Tau day, celebrated on June 28th, is almost upon us again. Last year I had great fun making a video about tau and appeared in national newspapers and on radio and TV. Though I had helped kick off a story that went viral igniting millions of pixels across the globe, even I felt that it received more coverage than it merited. Don’t get me wrong, it was great fun. Anyone who watched my video could tell from the sound effects, the newspaper headline about Pi is 5.14 and the code hidden in the digits of pi that for me this was not obsessional rage coming out but was instead a reasonably light-hearted look at an irrational bit of maths. Unfortunately, I received a lot of flak and a fair amount of abuse such as being called “peace of sh*t”[sic], “burro” (it’s a Portuguese insult, shame on you BBC Brasil!) and even, rather strangely, bald-headed. (You can hear the inside story in a Math/Maths Podcast.) However, it is not insults that cause me to pass on two rounds of pie this year. Insults are not a problem, I’m a grown up and know that sticking my head above the parapet will give at least someone the opportunity to take a shot. Instead I have two main reasons. 1. The issue is controversial and although controversy and debate are vital for any subject it should be about the significant issues. Tau is important but not major league important. I don’t want disagreements between mathematicians to obscure our central message that maths is vital to society (see here for example). One of our responsibilities is the health of our subject and a basic tenet, like a doctor’s, should be “Do no harm”. In this case I think...

## The origin of x in maths...

posted by Kevin Houston

I’m still wrestling with the fallout from marking exams. Despite this, I found time to watch a short TED video posted recently that features Terry Moore explaining why x is used as an unknown in mathematics. Watch the video – only 4 minutes – or jump to the spoilers below if you want to know more. The main idea is that the we use x because the Spanish used (chi) as the first sound of the Arabic word for “something” because they couldn’t say the correct “sh” sound. I recollect a similar argument made somewhere else with slightly different details, though, sadly, I cannot remember them precisely, nor their location. I was unable to track down references at the time to verify this argument and so dismissed it as a Just So Story. Since it has resurfaced it would be interesting to see evidence. Does anyone know of any? My reason for asking is that I’ve spent the last few years learning about Greek mathematics and I am interested in how it has been transmitted to us via the Arabic scholars and scientists. So far I’ve only read the popular accounts, Science and Islam: A History by Ehsan Masood and Pathfinders: The Golden Age of Arabic Science by Jim Al-Khalili. The latter is good but spends the first few chapters explaining the history of Islam and various empires. Furthermore, one of the first bits, maybe the first bit, of science to be explained in depth is Eratosthenes’ measurement of the Earth, i.e., a high point of Hellenistic science. Obviously providing a context is important in a book but I still feel as though I don’t know much about the science from the Arabic world between the end of the Greek era and the beginning...

## Cool proofs again

posted by Kevin Houston

In between marking exams, marking essays, external examining, getting my two PhD students to submit their theses, and, well you get the idea, I’ve been trying to come up with a cool proof of a theorem in complex analysis: Let be a power series with radius of convergence . Then, . I.e., the derivative of is what you expect it to be, the termwise differentiation of the series. I’ve not been able to find a good proof of this. My plan of attack has been to show first via the root test that the formal derivative has radius of convergence . The main sticking point is then to show that this formal derivative really is equal to . The clearest proof I found was in James Pierpoint‘s book Functions of a Complex Variable which you can find online here. Like many old books (this is from 1914) I’ve found that, if you allow for slightly odd notation and nomenclature, it contains excellent material that is currently passed over. (Does anyone still teach Raabe’s test?) Anyhow, the proof is on pages 172-173 and relies on pages 84-85. For me the proof is very clear because of equation 3 on page 84: the expansion of via rows can be turned into a power series in by summing the columns. My problem is that when I try to turn everything into a rigorous proof this becomes obscure. Also, we have to prove that all the formal derivatives of have radius of convergence . This in itself is not difficult but it means we have to set up the notion of all formal derivatives rather than just the first one. For me this may be too much extraneous clutter for students. The hunt...