# Michael Atiyah’s Birthday!

Heads up!  In  a couple of days (April 22nd) it is the 87th birthday of “Britain’s mathematical pope”, (not just Britain’s, either, IMO), otherwise known as my doctoral advisor, Professor Sir Michael Atiyah.   HAPPY BIRTHDAY MICHAEL!

To celebrate, his son David is assembling an online tribute – see http://www.atiyah.eu/mfa87/    Please consider sending a tribute message to david@atiyah.eu  Here’s what hes ays:

We are collecting messages of congratulations on the occasion of Michael Atiyah‘s 87th birthday Friday, April 22, 2016.

If you have the time, memory, and an inclination, please also include your favourite personal story about Britain’s Mathematical Pope*. I keep hearing every mathematician has one – it would be a shame not to collect and archive them for posterity.

Bonus points awarded for photographs, with prizes for the best MP4 video message we can share on the night.

Pls include:
– your current position, & location (if appropriate)
– when and where you first met Michael

We will keep it simple and hope to collate and publish submisssions in due course.

* = with thanks to Siobhan Roberts for the expression used in her recent biog of J H Conway – i have simply extended his Popedom from England to Britain.

If you haven’t seen it, here is a great article from Wired last week: Mathematical Matchmaker Atiyah Dreams of a Quantum Union.

# Jost Bürgi’s Method for Calculating Sines

Jost Bürgi (28.2.1552 -31.1.1632)
Astronom, Mathematiker, Instrumentenbauer, Entdecker der Logarithmen.
aus:7523 (Rar);Frontispiz

I just learned (via Facebook, no less) of a fascinating paper with the above title by Andreas Thom and coauthors.

Jost Burgi (1552-1632) was a Swiss mathematician, astronomer and clockmaker.  He worked with Johannes Kepler from 1604 and is thought to have arrived at the notion of logarithms independent of Napier.  He was also reputed to have constructed a table of sines by a brand new method, but until now the details of his Kunstweg (“artful method”) for computing sines were thought to have been lost.  The beautiful book of van Brummelen, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry,  (Princeton University Press, 2009) documents how computing trigonometric ratios was  a central theoretical and practical preoccupation of ancient mathematics. We know of Burgi’s Kunstweg via a statement of his colleague and friend Nicolaus Ursus: “the calculation (of a table of sines)… can be done by a special way, by dividing a right angle into as many parts as one wants; and this is arithmetically. This has been found by Justus Burgi from Switzerland, the skilful technician of His Serene Highness, the Prince of Hesse.”  But the details are not clear and apparently nobody, starting with Kepler himself, was ever able to reconstruct Burgi’s method.

# Artin’s Criterion

Emil Artin, picture from Wikipedia

There’s been a long lull in updates to this page.  I’ve posted elsewhere about the reason for that: in brief, I was found to have cancer, and subsequent treatments have kept me busy for months.  You can read about this on my personal website, but I’m not going to write more about it here.

Meanwhile though I have been slowly writing up a book-length version of my MASS 2013 course, “Winding Around”, whose central theme is “The Winding Number in Topology, Geometry and Analysis”.  As I was “winding around” myself and trying to complete Chapter 5 in a way that was satisfactory, I ran into an interesting “gap” in my own understanding.  This is related to the homology version of Cauchy’s theorem.  This is usually stated in the following way.

Theorem  Let $$f$$ be a function that is holomorphic on an open subset $$\Omega\subseteq\mathbb C$$, and let $$\Gamma$$ be a cycle in $$\Omega$$ that is nullhomologous, this being defined to mean that the winding number of $$\Gamma$$ about each point of $${\mathbb C}\setminus\Omega$$ is zero.   Then

$\int_\Gamma f(z)dz = 0.$