By Marcus du Sautoy Platonic solids. Galois groups. The Monster. Just as with children, the naming of a mathematical object is part of giving birth to your creation. It is what gives it its own identity, distinguishing it from all the other mathematical objects out there. 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 Conway group discovered by Princeton University mathematician John Conway, who famously invented the Game of Life and the Thompson Group named after John Thompson at the University of Florida in Gainesville and joint winner of this year’s Abel prize. I’m now offering one lucky New Scientist 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,