Robyn Arianrhod’s new book celebrates the power of signs and symbols.
Without them, Einstein wouldn’t have been able to imagine the curving of space-time
and you wouldn’t have a smart phone. The Post asked our resident mathematician and science writer to tell us more – in simple terms.
Without them, Einstein wouldn’t have been able to imagine the curving of space-time
and you wouldn’t have a smart phone. The Post asked our resident mathematician and science writer to tell us more – in simple terms.
Bass Coast Post: So what’s the point of maths now that we’ve all got smart phones?
Robyn Arianrhod: For those of us who aren’t designing our improved smart phones and all the other maths-enabled technology we rely on, I guess it depends on taste, and on how much control we like to have over the tech that runs our lives. Understanding some of the maths and science that underpins modern life can give a sense of that control, rather than everything being a mysterious black box.
As for taste, for me an appreciation of the elegance and power of mathematics is like an appreciation of the arts. That’s what I hope to convey in my books – that the reader comes away not necessarily with a good grasp of higher maths but with an appreciation of it, and of what it can do.
Robyn Arianrhod: For those of us who aren’t designing our improved smart phones and all the other maths-enabled technology we rely on, I guess it depends on taste, and on how much control we like to have over the tech that runs our lives. Understanding some of the maths and science that underpins modern life can give a sense of that control, rather than everything being a mysterious black box.
As for taste, for me an appreciation of the elegance and power of mathematics is like an appreciation of the arts. That’s what I hope to convey in my books – that the reader comes away not necessarily with a good grasp of higher maths but with an appreciation of it, and of what it can do.
Post: What sort of response do you get when people discover you’re a mathematician?
| Robyn: I used to get a lot of polite silence, with occasional comments on how the person loved or, more commonly, hated maths. But here in Bass Coast, people have found out about my maths interest as a corollary to my writing, and I’ve been really heartened by the way they’ve been willing to forego any lingering fear of maths and give my books a go. I’ve really appreciated that. Post: Did you always love maths or was it a slow burning affair? Robyn: I always liked it, but I fell in love with it when I first learned about mathematical proofs – in about Years 10 and 11. I was entranced by the power and elegance of the way a neat set of steps, following logically and economically from the rules of maths, led to an unassailable truth. |  Vector was published by UNSW Press this month. It’s available in good bookshops. |
Post: Have you had your own Eureka moment?
Robyn: Yes, in a very modest but nonetheless thrilling way. It came during research for my PhD, in collaboration with my supervisor, Colin McIntosh, and it led to some interesting results in the analysis and classification of solutions of Einstein’s equations. In particular, we explored (and I am still occasionally exploring) a mathematical analogy between Einstein’s equations of gravity and Maxwell’s equations of electromagnetism. The idea is that this analogy can help researchers to find and interpret new solutions, with additional insights from existing knowledge of electromagnetic radiation.
Post: What’s your favourite equation and why?
Robyn: I love the beautiful vector form of Maxwell’s equations (four of them), where the symbols intertwine just like the electric and magnetic fields they represent. The repetitions of the symbols over the four lines makes for sublime visual poetry! Maxwell and his equations are the focus of my book Einstein’s Heroes, and they’re important in my new book, too, because Maxwell was the first major physicist to have recognized the power of the then-new language of vectors.
But my all-time favourite equation is Einstein’s equation of gravity (general relativity):
Robyn: Yes, in a very modest but nonetheless thrilling way. It came during research for my PhD, in collaboration with my supervisor, Colin McIntosh, and it led to some interesting results in the analysis and classification of solutions of Einstein’s equations. In particular, we explored (and I am still occasionally exploring) a mathematical analogy between Einstein’s equations of gravity and Maxwell’s equations of electromagnetism. The idea is that this analogy can help researchers to find and interpret new solutions, with additional insights from existing knowledge of electromagnetic radiation.
Post: What’s your favourite equation and why?
Robyn: I love the beautiful vector form of Maxwell’s equations (four of them), where the symbols intertwine just like the electric and magnetic fields they represent. The repetitions of the symbols over the four lines makes for sublime visual poetry! Maxwell and his equations are the focus of my book Einstein’s Heroes, and they’re important in my new book, too, because Maxwell was the first major physicist to have recognized the power of the then-new language of vectors.
But my all-time favourite equation is Einstein’s equation of gravity (general relativity):
The R’s on the left represent the geometry of the curved space-time, and the T on the right represents the matter and energy giving rise to the gravitational field that curves the spacetime. This is a ‘tensor’ equation, and Einstein’s thought processes on the way to discovering it are a key part of Vector.
Why do I like this equation? This handful of symbols contains the key to our understanding of the whole cosmos. Awesome!
Post: What mathematical problem would you most like to solve?
Robyn: Stepping right down from the lofty heights of my youthful desire to save the world through science, I’d love to prove a conjecture (about a gravitational analogue of magnetism) that Colin and I made many years ago. My colleague Tony Lun and I, along with quite a few other researchers, have spent many years trying to prove it – and given what I said earlier about proof, you can see why this one’s elusive nature tantalizes me!
Why do I like this equation? This handful of symbols contains the key to our understanding of the whole cosmos. Awesome!
Post: What mathematical problem would you most like to solve?
Robyn: Stepping right down from the lofty heights of my youthful desire to save the world through science, I’d love to prove a conjecture (about a gravitational analogue of magnetism) that Colin and I made many years ago. My colleague Tony Lun and I, along with quite a few other researchers, have spent many years trying to prove it – and given what I said earlier about proof, you can see why this one’s elusive nature tantalizes me!
"Maths is a language – a powerful, unique, universal language that can take us beyond everyday experience and into whole new ways of understanding the natural world." |
Post: How do you feel about people who say “I HATE maths!”
Robyn: I do understand that not everyone has a feeling for patterns and proofs, but I also think that maths is a difficult subject to teach (and therefore to learn) – especially for “out of field” teachers who don’t have a strong maths background themselves but are co-opted because of a shortage of maths teachers. Lack of training makes it very difficult to convey to students a love of maths.
From my own teaching experience, I think it helps if people understand that maths is a language – a powerful, unique, universal language that can take us beyond everyday experience and into whole new ways of understanding the natural world. The prescience of mathematical language sometimes borders on the miraculous! For example, Maxwell’s equations led him to conjecture the existence of radio waves, long before they were discovered. And Einstein’s equations led to the discovery of gravitational waves, black holes, gravitational lenses, and more – including the gravitational effect on time: along with the effect of relative motion on clock readings, this gravitational effect is now used to make our GPS directions so accurate. And these are just two examples of the way mathematics can reveal the secrets of the universe, before any physical discoveries or observations have been made.
Then there’s pure rather than applied maths, where the whole point is the language itself. What can you prove with it, what does it say? A lot of the techniques that end up helping with physics and technology started out as pure mathematics – maths for the love of it!
Robyn: I do understand that not everyone has a feeling for patterns and proofs, but I also think that maths is a difficult subject to teach (and therefore to learn) – especially for “out of field” teachers who don’t have a strong maths background themselves but are co-opted because of a shortage of maths teachers. Lack of training makes it very difficult to convey to students a love of maths.
From my own teaching experience, I think it helps if people understand that maths is a language – a powerful, unique, universal language that can take us beyond everyday experience and into whole new ways of understanding the natural world. The prescience of mathematical language sometimes borders on the miraculous! For example, Maxwell’s equations led him to conjecture the existence of radio waves, long before they were discovered. And Einstein’s equations led to the discovery of gravitational waves, black holes, gravitational lenses, and more – including the gravitational effect on time: along with the effect of relative motion on clock readings, this gravitational effect is now used to make our GPS directions so accurate. And these are just two examples of the way mathematics can reveal the secrets of the universe, before any physical discoveries or observations have been made.
Then there’s pure rather than applied maths, where the whole point is the language itself. What can you prove with it, what does it say? A lot of the techniques that end up helping with physics and technology started out as pure mathematics – maths for the love of it!
More reading and listening
- Vector: Read an extract. Vector takes readers on an extraordinary 5000-year journey through the human imagination.
- The hunt for a crucial update to Einstein's revolutionary theories The Science Show, ABC Radio National, June 29, 2024 - Robyn Arianrhod explains why we need another Einstein.
- A world of wonder July 4, 2018 - After turning her back on her scientific studies, author Robyn Arianrhod was lured back by some great men and women of science, writes Liane Arno.