# Answers With… Professor Nalini Joshi

8-12

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Professor Nalini Joshi

Professor Nalini Joshi AO currently holds a Payne-Scott Professorship in Mathematics at the University of Sydney and is Vice-President of the International Mathematical Union. Her research focuses on mathematical methods to study systems that arise as universal models in modern physics. In 2016, she was appointed an Officer of the Order of Australia for distinguished service to mathematical science and tertiary education as an academic, author and researcher, to professional societies, and as a role model and mentor of young mathematicians. She holds a PhD and MA from Princeton University in Applied Mathematics and a BSc (Hons) from the University of Sydney.

What scientific or medical breakthroughs or discoveries are you most excited to see within your lifetime? – Milena, year 11 student from Springbank Secondary College, SA

What I would like to see is a proof of the Riemann hypothesis in my lifetime.

It’s a millennial problem posed in the year 2000, now almost 20 years ago, but the original conjecture is over a century old. (There’s a million-dollar-prize for proving it.)

The reason why it is so important is two-fold. One is that it tells us about the distribution of the prime numbers. They are related to the zeroes of the Reimann zeta function, which lie in the complex plane. There is one line, where the real part of the variable is equal to a half, where all the experimentally known non-trivial zeros of the Riemann zeta function lie, and they correspond to the prime numbers.

Now the largest prime currently known as of August this year is 2^{82,589,933}− 1, a number which has 24,862,048 digits when written in base 10, and the reason why the knowledge of such things is so important is because we rely on primes to give us secure codes for the online transactions (banking, shopping, and so on) that we are carrying out every day of our lives. If the Riemann hypothesis holds, then we know where the primes are, and we know the distribution of those primes, then we will be able to crack (almost) every code being used today.

But the other reason to know about it is because once it is proved – and there is very little doubt that it is true – it will lead to so many new inventions, new methods in mathematics, that it will enable us to grow scientifically for a million years to come. So this is why I want to see it proved!

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