# Read Issue 06 now!

Our latest edition, Issue 06, is available now. Enjoy the articles online or scroll down to view the magazine as a PDF.

## Features

• ### In conversation with… Cédric Villani

We feel underdressed for Breakfast at Villani's
• ### Cardioids in coffee cups

Staring at your coffee, you wonder whether the light reflecting in cup really is a cardioid curve...
• ### Mathematics for the three-fingered mathematician

Robert J Low flips one upside down.
• ### The mathematics of Maryam Mirzakhani

We take a proper look at her mathematical accomplishments
• ### Biography of Sophie Bryant

A biography of Sophie Bryant
• ### Geographic profiling

Murder, maths, malaria and mammals
• ### Roots: Blaise Pascal

Blaise Pascal was driven to begin the mechanisation of mathematics by his father's struggles with an accounts book in 17th century France.
• ### On the cover: Euclidean Egg III

Euclidean Egg III makes the cover of issue 06!
• ### Pretty pictures in the complex plane

Contemplate the beauty of the Julia and Mandelbrot sets and an elegant mathematical explanation of them
• ### Pretend numbers

20 questions, the axiom of choice and colouring sequences.

## Fun

• ### Prize crossnumber, Issue 06

Win £100 of Maths Gear goodies by solving our famously fiendish crossnumber
• ### Dear Dirichlet, Issue 06

Prof. Dirichlet tackles archaeology and supercomputers in answering your personal problems
• ### Comic: The Inverse Homotopy, part 5

Part 5 of our mathematical comic's adventure
• ### Which mathematical software are you?

"R" you a Matlab or a Python? Fortran or Mathematica? Find out which package suits you best.
• ### Top Ten: Geometry instruments

The definitive chart of the best tools
• ### What’s hot and what’s not, Issue 06

Mathematical fashion advice for an ever-changing world
• ### Top ten vote issue 06

Vote for your favourite mathematical celebration day
• ### Page 3 model: Crowd control

Modelling a Saturday afternoon on Oxford Street
• ### How to make: a hyperbolic plane

A great way to waste a lot of paper

or

# In conversation with… Cédric Villani

Early on a February morning, we’re standing outside one of the many trendy cafes in Fitzrovia. Down the street we spot a man striding our way, wearing a full suit, a hat, a giant spider brooch and hastily tying a cravat. It could only be superstar mathematician Cédric Villani.

Cédric is passing through London on his way back from the US, but this is no holiday. In his two days here, he is attending a scientific conference, giving a public lecture, and taking part in a political meeting. His packed schedule leaves the increasingly-busy Fields medallist just enough time to join us for breakfast.

## Fields medal

One afternoon in early 2010, Cédric was in his office at the Henri Poincaré Institute in Paris, getting ready to pose for publicity photographs. The photographer, from a popular science magazine, was setting up his tripod when the office phone rang. Cedric leant over and picked it up. It was Lázló Lovász, president of the International Mathematical Union.

Fields medal ceremonies are held every four years, and six months before each ceremony, the winners are alerted by telephone about their success. During these six months, they are sworn to secrecy, but with the photographer in the room, Cédric suddenly realised that he might be in possession of the shortest-kept secret ever. By some miracle, the tripod had proved sufficiently interesting for the photographer, or perhaps he didn’t follow the English conversation, and the secret remained safe.

If you try too hard to win a Fields medal, you will fail.

Cédric had first realised that winning the Fields medal was a possibility at some point in 2004, when he was 31. Fields medals are only awarded to mathematicians under the age of 40, and until the phone call arrived, Cédric only placed his chances of winning at around 40%. “The prospect of winning the medal does put some pressure on you during your 30s. But everybody knows—it’s part of the common mythology—that if you try too hard to win it, you will fail.”

## Explore the sets yourself

I hope to have displayed the beauty behind these pictures by emphasising the extraordinary quantity of information contained in such a simple procedure, as well as through highlighting the complexity of each image, in the variety of fractals and colours visible, which further enhances the beauty.

If this article has sparked an interest in fractals, then why not try exploring these sets for yourself? You could do this by magnifying different sections of the Mandelbrot set to explore the countless shapes and patterns that exist within. You could also go deeper into exploring individual orbits.

All of these pictures are generated using simple quadratic formula. However, the Julia and Mandelbrot sets can be produced for a wide variety of functions in a similar manner to obtain countless pretty pictures.

These images are already becoming dated, having been taken for granted for so many years since they were first produced on the big bulky computers of the 1980s. The Julia set of the quadratic function, and the corresponding Mandelbrot set, could be inspiration for pretty pictures which are yet to be fully explored, or even discovered. Largely, the discoveries discussed here have been recorded in recent years. Furthermore, there could still be vast amounts of information within these sets that are yet to be discovered. Could you be the one to make a discovery?

## References

1. Franke, H. (1986). Refractions of Science into Art. In: H. Peitgen and P. Richter, ed., The Beauty of Fractals, 1st ed. Berlin: Springer-Verlag, pp.181-187.
2. Mandelbrot, B. (2004). Fractals and chaos. 1st ed. New York: Springer.
3. Peitgen, H., Jurgens, H. and Saupe, D. (1992). Fractals for the Classroom: Part 2: Complex Systems and Mandelbrot Set. 1st ed. New York: Springer-Verlag, pp.353-473.
4. Hall, N. (1992). The New Scientist guide to chaos. 1st ed. London: Professional Books.
5. Douady, A. (1986). Julia Sets and the Mandelbrot Set. In: H. Peitgen and P. Richter, ed., The Beauty of Fractals, 1st ed. Berlin: Springer-Verlag, pp.161-173.
6. Fraser, J. (2009). An Introduction to Julia Sets. 1st ed. [ebook] Available at: http://www.gvp.cz/~vinkle/mafynet/GeoGebra/matematika/fraktaly/linearni_system/julia.pdf [Accessed 4 Apr. 2017].
7. Peitgen, H., Jurgens, H. and Saupe, D. (1992). Fractals for the Classroom: Strategic Activities Volume two. 1st ed. New York: Springer-Verlag.
8. Devaney, R. (2006). Unveiling the Mandelbrot set | plus.maths.org. [online] Plus.maths.org. Available at: https://plus.maths.org/content/unveiling-mandelbrot-set [Accessed 4 Apr. 2017].
9. Moler, C. (2011). Experiments with MATLAB. 1st ed. [ebook] MathWorks, p.Chapter 13 Mandelbrot Set. Available at: https://uk.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf [Accessed 20 Apr. 2017].
10. Peitgen, H. and Richter, P. (1986). The Beauty of Fractals. 1st ed. Berlin: Springer-Verlag.
11. Mandelbrot, B. (1986). Fractals and the Rebirth of Iteration Theory. In: H. Petigen and P. Richter, ed., The Beauty of Fractals, 1st ed. Berlin: Spring-Verlag, pp.151-160.
12. Uk.mathworks.com. (2017). Illustrating Three Approaches to GPU Computing: The Mandelbrot Set – MATLAB & Simulink Example – MathWorks United Kingdom. [online] Available at: https://uk.mathworks.com/help/distcomp/examples/illustrating-three-approaches-to-gpu-computing-the-mandelbrot-set.html?searchHighlight=mandelbrot%20set&s_tid=doc_srchtitle [Accessed 20 Apr. 2017].

# Four things you didn’t notice in Issue 05

With just a couple of days to go until we launch issue 06, we thought it’d be fun to share a few bits and pieces that we hid around issue 05. If this gets you excited for issue 06, why not come to the launch party on Thursday?!

## Scorpions

Since we published the horoscope in issue 03, scorpions have been running around all over Chalkdust HQ. Seven of them managed to sneak into issue 05.
Continue reading

# The kind of problems black mathematicians wish didn’t need solving

John Derbyshire, columnist for the National Review, wrote an essay implying that blacks are intellectually inferior to whites: only one out of six blacks is smarter than the average white. Derbyshire pulled these figures from a region near his large intestine.

One of Derbyshire’s claims, however, is true: there are no black winners of the Fields medal, the ‘Nobel prize of mathematics’. According to Derbyshire, this is “civilisationally consequential”.

Derbyshire implies that the absence of a black winner means that blacks are incapable of genius. His ilk are only able to sustain such lies because 150 years of racial terrorism have ensured that few dare to challenge them, and, when we do, the consequences are dire. His ilk can get away with thinking that Euclid and Eratosthenes were not Africans working in Africa (even “sub-Saharan Africa”, if they want to make that idiotic distinction), but Greeks with blond hair and alabaster complexion (much like Jesus).

In reality, black mathematicians face career-retarding racism which white Fields medallists never encounter. It’s hard to focus on abstract algebra after Belgian King Leopold has hacked off your hands. Three stories will suffice to make this point. Continue reading