And just as children give parents the hope to continue their genetic inheritance, mathematical creations provide the architect with a chance of a little bit of immortality.

But the naming of mathematical objects is fraught with difficulties. Unlike in astronomy, there is no central registry where you can record your choice of name. It is only by a process of communal acceptance and use that a name takes off. You can’t simply put your own name on a new group of symmetries. For that to come about, you must wait for others to start referring to it, as happened with the discovered by Princeton University mathematician John Conway, who famously invented the and the Thompson Group named after John Thompson at the University of Florida in Gainesville and joint winner of this year’s .

I’m now offering one lucky żěè¶ĚĘÓƵ reader the chance to name a group of symmetries that I have created.

As I explain in my feature, symmetry is an important concept across the sciences. From viruses to fundamental particles, equations to crystal structures, understanding the underlying symmetrical object is often the key to unlocking some of science’s deepest secrets.

The symmetries of the group I have created are intimately connected to another important area of mathematics: elliptic curves. The elliptic curve behind the group of symmetries I am giving up for adoption is defined by the equation:

y² + xy + y = x³ – x² – 2x

These equations are some of the most fascinating in mathematics and were key to the resolution of Fermat’s Last Theorem. It is one of the holy grails of mathematics to understand what choices of whole numbers x and y will solve equations like this one.

To enter the competition, all you need to do is answer a simple question and leave your name and email address. Click here to fill in the form.

Perhaps you think mathematicians should be a little more imaginative when christening their offspring, as they were when the named the Monster. Let us know what you’d call the unnamed symmetry group and your reasoning behind the name, or leave your thoughts on other peoples’ suggestions.

I Read A Mathematician’s Apology by G. H. Hardy when I was about 13 or 14 because my teacher recommended it. For the first time I realised how exciting being a mathematician could be. Before that I had thought mathematics was a science, and as a kid I enjoyed artistic things rather than science. By comparing it to music, poetry, painting, he made me see that mathematics wasn’t about doing multiplication or long division but about searching for patterns. I saw that, more than with any other science, I could make mathematics part of the artistic and creative side of my life.

I go back to the book all the time. In later life, it has become a book I love and hate. The opening sentences are especially poignant: “It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something to prove new theorems.” Hardy was nearing the end of his career when he wrote this, so he expresses his frustration about having to write a book about being a mathematician rather than doing mathematics. As a practising mathematician and someone who also likes to excite people about mathematics, I’m trying to prove Hardy wrong – that you can do both.

In the book, Hardy does actually do some mathematics, proving two theorems. One is about why there are infinitely many prime numbers, the other about why the square root of 2 cannot be written as a fraction. Both are useful and simple, with surprising results. When I first read those proofs, it made me want to find my own proofs.

There’s another nice side to it: a foreword written by C. P. Snow. This is important, because it is about Hardy’s life and the romantic tale of how Hardy discovered Indian mathematician Srinivasa Ramanujan. That story helps to bring mathematicians alive as people.

Hardy was also adamant that he only did mathematics for the beauty and the love of it, and the fact that he was getting at eternal truths. I like that non-utilitarian philosophy. Hardy says mathematics is wonderful because it will never be applied, for example, in warfare. Sadly, a few years later, mathematics was at the heart of proving that the atomic bomb would work. And prime numbers, which Hardy loved and said would never be useful, are at the heart of the encryption that makes internet transactions secure.

As told to Eleanor Harris