Asaf Karagila
I don't have much choice...

## What can you learn about writing papers from cooking pasta?

Those who know me in real life will know that I enjoy cooking. I particularly enjoy cooking pasta. Most authentic Italian recipes are so simple (algio e olio anyone?) that it's just wonderful.

I was cooking dinner today, bucatini alla matriciana if you must know, and I realised that cooking pasta and writing papers have nothing in common. Exactly one of those things is enjoyable, and it is not the writing part of papers (I do love the research part, of course).

## On "trivial" statements

Last night someone asked a question on Math.SE regarding a lemma used in proving certain chain conditions hold when iterating forcing with finite support. The exact details are not important. The point is that the authors, almost everywhere, regarded this as a trivial case.

Indeed, in my answer I also viewed this as trivial. It was tantamount to the claim: If $$\cf(\alpha)\neq\cf(\kappa)$$, then every subset of $$\alpha$$ of size $$\kappa$$, contains a subset of size $$\kappa$$ which is bounded.

Oh, have I been waiting to tell you something... Yes, I am a Future Leaders Fellow. But as my three regular readers know, this blog is not about announcements, it's about my experience.

In early January 2019, I was told that I can try and apply for a new scheme in the United Kingdom called "Future Leaders Fellowship". At the time not a lot was known about it, the first round winners were due to be announced, so it was unclear what are the success rates, or the "desired candidates" might be.

I've decided to design a small "choose your own adventure". For fatalists. You can also play the interactive version here!.

This was originally "in-blog", but I decided that the interactive version is a bit more interesting. Enjoy it while it lasts!

## Countable sets of reals

One of the classic results of Sierpinski is that if there are as many countable sets of reals as there are reals, then there is a set which is not Lebesgue measurable. (You can find a wonderful discussion on MathOverflow.)

This is fact is used in the paradoxical decomposition theorems (which I often enjoy bringing up as a counter-argument to bad arguments that the Banach–Tarski paradox implies we need to accept that all sets are measurable as an axiom):