It sounds like an impossible puzzle. How do you program a classical concert with a saxophonist, a mathematical physicist and 12 of Australia’s emerging string players that explores the relationship between music and equations AND appeals to everyone, from schoolchildren to curious concertgoers?
For leading UK saxophonist Jonathan Radford, it was a case of “challenge accepted” when his friend and collaborator, composer Cheryl Frances Hoad, first floated the idea in Oxford, England.
Cheryl was writing a new saxophone concerto for Jonathan based on mathematical theories and equations, inspired by conversations with her friend Professor Yang-Hui He. “Cheryl studied these complicated mathematical theories and equations in depth. Hearing her talk about them inspired me,” says Jonathan, who previously worked with Cheryl on a piece for saxophone and piano called Algernon. “That’s how the project began – through friendship, conversation, and interdisciplinary collaboration.”
From there the idea grew into a world-first global project with Jonathan, Professor He and the musicians of AYO Momentum Ensemble bringing the Beautiful Equations concert to Australian audiences in QPAC in Brisbane as part of the World Science Festival Brisbane and Sydney Conservatorium of Music.
“It’s not just for people with a PhD in mathematics. It’s for everyone. This will be a concert that is accessible to all ages and levels of understanding, whether you’re a scientist, musician, mathematician, or music lover.”
Jonathan Radford
An Australian premiere
At the heart of the concert is the saxophone concerto Three Mathematical Diversions, which will receive its Australian premiere in Queensland.
The first movement is based on the Einstein tile, a newly discovered shape that can be tiled infinitely without repeating. “In the piece, Cheryl created a series of chords and notes that never repeat. She took that idea and applied it musically. The discoverer of the Einstein tile was a mathematician called Roger Penrose. The saxophone part represents Penrose on a quest to discover the tile – moving in and out, searching. It’s fascinating.”
See Jonathan Radford with AYO
The second movement, Elliptic Murmurations draws on modern mathematics – elliptic curves and prime numbers used in cryptography and security. “These numbers and ideas move like flocking birds – murmurations going up and down, in and out. In Cheryl’s score, you can see these shapes in the music as it moves through the strings and saxophone lines. It’s a highlight of the concerto.”
The last movement is The Search for the Theory of Everything which links with Professor Yang’s research on the search for a unifying theory that explains the universe. “It explores the beauty of mathematics, which is at the heart of the program. Yang advocates for the beauty of maths, showing that equations can have the same beauty as a musical melody. Also on the program are works by Stravinsky, Elena Katz-Chernin, Philip Glass and Alex Baronovski.
“Each piece was chosen carefully to extract mathematical ideas and portray them through music. We started with the idea of Cheryl’s new concerto, which already contains so many mathematical ideas. It’s a gift to have a concerto linked with maths. We can demonstrate and discuss how the compositional process links with mathematical ideas.”
For the other pieces, Jonathan wanted a varied program that drew on various mathematical concepts, while appealing to different audiences.
“For example, Alex Baranovski’s Musical Universalis draws on ancient ideas attributed to Pythagoras – musical harmony emerging from simple numerical ratios that reflect balance in the natural world. It offers an entry point into the program,” explains Jonathan. “Elena Katz-Chernin’s Reinventions after Bach shows how simple ideas can be developed, adapted, and transformed in her playful style. We’re also performing a great piece from Philip Glass’s A Brief History of Time. Like much of his music, it’s built from repetition and gradual change – cells repeating with small additions that shift our perception of time. It reflects mathematical ideas and connects with Stephen Hawking’s work.”
‘Accessible to all’
Throughout the concert, Professor Yang – whom Jonathan describes as “one of the most amazing mathematicians in the world” will give short lectures explaining the mathematical relationships.
“The great thing about Professor Yang is how he presents his ideas. He explains theories in a way that’s accessible for everyone, no matter how much they understand. If someone feels unsure about attending because they think it might be complicated – it won’t be. It’s accessible to all ages and levels of understanding, whether you’re a scientist, musician, mathematician, or anything else.”
School children can also get in on the action, with two special concerts scheduled for primary and secondary school students at QPAC.
“I’m so happy we’re doing these school concerts. Opportunities like this can shape a young person’s future. I remember similar events that changed my thinking and opened my mind.”
Jonathan Radford
Sax virtuosity
As a saxophonist, Jonathan is also looking forward to showcasing the versatility and virtuosity of the instrument.
“The saxophone is often misunderstood. It’s a hybrid instrument with many identities. Many people know it only as a jazz or pop instrument, but it existed before those styles. It has a unique voice. It blends well, is incredibly versatile, fits between woodwind and brass, and can play both very quietly and very loudly.”
He said audiences – and the AYO musicians alike – will be surprised by its virtuosity. “In some pieces it’s very much a solo instrument; in others, it functions like a chamber instrument, blending with the strings.”
Jonathan said he is excited to be working with the AYO musicians. “There will be so much energy, curiosity, and openness… It’s a small group, so we’ll have many possibilities for creating textures, colours, and sounds.”
“The program doesn’t portray maths as something abstract or distant. It’s musical, human, full of wonder and beauty. We want audiences to listen for patterns, listen for the beauty in the maths, and experience an immersive concert connecting sound, numbers, equations, and the world around us.”
Jonathan added that bringing music into a festival at the forefront of science “is an amazing privilege”. “My hope is that Beautiful Equations will be an inspiring concert – showing how two subjects that people often see as contrasting actually fit together and enhance our understanding and enjoyment of both.”
