What is infinity? What is infinity plus 100? What is infinity plus infinity?
Today's podcast was inspired by questions sent in by our friend Ash. To answer Ash's questions we take a trip to our favourite hotel, and we revisit our 2012 interview with our late boss, John D. Barrow, when we asked him – does infinity exist? Listen to the podcast to find out how infinity can corrupt the youth, why subtracting infinities can give you the right answer, and the weirdness that might be lurking out there in the cosmos...

Image created by FAVIO.
You can read more about infinity on plus.maths.org. And if you have a question about life, the universe and everything you'd like us to answer – email us as plus@maths.cam.ac.uk or contact us on twitter.

Does infinity exist?

Maths on the Move, the podcast from plus.maths.org, will bring you the latest news from the world of maths, plus interviews and discussions with leading mathematicians and scientists about the maths that is changing our lives. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.

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Artificial intelligence is changing our lives. Many of us use the voice activated features on our phones to recognise, understand and fairly complex speech. Students use ChatGPT to do their homework. And doctors use AI algorithms to help diagnose many diseases from medical data. But how is AI changing the lives of mathematicians?
In this podcast we speak to Yang-Hui He from the London Institute of Mathematical Sciences about his recent work on the evocatively titled murmuration conjecture. This exciting new conjecture came about due to both artificial and human intelligence, and reveals patterns in the prime numbers that look like flocks of birds.
 
A murmuration of starlings. Photo: Walter Baxter, CC BY-SA 2.0.

 
We were speaking to Yang as part of our coverage of the research programme, Black holes: bridges between number theory and holographic quantum information, held at the Isaac Newton Institute for Mathematical Sciences  in Cambridge.  The programme  brought together a fascinating array of experts in black holes and quantum theory, with mathematicians and computer scientists. You can read more in our coverage of the programme here.
This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from our collaboration here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

The murmuration conjecture: finding new maths with AI

"The 20th century was the interaction of geometry and physics, and the 21st century is the interaction of number theory with physics." This intriguing insight comes from our recent discussion with Yang-Hui He from the London Institute of Mathematical Sciences.  Yang told us an amazing story about the flow of ideas between mathematics and physics, that involves some of the most celebrated achievements in the last century.
Yang-Hui He (Photo Rajarshi Maiti – CC BY-SA 4.0)

You can find out more about the ideas we discussed with Yang in this podcast in the accompanying articles String theory: A promise from physics and String theory: Convincing mathematics. And stay tuned for the second part of our conversation with Yang in the next episode!
We were speaking to Yang about a research programme, Black holes: bridges between number theory and holographic quantum information, held at the Isaac Newton Institute for Mathematical Sciences  in Cambridge.  The programme  brought together a fascinating array of experts in black holes and quantum theory, with mathematicians and computer scientists. You can read more in our coverage of the programme here.
This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from our collaboration here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

Tying together black holes, quantum gravity and number theory

Mathematics is a creative pursuit so it's not surprising that there are communalities between maths and art in all its forms. In this episode we explore the intersection between maths and art with physicist Andrzej Herczyński and mathematician Paul Glendinning.
Andrzej Herczyński

Andrzej and Paul were two of the organisers of the workshop Space, scale and scaling in art, which recently took place at the Isaac Newton Institute for Mathematical Sciences in Cambridge. We find out about the rich dialogue that can ensue between artists and mathematicians, how maths and physics can help us understand the power of art and how we perceive it, and provide insights into how a particular piece of art was made.
The Space, scale and scaling in art workshop was part of a larger research programme funded by the National Science Foundation on the intersection of science and art.
You can see Agnes Martin's painting Morning, which is mentioned in this episode, here (though the digital version does not do it justice). To see Jackson Pollock's works, which are also discussed in this episode, go to the Jackson Pollock website. The image above has been generated by AI.
Paul Glendinning

To find out more about some of the topics mentioned in this episode, see the following articles:
Fractal expressionism looks at fractal structures in works by the abstract expressionist Jackson Pollock.
The Artist's fractal fingerprint explores Pollock's paintings further.
Sine language looks at a song by our musician friend Oli Freke which explores the idea of sine waves, and how they relate to other concepts such as the Western tuning system known as equal temperament and even to ancient Greek cosmological ideas.
Fractal music has composer Dmitry Kormann explaining how he brings fractal-like patterns to the very structure of his music, with beautiful results.
Restoring profanity explores how the heat equation can help restore damaged art works.
Where to stand to look at sculptures uses some simple geometry to find the perfect vantage point from which to take in a sculpture (or painting).
To see all our content on maths and art see here, and for everything on maths and music see here.
This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from our collaboration here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

The art of maths and the maths of art

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.

Ramanujan: Dream of the possible

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.

You can listen to the podcast using the player above, and you can listen and subscribe to our podcast through Apple Podcasts, Spotify and through most other podcast providers via podbean.

Does infinity exist?

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