following sentence:

« Robert Colwell, an ecologist from the University of Connecticut, and I were sitting in a bar drinking Antarctica and excitedly drawing lines on paper napkins, the preferred medium of serious scientific discourse worldwide. »

Shortly afterwards, I learned about the blog What’s on my blackboard? showing people’s blackboards (or whiteboards) which are often stunning.

Hence my question: what’s on your napkin? I dare you: grab your smartphones and share images of your napkins full of scientific sketches and/or formulas!

Believers in the Axiom of Choice

There was a time back at the university, when pretty much any question about mathematics I came up with led to the axiom of choice. This seemingly innocuous and at first sight quite reasonable axiom leads to pretty strange conclusions such as the Banach–Tarski paradox. Roughly speaking, it requires that for any collection of non-empty sets it should be possible to construct an element of the Cartesian product.

Here are two of the questions I had at the time: