Show your mathematics to the world!

A mathematician's blackboard can evoke feelings of wonder, beauty, awe, confusion and curiosity. Send me photos of your black (or white!) board, what's on it and why you think it's interesting.


Backdrop for Sir Michael Atiyah

(c) James GlossopToday the University of Edinburgh was privileged to welcome award-winning photographer James Glossop to the School of Mathematics. His task was to photograph Sir Michael Atiyah for an article in The Times (to appear next week) and he asked for a blackboard to be decorated with mathematical equations to form the backdrop to this photo. It was a joint effort between Andrew Ranicki, Julia Collins, Patrick Orson, and (of course) Sir Michael, and contains all their favourite formulae, numbers and ideas in mathematics. What would you have drawn on the board?

James kindly took this photo of the board after he was finished getting his shots of Sir Michael. I like the heavenly light shining in from above!

Niels Bohr Institute

Copenhagen Niels Bohr Institute blackboard

This is the blackboard in the common room at the Niels Bohr Institute in Copenhagen, taken by Andrew Jackson. It is advertising a colloquium given by Julia Collins about Peter Guthrie Tait, with a helpful diagram of a vortex cannon to show people what to expect in the talk.  Unrelatedly, there is a lot of matrix algebra on the left and what seems to be a half-rubbed-off torus on the right. Proof that even in a physics institute, much of the work is really mathematics! We have no idea what the cartoon at the top signifies.

Inverse blackboard

Inverse blackboard Christian Perfect and David Cushing spent the morning computing inverses using their special inverse blackboard.

Going left-to-right and top-to-bottom, we have:

  • The inverse of a 2×2 matrix;
  • The commutative diagram for the universal property of the inverse limit;
  • A variable which is inversely proportional to another;
  • The inverse of a complex number;
  • The derivative of the inverse of a function;
  • The inverse tangent of 1;
  • The axiom for group inverses;
  • Part of the definition of the logical inverse.

Thanks Christian and David for this wonderful idea!


Doors Open Day

Blackboard from ICMSOn Saturday 28 September 2013 many interesting buildings in Edinburgh opened their doors to the public for Doors Open Day. One of these was ICMS – the International Centre for Mathematical Sciences – on South College Street. ICMS are in a building that used to be a church and still has a beautiful stained glass window, but now the only worshipping which goes on is for mathematics! Visitors were invited to solve puzzles and play mathematical games, and to draw their favourite maths on this blackboard. What would you have drawn?

Deformation theory and 3-folds

blackboard in University of Edinburgh common roomThis photo is of the blackboard in the common room of the School of Mathematics at the University of Edinburgh. The workings on the left are by Michael Wemyss, drawn while he was talking about deformation theory (a generalization of differential calculus) with Will Donovan, as part of their work on the geometry of certain spaces, known as 3-folds. Will says, “Deformation theory lets us express the way in which a curve in a 3-fold can `move’ infinitesimally: we can then relate this to the (quantum) geometry of the 3-fold. I’ve tried to emulate Michael’s calligraphic F’s and G’s, but I haven’t had any success yet.” We don’t know who did the workings on the right.

Knot concordance and slice movies

Brendan Owens blackboardThis board belongs to University of Glasgow researcher Brendan Owens. The pictures on the right show a ‘slice movie’ which is used to prove that two knots are concordant to each other. The pictures are essentially 3D slices through a 4D disc; the ‘singularity’ where two parts of the knot appear to intersect is an illusion caused by the particular projection.  The long exact sequences on the left are the technical algebraic topology used to explore the crazy world of 4-dimensional knot theory, where geometrical intuition so frequently fails.

Cubic derivation

David Cushing blackboardThis photo is from PhD student David Cushing from Newcastle University. He was deriving the formula for solving a cubic equation, and says it looks messy because it was done ‘live’! The history of the solution to the cubic is a very interesting one, with all sorts of mathematical duels and underhanded dealings by 16th century mathematicians: Tartaglia, Cardano and Ferrari. You can read one account of it here: The solution to the cubic was actually what started the development of complex numbers!

Portable whiteboard

portable-noteboardThis photo sent in by Colin Beveridge is not your usual whiteboard! It’s a foldaway portable whiteboard called a Noteboard. Find out more details at Colin was using this to work on a puzzle from MathsJam: “A chopstick (a thin uniform rod) lies at rest in a smooth, hemispherical bowl. The chopstick is longer than the diameter of the bowl.  What fraction of the chopstick is inside the bowl?”.

Kernels and cokernels

Homological algebra blackboardThis board belongs to Newcastle University PhD student Tom Fisher, who is doing research in homological algebra. He was proving that the category of chain complexes over a ring is abelian; this bit is concerned with showing that it has kernels and cokernels.

[Thank you to Christian Perfect for sending in the photo!]

Shmooing with the biologists

ShmooI couldn’t resist taking this photo in the office of Edinburgh mathematician Nikola Popovic. The central image is the result of a conversation between Nikola and visiting speaker Vahid Shahrezaei about the reproduction of yeast. Yeast cells normally reproduce asexually by budding, but cells of opposite mating types (a and α) can also reproduce sexually. The bulge which forms when a cell responds to pheromones of the opposite type is called a shmoo – this is a reference to a cartoon character of that shape invented in 1948. It’s a brilliant word which has found its way into other areas of science too, including a type of reproducing material good in economics, a larva found in sea urchins, and high energy cosmic ray survey instrument.

Other parts of the board refer to Nikola’s work on gene regulatory networks, where he is trying to model processes which have both ‘fast’ and ‘slow’ components, and to see how these components interact with each other.


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