One of the most fascinating figures in the history of mathematics was Srinivasa Ramanujan, a self-taught Indian genius who formed a remarkable relationship with the Cambridge mathematician GH Hardy. Ramanujan was interested in problems in number theory, which are often easy to state, but incredibly difficult to prove. One amazing thing about Ramanujan's work is that it still finds applications today, in areas you'd never imagine are linked to number theory. An example is the study of black holes, those gravitational monstrosities that lie at the centres of galaxies.

We will explore this surprising link in an upcoming episode, but for now we revisit a 2018 interview with mathematician Ken Ono (pictured above), who was an advisor and associate producer on the well-known film about Ramanujan, The man who knew infinity. Talking to Plus Editor Rachel Thomas, Ken explores just what made Ramanujan's work so special and the piece of mathematics that is relevant to black holes. Rachel talked to Ken at the Royal Society's celebration of the centenary of Ramanujan's election as a Fellow of the Royal Society.

You can also read an article accompanying this podcast, which looks at the mathematics relevant to black holes. For more about Ramanujan's mathematics, and Ken's research into it, see Ramanujan surprises again. To find out more about the Spirit of Ramanujan project, which Ken mentions in this episode, see here.

In this episode of Maths on the move we look at some favourite pieces of maths we have worked on so far this year. From a revolutionary new tile to new insights in topology, and from fooling cancer cells to bringing mathematical research into the classroom, we hope there's something interesting there for everyone.

To find out more about the topics mentioned in this episode see the following articles:

• A tip of the hat: Celebrating an aperiodic monotile — meeting the discoverers of the hat
• Contagious maths — bringing epidemiological research into the classroom
• The mathematics of movement — what do cancer cells, birds, and whales have in common (and can a slime mould be intelligent)?
• Outraged by not knowing— new insights in topology with Oscar Randal-Williams

To find out more about our work with the JUNIPER network of disease modellers see here and to find out more about our work with the maths4DL research project see here.

It's always exciting to have a glimpse at new mathematics and technology as they take shape. In this podcast we talk to Georg Maierhofer, from the University of Oxford, about an exciting new idea that is only just emerging – physics informed neural networks (PINNs for short) – where you add in the laws of physics to machine learning methods.

We have been able to sit in on a number of meetings of our colleagues from Maths4DL (the Mathematics for Deep Learning research group) as they explore this idea. Georg explains why PINNs are a bit like learning golf, tells us about the exciting opportunities and challenges, and why the key part to developing new ideas is getting the right people together at the right time.

You can find more about the machine learning and the some of the work that Maths4DL is doing at https://plus.maths.org/maths4dl, including our recent podcast How does AI work? and our collection Predicting the weather with artificial intelligence.

This content is part of our collaboration with the Mathematics for Deep Learning (Maths4DL) research programme, which brings together researchers from the universities of Bath and Cambridge, and University College London. Maths4DL aims to combine theory, modelling, data and computation to unlock the next generation of deep learning. You can see more content produced with Maths4DL here.