We recently found out why pieces of toast tend to land butter side down. It' because the physical factors at play, including the typical height of breakfast tables and the strength of the Earth's gravity, are just right to allow a piece of toast to perform one flip on its way to the floor: from butter side up to butter side down.

The strength of the Earth's gravity is measured by the gravitational constant g, one of the constants of nature. These constants are special not just when it comes to toast. If their values were just a tiny bit different, life as we know it couldn't exist. This begs the question of why — why are the constants fine-tuned for our existence? Some people have taken this fine-tuning as evidence of the existence of a god who wanted us to be here, but there's also another explanation: perhaps our Universe is just one of many, all with different values for the constants of nature? If such a multiverse exists, then the existence of our Universe within it is no longer surprising. It's just one of many.

All this reminded us of an interview we did in 2016 with astrophysicist Fred Adams at the FQXi international conference in Banff, Canada. In this episode of Maths on the move we bring you this interview. Adam tells us all about the multiverse and how knowledge about our own Universe can help us to calculate how many of those other universes could be similar to our own. We hope you enjoy it, but if it's too mind-boggling, have a piece of toast.

Fred Adams

A Gömböc is a strange thing. It looks like an egg with sharp edges, and when you put it down it starts wriggling and rolling around as if it were alive. Until not so long ago no-one knew whether Gömböcs even existed. Gabor Domokos, one of their discoverers, reckons that in some sense they barely exists at all. So what are Gömböcs and what makes them special?

In this episode of Maths on the move we revisit an interview with Domokos from all the way back in 2009.

We were reminded of this interview when we thought about what makes a good mathematical story and the story of the Gömböc has it all: beautiful mathematics, an exciting discovery, a beach holiday, romance (sort of) and even turtles. We hope you enjoy it!

You can read the article that accompanies this this episode here.

Gábor Domokos

Over the summer we've been incredibly lucky to have been working with Justin Chen, a maths student at the University of Cambridge who is about to start his Masters. Justin has done some great work on how to explain the concept of a mathematical group, and group theory as a whole, to non-mathematicians. In this episode of Maths on the move he tells us how groups are collection of actions, akin to walking around on a field, and why group theory is often called the study of symmetry. He also marvels at the power of abstraction mathematics affords us, tells us about what it was like diving into the world of maths communication, and what his plans are for the future.

You can find out more about groups in the following two collections Justin has produced:

• Groups: The basics
• Groups: A whistle-stop tour

You might also want to read Justin's article Explaining AI with the help of philosophy mentioned at the beginning of the podcast. It is based on an interview with Hana Chockler, a professor at King's College London, conducted at a recent event organised by the Newton Gateway to Mathematics and the Alan Turing Institute.

This article was produced as part of our collaborations with the Isaac Newton Institute for Mathematical Sciences (INI) and the Newton Gateway to Mathematics.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. The Newton Gateway is the impact initiative of the INI, which engages with users of mathematics. You can find all the content from the collaboration here.