**NOT SO HIDDEN FUTURES **

Centred on the achievements of three female mathematicians at NASA, Theodore Melfi’s movie, *Hidden Figures *challenges gender bias and highlights mathematics as an innovation driver. We need narratives like this as we seek to engage women and girls and rebrand maths as an exciting pathway to emerging career opportunities. The movie has been well received globally, including by those who attended the recent AMSI ChooseMaths screenings.

Mathematics and statistics research underpins innovation capacity across nearly every discipline. If we are to succeed as

a STEM driven economy, Australia needs to change how maths is valued across the community. This remains a core focus

across AMSI’s policy agenda, *Securing Australia’s Mathematical Workforce*. In addition to addressing university maths prerequisites, out-of-field teaching and industry engagement, measures to tackle careers awareness are critical to protect mathematical skill supply. The need for such action is supported by recommendations delivered by the AMSI Industry/Mathematical Sciences Engagement Taskforce to address industry engagement and future workforce challenges.

The mathematical sciences’ impact on innovation is no secret to industry and government who have been quick to recognise the economic benefits of a strong mathematical workforce. Further down the pipeline, however, the message that maths opens powerful career pathways is not getting through to teachers, students and parents. If we want to equip children to succeed we need to give them skills that provide the resilience and agility to navigate an increasingly dynamic world. In her call to arms on page 2, Sally Saviane, parent and primary teacher, sets out a powerful case to parents supporting the value of mathematics as a flexible and essential pathway to future prosperity.

**CAREERS AWARENESS**

The recently launched ChooseMaths Careers Awareness campaign represents a significant milestone in tackling this challenge. Almost 10,000 schools across the country have received launch careers awareness packs, including a poster series featuring inspiring women in maths. *More than a number*, these mentors are accessibly representative of the wide-ranging industry impact of mathematics. The campaign will expand on our existing ChooseMaths outreach events, as well as drawing on topical resources including our successful video series already viewed by over 40,000 people. As the current mathematical workforce ages, resupply is dependent on strong participation of women in mathematics.

** **

**MATHS ADDS: CAREERS GUIDE**

The mathematical sciences has a long-standing entrenched gender divide, in 2015 only 6.9 per cent of Year 12 girls undertook advanced maths compared to 12.6 per cent of boys with women accounting for only one third of Australian undergraduate maths students. The Women in Maths Network will bolster engagement of women and girls, essential to securing future skill supply across the pipeline, through establishment of a network of female mentors. This community of passionate and inspiring STEM professionals will support, motivate and advise young women pursuing mathematical careers.

Now in its twentieth year, MathsAdds is the acknowledged ‘go to’ guide for information on maths and statistics careers. Featuring over 140 examples of maths dependent job ads, real-life profiles instead of case studies and other resources, the launch of the MathsAdds website has expanded this resource to create an interactive online tool responsive to the changing demand for these skills. Aimed at both secondary and higher education students, MathsAdds remains a core resource for careers awareness across all AMSI programs. Industry support for MathsAdds is growing, with a number of sector leaders on board in 2017. This is recognised as a quality platform to both communicate skills needs and help create a future proof workforce.

RESEARCH-INDUSTRY: THE MISSING LINK

Despite it being recognised as a key innovation driver, Australian industry’s engagement with the mathematical sciences remains below the OECD average. This needs urgent action if we are to transition to a STEM driven economy. Critically, universities need to better highlight industry pathways to university mathematics students contemplating their next steps. Embedded in AMSI flagship events such as the annual Summer School, careers afternoons have opened direct research-industry engagement highlighting cross-benefits of these linkages. With organisations such as the Commonwealth Bank, Google, PwC and RBA engaging with students, these vital networking opportunities often reveal emerging career pathways.

** **

**THE THREE C’S FOR INDUSTRY READINESS **

As we seek to foster research-industry engagement, it is essential to provide a supply of work ready mathematics graduates. A workforce equipped not only with the required specialist knowledge but also the soft skills needed to navigate and thrive in commercial environments. As part of its engagement with industry, AMSI’s Industry Advisory Committee asked senior company executives to identify the skills in most demand. As expected the ability to communicate and collaborate were at the top of this list, as was the almost universal demand for maths graduates with the ability to code. This gives weight to the benefits of inclusion of coding in the school syllabus, and keeping these skills front of mind for maths and stats postgraduates as they compete for the new generation of roles in the innovation system.

AMSI’s Vacation Research Scholarship program plays an important role in transition from classroom to career, teaming undergraduate students such as Asem Wardek featured in this *Update *issue, with established researchers for short-focused projects with real outcomes. You can read about Asem Wardek’s experience and the benefit of the program on page 17.

Integrated learning opportunities (WIL) expose university students to industry and opening essential industry-research pathways. Industry focused postgraduate internships are a proven model to equip the emerging research workforce to engage with industry and open new avenues for future collaboration.

Launching in June 2017, AMSI Optimise seeks to strengthen mathematical-industry ties and build essential commercial optimisation capacity. Featuring a mix of presentations and practical challenges, AMSI Optimise will create strategic pathways for researchers to collaborate with the public and private sector in areas such as transport and supply chain logistics, energy pricing and communication networks.

**NATIONAL INTERNSHIP PROGRAM**

Australia’s only national, university-owned PhD internship program, AMSI Intern has already made a considerable impact on the innovation landscape, placing over 200 interns across all disciplines and industry sectors into four to six-month industry research projects. This has served to not only increase industry led university- research collaboration but has led to growth in the employment of specialist research staff across both SMEs and big business. We are now preparing to bring the program to national scale, with the government announcing a $28.2 million funding package to place 1400 interns over four years.

One of the strengths of AMSI’s internship model is the participation of academic mentors to support postgraduate researchers. This has proven effective in building research-industry partnerships well beyond the internship. For industry, the opportunity to see first-hand the benefits of accessing specialised research skills establishes new need for collaboration and, in some cases, leads to employment of interns to enhance internal research capabilities.

**MAKING MATHS THE FUTURE**

The rapid pace of technological development continues to open new opportunities and exciting career pathways not yet found in MathsAdds or any other career resource. Careers awareness is about more than jobs, it is about futures. And in our shared and individual futures mathematics continues to be both a fundamental foundation and at the very frontier of what we know. By choosing maths and encouraging our children to choose maths we equip ourselves to evolve with the world and be part of the extraordinary. Much like Astronaut John Glenn in Hidden Figures, industry innovators know you ‘can’t get anywhere without the numbers.’

This story was originally published in the Update issue 5 – winter 2017 Careers Special. Go online to read the full issue.

Full link – http://amsi.org.au/wp-content/uploads/2017/06/the_update_5th-ed_web.pdf

]]>Currently studying PhD in bioinformatics, Russul Alanni hopes to use maths to help cancer patients. Her research involves modelling gene mutations to increase understanding of cancer growth, survival time and recurrence in the hopes of improving treatment outcomes.

“Clinical application of machine learning approaches and biological data analysis is still open, as they are theories. My dream, however, is to develop an accurate prognosis model that can deliver clinical benefit,” says Russul.

With such big ambitions, Russul knows it is important to establish collaborative networks and engage with experienced mentors as early as possible. However, with husband Haseeb also pursuing a career in science and two boys to care for, this can seem like an out-of-reach luxury.

“With research a bit of a family business, it is often difficult to balance home and work commitments and, as is the case in many families, the sacrifices come back to me,” says Russul.

With the chance to expand their field expertise and network with global leaders at AMSI Winter School beckoning, the pair received a much-needed helping hand through the CHOOSEMATHS grant program. Covering childcare expenses, this funding meant both Russul and Haseeb could not only attend the event but engage fully with everything on offer.

“Both my husband and I wanted to be part of this opportunity, but with the need to cover childcare this seemed impossible. The CHOOSEMATHS grant meant I could also attend and be part of this exciting conversation, “ she said.

Seeking answers to questions not covered in her textbooks and studies, it was also a chance for Russul to deepen her field knowledge and seek out new tools to aid her quest against cancer. For Russul the true value of the grant as an access pathway was immeasurable.

“So often for women in particular, additional networking and training seems like an unattainable luxury. This grant meant I had access to expert knowledge and new tools and techniques at the cutting-edge of my field. This is invaluable as an establishing researcher in a male dominated and hugely competitive field,” says Russul.

A step closer to her dream, Russul now plans to build on her newly expanded networks as she draws on her Winter School experience as she makes cancer treatment add up for patients.

In partnership with the Australian Government, AMSI will deliver Securing Australia’s Mathematical Workforce, a $4 million four-year jointly funded national project.

Aligned to meet the challenges facing Australian innovation and science into the 21st Century this project will improve outcomes for higher education students in science, engineering, technology and mathematics (STEM). The project will strengthen research training for STEM graduates in Australia and contribute to a highly skilled mathematical sciences workforce.

Building on the success of the AMSI Vacation Schools and Scholarship Project it will deliver:

- industry based internships for PhD students that provide work experience in commercial research and innovation, and develop students’ entrepreneurial skills and work-readiness
- opportunities for university students in mathematical sciences to advance their knowledge through annual summer and winter schools as well as through vacation research scholarships placements
- industry research training symposia in bioinformatics and optimisation, engaging students, researchers and industry
- support to strengthen participation of women and Aboriginal and Torres Strait Islanders in graduate programmes in the mathematical sciences.

The project was announced by the Minister for Education and Training, Senator the Hon Simon Birmingham on 14 April 2016 in his address to the Knowledge Nation summit.

**MEDIA**

Commonwealth Invests in Australia’s Maths Future

14 April 2016, AMSI, Laura Watson

Funding Boost for Programs Linking Students with Industry

15 April 2016, Education HQ, Sherryn Groch

$2 Million Lift for Maths Programs

20 April 2016, The Australian, Julie Hare.

The AMSI Summer School 2016 included a series of lunchtime lectures. Professor Peter Taylor (The University of Melbourne) discusses the Paradox of Parrondo’s Games.

**Abstract**

In 1998, a colleague at the University of Adelaide knocked on Professor Peter Taylor’s door and showed him some interesting simulations, implementations of two games developed by a Spanish physicist Juan Parrondo, which are both biased against the player. However, if the player alternates between the games or chooses which game to play in a random fashion, the ensuing game is biased in favour of the player.

This talk discusses the definition of what it means for a game to be fair, a rigorous proof that Parrondo’s drift criteria do imply that a game is losing, fair or winning respectively and the observation that the phenomenon observed by Parrondo should be thought of as ubiquitous, rather than unusual. Peter also shares the story of his involvement with Parrondo’s games.

**Biography **

Peter Taylor received a BSc (Hons) and a PhD in Applied Mathematics from the University of Adelaide in 1980 and 1987 respectively. In between, he spent time working for the Australian Public Service in Canberra. After periods at the Universities of Western Australia and Adelaide, he moved at the beginning of 2002 to the University of Melbourne. In January 2003, he took up a position as the inaugural Professor of Operations Research, and was Head of the Department of Mathematics and Statistics from 2005 until 2010.

Peter’s research interests lie in the fields of stochastic modelling and applied probability, with particular emphasis on applications in telecommunications, biological modelling, healthcare and disaster management. Recently, he has become interested in the interaction of stochastic modelling with optimisation and optimal control under conditions of uncertainty. He is regularly invited to present plenary papers at international conferences. He has also acted on organising and program committees for many conferences.

Peter is the editor-in-chief of ‘Stochastic Models’, and on the editorial boards of ‘Queueing Systems’, the ‘Journal of Applied Probability’ and ‘Advances in Applied Probability’. He served on the Awards Committee of the Applied Probability Section of the Institute for Operations Research and Management Science (INFORMS) from 2005-2007 and is currently on the committee for the Nicholson Prize, awarded for the best student paper in operations research. In 2008, Peter became one of the five trustees of the Applied Probability Trust. This trust, which is based in Sheffield UK, is the body which publishes the Applied Probability journals plus ‘The Mathematical Scientist’ and ‘Spectrum’.

From February 2006 to February 2008, Peter was Chair of the Australia and New Zealand Division of Industrial and Applied Mathematics (ANZIAM), and from September 2010 to September 2012 he was the President of the Australian Mathematical Society. In 2013 he was awarded a Laureate Fellowship by the Australian Research Council.

The AMSI Summer School 2016 included a series of lunchtime lectures. Professor Jerzy Filar (Flinders University) discusses a career in mathematics.

**Abstract**

This talk discusses the following questions/issues about a career in mathematics:

• Why be a mathematician

• PhD supervisors want the best for you, so be kind to them

• Industry versus Academia

• Applied versus Pure (or does it matter?)

• Depth versus Breadth (or does it matter?)

• Learning from your failures

• Mathematical models and product stewardship

• Amadeus & football

**Biography **

The AMSI Summer School 2016 included a series of lunchtime lectures. Professor J. Hyam Rubinstein (The University of Melbourne) discusses 2, 3 and 4 dimensional worlds.

**Abstract**

There have been spectacular advances in the study of how 2, 3 and 4 dimensional spaces work over the last several decades, including multiple Field medal winning work. The talk reviews geometry and topology interaction in exciting ways in `low dimensions’. Physics comes into the picture, especially in dimension 4.

**Biography **

Hyam did his honours in maths and stats at Monash University then a PhD at the University of California, Berkeley. He was a postdoc then lecturer at The University of Melbourne and in 1982 he was appointed as a Professor.

Hyam has been head of department twice, President of the Australian Mathematical Society and Chair of the National Committee for Mathematical Sciences. He has supervised around 25 Masters and PhD students and his research interests are in low dimensional geometry and topology, minimal surfaces, differential geometry, shortest networks, optimisation and machine learning.

Hyam is also involved in MineOptima which sells software to design access infrastructure for underground mines.

Welcoming the $2 million investment, AMSI Director Professor Geoff Prince said the institute looked forward to closely engaging over the next four years with the federal government’s National Science and Innovation Agenda (NISA) to strengthen Australia’s mathematical capability.

“This funding is an acknowledgement of our outstanding track record in delivery of research and higher education programs. As well as building on the success of our flagship events and scholarships we will expand the program through new initiatives such as AMSI Optimise,” he said.

With a need to prepare students for private sector and cross-discipline research opportunities, AMSI will strengthen industry pathways by linking its key events such as BioInfoSummer and AMSI Optimise to industry placement opportunities to foster work readiness. Retention of senior undergraduate students, in particular women and indigenous students will also be a priority.

The key to AMSI’s success, according to Professor Geoff Prince, is its position as the national peak body with access to both academic and industry networks.

“AMSI is uniquely placed to secure Australia’s mathematical workforce into the 21^{st} Century.”

**Additional Information**

The AMSI Higher Education program sets the gold standard for research training infrastructure. Our intensive program of training events and scholarships exposes undergraduate and postgraduate students to cutting-edge methodologies and field areas in the mathematical sciences and related disciplines not routinely covered in academic courses. Our aim is to enhance the student experience and prepare tomorrow’s leaders to drive innovation through cross-discipline and industry based research.

For further information on our higher education programs including BioInfoSummer, AMSI Summer School, AMSI Winter School and our Vacation Research Scholarships, visit

http://highered.amsi.org.au

**Interview: **

**Professor Geoff Prince, AMSI Director **

**Media Contact: Laura Watson**

**E:** media@amsi.org.au

**P:** 04215 18733

Courses can be tightly focussed or a more general overview of a topic – a great opportunity to share your research expertise. The duration of the short course can be anywhere from an intensive 3 days to a distributed 3 weeks. The lecturer is responsible for delivering the content, AMSI will organise and coordinate marketing, enrolments, and Visimeet access . Courses are not for credit – no exam setting or marking is required.

The only limit is that the course would have to be delivered in the common non-teaching period to prevent clashes with the delivery of Honours courses through the ACE network in teaching periods. Of course, if you are interested in offering a short course next summer or next year, we would love to hear from you as well.

More information on AMSI ACE Short Courses here.

For further information and communicating your expression of interest, please contact Maaike Wienk at ace@amsi.org.au.

]]>Outlining key recommendations from the National Committee for the Mathematical Sciences headed by Professor Nalini Joshi, The Mathematical Sciences in Australia: A Vision for 2025 provides a blueprint to transform mathematics education, research training and industry innovation in Australia.

Committee Member and Director of AMSI, Professor Geoff Prince warns that with up to 40 per cent of mathematics classes in schools taught by out-of-field teachers and Year 12 participation in higher-level mathematics continuing to fall, immediate and decisive action is needed to secure Australia’s mathematical future.

Read the media release <here>.

Full report available here <here>.

For information on the National Committee for the Mathematical Sciences and background documents, click here.

**Media Coverage**

Thursday, 17 March 2016

ABC World Today, Lucy Carter, Maths Must Be Mandatory University Degree Prerequisite Experts

The Australian Financial Review, Tim Dodson, Falling Maths Standards Risk the Economy, Science Academy Warns

The Australian, Julie Hare , Low university entrance bar doesn’t add up for maths students

The Age, Kate Aubusson, Push For Year 12 Maths Prerequisites For Stem Degrees

The Sydney Morning Herald, Kate Aubusson, Push For Year 12 Maths Prerequisites For Stem Degrees

Educator, Robert Ballantyne, Urgent Attention Needed on Maths Deficit

]]>Jonathan Borwein (Jon), *University of Newcastle*

Pi Day is upon us again, for those who note today’s date in the format 3/14 (March 14). But rather than talk about Pi Day itself, as I did last year, this year I want to talk about Pi and mathematical notions of beauty.

How better to do so than to talk about the 18th century European scholar Leonard Euler’s famous formula:

The Conversation, CC BY

Often described as “the most beautiful formula in mathematics”, Euler seems never to have actually written it down – naming conventions in mathematics are a bit dodgy. Rather, it is a special case of Euler’s discovery that exponential growth and circular motion are equivalent, given by the following formula:

The Conversation, CC BY

The US theoretical physicist Richard Feynman called this “the most remarkable formula in mathematics”.

Ed Sandifer, a founder of the Euler Society, has a lovely 2007 article discussing in detail Euler’s approaches – over 40 years – to show how the formula (above) worked.

I shall try to get the story of this formula across with very few more symbols.

Euler’s formula involves five fundamental constants: 0, 1, i, e, and Pi, and on adding equality, addition and exponentiation, combines them into a seven-symbol word in a mysterious and useful way.

Equivalently, it can also be written:

The Conversation, CC BY

This is even more succinct and introduces negative numbers.

It is a common feature of mathematics that discoveries are often first used and only later understood. As the 18th century French mathematician Jean d’Alembert wrote: “algebra is generous, she often gives more than we ask”.

Let me discuss the 2,000-year history of the building blocks of Euler’s formula. You don’t have to understand the actual mathematics, just gain an appreciation of the origin of the various elements of the formula and how they combine so neatly together.

The “=” symbol is attributed to the Welsh scientist Robert Recorde in 1557.

Arguments about the meaning of equality in mathematics have mirrored and driven discussions about definite descriptions in philosophy more generally.

The British logician Bertrand Russell’s famous example is Venus, described as the morning star and as the evening star. An over-discussed example in mathematics is whether 0.99999999… and 1 are equal. They are and they aren’t.

Notions of nothingness and the void or infinity go back much further, but the Greeks and others had not discovered rules to manipulate with “0”.

A mathematically tractable notion of zero is attributed to the great Indian thinker Brahmagupta around 650CE.

When married with the other Indian discovery of positional notation, calculation became much more accessible. This ability did not come fully to Europe until the 15th century and later.

Without “1” there would be no advanced arithmetic. With “0” and “1”, we also have binary notation and modern digital computers. What the US theoretical physicist John Archibald Wheeler called “it from bit”.

This leads to modern group theory, algebra, cryptography and much, much else.

The use of imaginary numbers also dates largely from the 16th-17th century. The French philosopher and mathematician René Descartes used the term disparagingly.

Mathematical concepts we now take for granted sometimes took centuries to be adopted and understood. No wonder school children rebel.

It took Euler and then German mathematician Carl Friedrich Gauss to truly exploit imaginary numbers and make the word “imaginary” have a positive mathematical connotation.

Defining “i” as the square root of -1 has the wonderful consequence that a polynomial of degree n has n (complex) roots.

For example x^{4}-1 = (x+1) (x-1) (x-i) (x+i), it has four roots. This leads to what is now called complex analysis.

Most of modern mathematics and mathematical physics (such as quantum theory) could not be done without complex analysis.

Pi originates as the area of the circle of radius one or the circumference of a circle of diameter one.

The great Greek mathematician Archimedes of Syracuse (287-c212 BCE) used this idea to provide the approximation of 22/7 for Pi (3.141592…).

Euler discovered the modern definition which takes Pi/2 as the smallest positive zero of the cosine function defined by what is known as a Taylor series. This is a bit complicated but if you just think of the series as a very large polynomial you will get the idea.

The Conversation, CC BY

Here n! = 1 x 2 x … x n is called the factorial of n. This was another 17th-century discovery.

The constant “e” originated in the 17th century as the base of the natural logarithm, and to three decimal places is 2.718…, though like Pi, it’s a transcendental number and continues without repeating to countless decimal places.

Euler, the master of us all – who named both “pi” and “e” – realised that e^{x} also had a dandy Taylor series:

The Conversation, CC BY

Then setting theta (θ) equal to one, gives an efficient formula for e.

Now we know all the building blocks all we need do in the second equation (above) is set Theta to be Pi, and with a little trigonometry, knowing that sin (π) = 0 and cos (π) = -1, then reducing the formula step by step, out pops the original beautiful formula.

The Conversation, CC BY

As you can see, to view the formula as beautiful it is necessary to understand the elements, at least roughly.

Bertrand Russell in his History of Western Philosophy

put it so:

Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.

Most mathematicians would agree that to be beautiful a formula must be unexpected, concise and useful – in the rarefied sense that professional mathematicians recognise.

When forced to, most mathematicians will list Archimedes, Gauss and Euler among the top five mathematical thinkers of all time. The other two are Isaac Newton (for calculus and mechanics) and Bernhard Riemann (for the Riemann hypothesis and Riemannian geometry).

With three of these brilliant thinkers and fundamental constants engaged, it is no wonder that Euler’s formula is lionised as it is, as the most beautiful formula in mathematics.

Jonathan Borwein (Jon), Laureate Professor of Mathematics, *University of Newcastle*

This article was originally published on The Conversation. Read the original article.