As a frequent traveller, I find it convenient to arrange my finances remotely, a few taps transfer funds effortlessly around the world. I should be more vigilant about password management, but the on-line exchange of sensitive information is secure thanks to cryptographic algorithms.
Even for a mathematician, it is difficult to recognise tangible outcomes of mathematical research in daily life. Like most people, I hardly take notice because the maths is invisible.
That’s a pity. The encryption algorithms are beautifully designed and make ingenious use of mathematical problems that are very hard to solve, involving prime numbers and elliptic curves (an elliptic curve is the set of solutions to an equation of the form y2 = x3 + ax + b).
Imaginative maths as solutions to complex problems are found in process optimisation in manufacturing, blockchain technology, quantum information, epidemic and weather forecasting, artificial intelligence, and space exploration. The rate of return on mathematical sciences research has never been higher, a fact which seems hopelessly lost on Australia, which lacks sound long-term investment in fundamental research.
How do people come up with these incredibly deep and creative ideas that so profoundly change the world? Reflecting on my own experiences, ingenious ideas arise serendipitously. Yes, hard work is involved, but the unexpected step-change comes about by creative opportunity and ample human interaction.
In maths such opportunity takes the form of extended international research programmes. The US-based Institute for Pure and Applied Mathematics (IPAM) at UCLA that I visited last month is one of several institutes that act as a gold-standard for many others around the world. Generously funded by the US National Science Foundation and donors, IPAM creates a stimulating environment in which mathematical scientists and students from around the world are supported to advance knowledge and set new research agendas.
Almost all developed countries invest in this type of research infrastructure, because it works. In Australia, sustained funding streams for an internationally prominent mathematical sciences residential research institute are non-existent. This deprivation of financial oxygen precludes impactful home-grown outcomes and causes departure of talent.
At UCLA I caught up with Australia’s Terry Tao, who now lives in California and is widely regarded as today’s most influential mathematician. One of Terry’s many contributions is in compressed sensing, and his maths resulted in hundreds of millions of savings due to improved image processing in MRI scans, geological data analysis, and internet delay and congestion estimation.
A recent MATRIX-AMSI report shows that the National Collaborative Research Infrastructure Strategy completely ignores the mathematical sciences, with no identifiable maths project funded despite an anticipated $4 billion investment between 2018 to 2029. Moreover, investment in mathematical sciences research by the tertiary sector as indicated by higher education research and development expenditure has dropped to critically low levels in recent years.
The Australian residential research institute, MATRIX, receives basic funding from several leading institutions (Melbourne, Monash, Queensland and Australian National universities). Lack of sustained Government investment is shortsighted. Australia needs to get serious if it aspires to sovereign knowledge capability and readiness to capitalise quickly on new opportunities.
Professor Jan de Gier is Director of MATRIX at The University of Melbourne
