Today, 今日吃瓜 release their fourth annual Discipline Profile of the Mathematical Sciences. At a time when the Australian government is responding to the Chief Scientist鈥檚 call for a strategic plan for Science, Technology, Engineering and Mathematics (STEM) it is a reminder that we cannot continue to rely on piecemeal programs tied to the electoral cycle.

The data collected for the 2015 publication paints a mixed picture of Australian engagement with the mathematical sciences.

86 per cent of science degrees听do not have intermediate mathematics as an entry prerequisite while Year 12 enrolments slide听

In fact, mathematics prerequisites for entry into science, commerce and engineering degrees are at historic lows.

今日吃瓜 Director, Professor Geoff Prince insists: 鈥淯niversities must phase in restoration of maths prerequisites; the lack of them sends a negative and misleading message to schools about the value of these subjects.鈥�

Intermediate and advanced mathematics subjects are the gateway to quantitative professions; the 20-year decline in participation is choking the country鈥檚 galloping demand for graduates with these skills. And it has the potential to halt the nation鈥檚 productivity growth.

At least 30 per cent of Year 7-10 maths classes are taught without a qualified maths teacher

This figure is more than double the international average and must be repaired as part of our STEM planning.

In order to secure the future supply of mathematics teachers we need to know why potential educators aren鈥檛 choosing to be maths teachers. The only immediate solution is to provide professional development to the many conscientious and professional educators teaching maths out-of-field.

This is a national issue requiring national leadership; state and federal governments must act together to solve the teacher supply problem.

Women make up only 30 per cent of undergraduate maths enrolments holding back our STEM workforce and productivity growth

The proportion of young women represented at all stages of the mathematics pipeline is inadequate. A significant consequence of this is that adult women numeracy is below that of men 鈥� around 30 per cent in some age groups. And, in terms of the national economy, it is widely recognised that weak participation by women in STEM fields is handicapping Australia鈥檚 productivity and competitive advantage.

鈥淲e are proud to be working with the BHP Billiton Foundation to increase participation of girls and women in study and career pathways involving mathematics and statistics,鈥� says Professor Prince.

Maths鈥� multi-billion dollar value to the economy under threat as PhD rate stagnates

A 2015 report by the Australian Academy of Sciences indicates that, of those business sectors based on a single core discipline, mathematical sciences account for the top three (and five of the top seven). The report also highlighted that the direct impact of advanced physical and mathematical research is worth $145 billion to the economy per year, the flow-on impact amounts to $292 billion per year. This is in stark contrast to 54 per cent of adult Australians having only basic numeracy skills and the proportion of Year 12 students studying 鈥渉arder鈥� maths in steady decline.

鈥淯nfortunately, this stellar contribution hides an alarming trend,鈥� says Professor Prince. 鈥淕overnments are trying to drive up business employment of STEM trained research professionals, however, domestic PhD numbers in the mathematical sciences are among the very lowest in the OECD. Universities and businesses must improve engagement to maximise the economic benefits of mathematics and statistics.鈥�

The 听is accompanied by a policy document 鈥�听鈥� that identifies four key priorities to reverse these confronting trends:

1. Restore university maths prerequisites from their historic low and turn around declining school mathematics enrolments
2. Train the unqualified teachers of school mathematics and secure the supply of future qualified maths teachers
3. Increase the number of girls studying maths and women employed in the quantitative professions.
4. Boost the engagement of Australian business with mathematical sciences research

Australia鈥檚 Chief Scientist, Professor Ian Chubb, has called for action: 鈥淚t鈥檚 time to do what so many other countries have already done: take a long-term strategic view of STEM鈥檚 pivotal role in securing a stronger Australia.鈥�

— ends —

For Interview:
Professor Geoff Prince
Director, 今日吃瓜
M: 0407 546 336
E: director@amsi.org.au

Media contact:
Stephanie Pradier
Media Communications, 今日吃瓜
M: 0424 568 314
E: stephanie@amsi.org.au

RESOURCES:

Prerequisites, or lack thereof:听Data can be found in Table 2.10 (page 13)听

Value of the mathematical sciences to Australia鈥檚 economy, looking at the top seven sectors that use a single science discipline. The mathematical sciences have a value of $18 billion of the $22 billion per year to the Australian economy of across these top seven sectors:听Data from Table 4.2 (page 38)听

Falling participation rates in advanced mathematics enrolments:听Figure 2.7 (page 12)听

听

A transcript of the interview is below and you can download a

PAUL TURTON: According to Professor Ian Chubb, Australia鈥檚 Chief Scientist, it鈥檚 time to do what so many other countries have already done: take a long-term strategic view of STEM鈥檚 pivotal role in securing a stronger Australia. The Chief Scientist will be speaking at a public meeting at Newcastle City Hall at 4.30 this afternoon. He joins us now to whet your appetite.

Professor Chubb, good morning. How are you?

IAN CHUBB: Morning Paul, I鈥檓 well. How are you?

PAUL TURTON: Fantastic thanks. Have we taken our eye off the ball in regard to science a little bit?

IAN CHUBB: Yes.

PAUL TURTON: So what should we do? Obviously the community鈥檚 approach to those key subjects needs to change and I guess that鈥檚 part of what you鈥檙e doing.

IAN CHUBB: Well, it is. I think the world around us is changing very rapidly and when you look at that world around us you see science well and truly embedded in the core of our lives. The better we are able to do science, or the better we鈥檙e able to understand at least how science works, then the better we鈥檒l be for it. When we have to make choices as citizens or when we鈥檙e trying to encourage political leaders to make decisions, the better informed the decision the better the outcome. And the better we understand the methods of science, the process of science broadly in the community, the better those outcomes will be.

PAUL TURTON: We鈥檙e told all the time via the popular art forms of this changing world, whether it鈥檚 the Jetsons or the Orwellian future or sci-fi at its most extreme, we鈥檙e getting clues all the time about what the future might hold for us and some of those predictions are already playing out. Are we totally embracing the concept? Do we get it?

IAN CHUBB: Well, not as well as we should. I think there鈥檚 been a rhetorical commitment for quite a while but the reality is we鈥檝e got to get some action now and the world, as I said earlier, is moving away from us. In the United States and the United Kingdom, most of the countries of Europe and certainly many of the countries in our region, they鈥檙e all basically focusing on a two-pronged agenda. One is to make sure that the level of science education broadly available across the community is quite high, so that when people finish school for example, even if they go on to be lawyers or accountants or farmers or miners, they have some understanding of how science works. So it鈥檚 increasing the level of science literacy within the community. But embedded within that of course you鈥檝e got the people who want to be scientists and who want to work as scientists, whether in a laboratory in a white coat or in another part of the economy, but using the skills that they鈥檝e developed through education in science to apply to whatever that industry might be.

PAUL TURTON: So how much of the change for the future is going to come from a different mindset? In other words just changing the way we think about how jobs will play out in the future, the fact that a lot of stuff is going to be done by machines for example, is it simply a matter of changing our mind and all of the little things will then follow?

IAN CHUBB: Well I think probably yes. I think it鈥檚 a deeply cultural thing. How many people have you spoken to in the last few months who have been virtually proud to say that they don鈥檛 understand mathematics or they鈥檙e no good at mathematics or they don鈥檛 understand science? Try saying that about Shakespeare or Renoir and there鈥檚 a completely different response.

I鈥檓 not saying this is a peculiarly Australian thing, I think it happens in many countries in the world. It鈥檚 just that most of those countries are now doing something about it, so they鈥檙e supporting their teachers better, they鈥檙e preparing their teachers better, they鈥檙e encouraging their teachers, they鈥檙e recognising the central importance of the teaching profession in all this. And I don鈥檛 think we鈥檝e done that yet, or not nearly enough anyway.

PAUL TURTON: Enrolments in the science courses tend to be down in our schools. I know depending on variations there can be said to be a recovery of sorts underway at the moment. They just seem to have lost their glamour though. Are we selling our sciences long enough to young people?

IAN CHUBB: I don鈥檛 think we are, and I don鈥檛 think we鈥檙e making them interesting enough when they do study them at school. I鈥檝e been saying for a long time now that science has got to be taught inspirationally and the best way to teach it inspirationally is to teach it the way it鈥檚 practised. Science in practice is awesome. If you鈥檙e actually an experimental scientist and you design an experiment and it goes wrong you learn a lot from that; it鈥檚 not that it goes wrong, it just informs you differently. You鈥檝e got a mix of responses as a scientist. But to teach it blandly out of a textbook I think doesn鈥檛 actually give the student that sense of excitement that there is when you suddenly understand something better, even if you don鈥檛 go on to be a scientist, or you do something that gives you some insights into something that wasn鈥檛 known before. All of those things are just mind-bogglingly awesome, so that鈥檚 how it ought to be taught. In order to do that we鈥檝e got to support our teachers, we鈥檝e got to recognise the importance of teaching and we鈥檝e got to make sure that we give them the maximum opportunity to draw the talent out of these students.

PAUL TURTON: Unfortunately you can鈥檛 have a Brian Cox in every classroom. Ironically now there鈥檚 never been more media focusing on science and nature. You look at the availability of audiovisual materials for young people and there鈥檚 plenty of material out there, so it鈥檚 not as though they鈥檙e not being exposed to the opportunities.

IAN CHUBB: Well that鈥檚 true and then they go back into a classroom where, in Australia for example, the 今日吃瓜 in Melbourne estimates that something like 40% of teachers teaching mathematics are out of field in early secondary school. So it鈥檚 hard for those teachers to encourage the students who might go off and see something or, watch Brian Cox in the evening, go back into class and I think come back to earth. So it is, I acknowledge, a very complex issue but the point is that we human beings tackle complex issues. It takes the will to do it.

PAUL TURTON: Newcastle has reinvented itself a number of times and there鈥檚 been a fair bit of innovation associated with the Hunter region over the years. How well are we placed in relative terms to move forward with what you would describe as a generation of ideas, or creating an environment where ideas proliferate?

IAN CHUBB: Well partly Paul I鈥檓 going up there to learn. I鈥檝e been told, and today I鈥檓 going to be able to see things that are being done. But from all that I鈥檝e seen and read and heard so far then I think Newcastle, the Hunter region, has taken some really good steps.

One of the things that we have to learn in Australia is that we can learn from the good things that are being done in various parts of the country, rather than quarantining them to one particular part because somebody with some spark and energy and drive and commitment has created a particular sort of environment. We need to make sure that we can learn from that and translate it across Australia. There are lots of good things being done in various parts of Australia but they鈥檙e relatively small-scale and relatively local in influence. So it鈥檚 really a question for me today of finding out, learning a lot, meeting a number of people and then thinking about how much of this could be part of a federal government push to improve science and science education in Australia.

PAUL TURTON: Professor Chubb, good to talk to you and best of luck with all of your meetings today.

IAN CHUBB: Thanks very much Paul.

PAUL TURTON: Professor Ian Chubb, Australia鈥檚 Chief Scientist, in the Hunter for a variety of meetings including a public lecture at Newcastle city hall at 4.30 this afternoon. That鈥檚 almost full, so if you鈥檇 like to be there you鈥檒l need to make a booking.

What does connect-the-dots have to do with watching a Pixar film? More than you might think.

A connect-the-dots page starts with nothing but some labelled points. As each dot is joined to the next, however, a picture emerges. Each step is simple 鈥� just add a line segment between two points 鈥� but the resulting image can be extremely complex.

Toddlers can produce masterpieces this way, but so can computers. When a computer needs to draw a curve, it starts by connecting a sequence of points. Using just a few points might result in a zigzag with sharp corners, but increasing the initial number of points makes the resulting curve look smoother. With enough points and line segments, we can approximate even the most complicated curves.

Dots lines and curves

But maybe you’re more ambitious. Suppose you’re not interested in drawing curves, but rather, in constructing two-dimensional surfaces. Can you use an analogous approach to build a plane or a sphere or something more elaborate?

Triangles 鈥� the simplest two-dimensional objects 鈥� serve as building blocks for more complicated surfaces. Just as we can connect a pair of points with a line segment, we can connect three points via a triangle. And, just as we can make complicated curves by gluing lots of segments at their endpoints, we can make complicated surfaces by gluing lots of triangles along their edges. We can approximate extremely complex surfaces as long as we use enough triangles.

Mathematicians started thinking seriously about constructing surfaces from triangles in the late 19th century, hoping to classify surfaces. In particular, they wanted to understand when two surfaces could be deformed to look the same without cutting or gluing. They developed mathematical tools to study this question, and a century later, it became clear that they’d also laid the groundwork for an important technique in computer graphics.

Imagine trying to model moving cloth, perhaps a flag flapping in the breeze. Since the flag changes shape as it moves through space, this is a much more difficult problem than simulating the movement of a rigid object like a table. If the flag is approximated by triangles, however, modelling it becomes possible because the computer only needs to keep track of sets of three points. When the points move, they carry the triangles with them.

Abstract? Applied? Both!

Mathematicians certainly weren’t thinking about computer graphics in the 1890s. They were studying abstract questions about two-dimensional geometry and developing beautiful mathematics. Nevertheless, the techniques they invented in order to state this question precisely and then answer it have turned out to be extremely useful. In fact, this theme recurs throughout human history: mathematics developed to solve abstract problems turns out to be useful. Maybe not always and definitely not quickly, but it happens over and over again.

The first mathematical objects most people meet are the counting numbers 1, 2, 3鈥� Most counting numbers are formed by multiplying smaller numbers, but not all of them. Some numbers have only 1 and themselves as factors, and these are known as prime numbers. For example, the numbers 2, 3 and 5 are prime, but 4 = 2 x 2 is not.

Prime numbers act as building blocks for the entire number system. Centuries ago, the mathematicians who studied primes didn’t think their efforts would defend a castle or build a better steam engine, but they were intrigued by the search for structure and patterns.

Some of the questions they posed continue to capture the mathematical imagination; today, the most famous unsolved problem in mathematics is the Riemann Hypothesis, which addresses how the primes are distributed among the counting numbers.

Pondering prime numbers might seem like an intellectual game that’s divorced from ‘real world’ concerns. But suppose you ask yourself, ‘Why is it safe to use my credit card to buy something online?’ (Or, maybe better: ‘Is it safe to use my credit card online?’) In fact, the basic techniques for sending data securely over the internet rely on what’s known about factoring a number into primes. Every time you enter your credit card number on a website and hit ‘send’, you have a number theorist to thank.

Likewise, Persian mathematicians began developing the subject we now call algebra in the Middle Ages. This field evolved over centuries, and today, it underpins the algorithms for internet search and Netflix recommendations.

Fourier analysis, which was developed as part of calculus in the late 1700s, provides the basic mathematical tools for signal processing in telecommunications and medical imaging.

Algebraic topology 鈥� a branch of mathematics that wasn’t even created until the 20th century 鈥� is being used in the 21st century to study artificial intelligence and cancer genomics.

The list goes on, but the striking thing in all these examples is that the original researchers couldn’t anticipate which applied questions would require their work. Plenty of important mathematics is specifically developed to solve real-world problems, but curiosity-driven research is as important today as it ever has been.

But back to triangles

New applications for old mathematics are exciting, but progress also comes in the form of new mathematics.

Computer graphics uses flat triangles to approximate smooth surfaces, but if you’re willing to allow triangles to bend a bit, then you can build any surface by gluing enough of them together. This is equivalent to saying that you can cut any surface into curved triangular pieces.

Sphere made of curved triangles

These curved triangles are an important tool for generalising what we know about geometry to higher dimensions – after all, mathematicians, scientists, and engineers don’t care only about surfaces.

Higher-dimensional spaces occur not only in pure mathematics, but also in nature as patterns in large data sets, as relationships between physical quantities, and in descriptions of the universe itself.

Mathematicians develop formal techniques to study them, compensating for the fact that a seven-dimensional space is harder to picture than a flag. Luckily, the idea of gluing triangles generalises to any dimension! In three dimensions, for example, the analogue of a triangle is a tetrahedron, and just as gluing triangles together builds surfaces, gluing tetrahedra together builds new three-dimensional objects. In higher dimensions, the analogue of a triangle is called an n-simplex, and gluing n-simplices together builds n-dimensional objects.

Tetrahedrons make up 3D objects

Since any surface can be cut into curved triangles, and it’s reasonable to ask if the analogous fact holds in higher dimensions: can any n-dimensional space be cut into n-simplices?

Mathematicians initially speculated that the phenomena they’d observed in dimensions one and two would generalise to all dimensions. This belief came to be known as the Triangulation Conjecture.

Decades of research failed to deliver a proof. Then, breakthroughs in the 1980s revealed examples of four-dimensional objects which can’t be cut into 4-simplices. But in 2012, the Triangulation Conjecture was finally proved false for all dimensions greater than four. The mathematical universe has some very strange shapes!

Disproving the Triangulation Conjecture is a triumph of curiosity-driven research, and the truth now sits on humanity’s bookshelf. It may rest there quietly. Then again, maybe some 26-dimensional space with no triangulations will lead to a cure for cancer.

You never know.

Understanding firewall rules is time consuming, complicated and hard. The majority of people know how to turn their firewalls off, but do these people know exactly what it is they are doing or even why?

Probably not, nor could they be expected to.

Viral Maniar, APR.Intern and RMIT Masters student, spends his days deciphering the complexity of firewall rules. He undertook an internship at Biarri Networks 鈥� an innovative commercial mathematics company 鈥� to investigate new methods of visually representing firewalls.

Firewalls are built with a set of do or do not allow rules, usually concerning where a computer is connecting from and what it is trying to do. Two or three rules are easy to follow and understand, however sometimes a firewall might have to follow a thousand (sometimes even a million!) rules.

Finding patterns or irregularities becomes harder the more rules there are.

Visualisation tools help people to “see” the data. By clustering common connections and using听colouring schemes in the visualisation, patterns that may be indicative of intrusions 鈥� such as the use of restricted communication protocols 鈥� can be clearly identified.

鈥淗umans are much better at seeing some types of irregularities than computers,鈥� Viral says. 鈥淏uilding a visualisation tool makes finding irregularities more interactive and aids in detecting security loopholes in some firewall rules.鈥�

During his internship Viral developed a web application able to load different sets of firewall rules visually. Someone using this application is able to modify and filter how the rules appear (using colour schemes etc.) to discover if any loopholes or irregularities exist.

鈥淰iral, Biarri and NBN Co used the tool to review a set of firewalls in use at NBN Co,鈥� says Paul Kennedy, CEO Biarri Networks. 鈥淣BN Co are using the results to inform firewall management procedures.鈥�

Viral has recently gained employment as a security analyst for a major consultancy and says having the internship experience under his belt made all the difference, 鈥淚 learnt a lot about firewall security and firewall management and gained invaluable industry skills.鈥�

Intern:听Viral Maniar, RMIT University听
Industry Partner:听Paul Kennedy, CEO Biarri Networks听
Academic Mentor:听听Assoc. Prof. Serdar Boztas, RMIT University

Australia’s Chief Scientist has unveiled an ambitious agenda for change to increase the focus on science, technology, engineering and maths (STEM) skills to help secure the country’s future prosperity.

Professor Ian Chubb AC has outlined a number of recommendations to the Federal Government in a national science strategy to build a more competitive economy.

His call for action involves a long-term strategic view from the classroom to laboratories and the boardroom to create and foster STEM skills, which he says are relevant to an increasingly wide range of occupations.

The strategy outlines a broad approach across four main areas, including building competitiveness, supporting high-quality education and training, maximising research potential and strengthening international engagement.

The strategy has been welcomed by the 今日吃瓜.

Institute director Professor Geoff Prince said a coherent national strategy is necessary.

“We absolutely have to have one. We’ve got ourselves in the situation we’re in through the absence of strategy and absence of strategy is not going to get us out that position,” he said.

Professor Prince agreed that mandating maths subjects for year 11 and 12 students would not be productive, but said studying mathematics is beneficial in a number of ways.

“I’d like [students] to [study maths] because they were engaged and because it was something that was going to be good for their life skills and their career skills,” he said.

He said the system is under-resourced, with 40 per cent of classes in years 7 to 10 not being taught by qualified maths teachers.

“I think we’re actually in that vicious spiral where the numbers of maths graduates are being choked by the declining numbers of kids taking intermediate and advanced maths in year 12,” he said.

“That’s being choked because of a failure to staff schools with inspiring maths teachers, and inspiring maths teachers can’t be had because there aren’t enough maths graduates.

“It’s at a critical level now and unless we act, it’s only going to get worse.

“The consequences, I think, would be absolutely disastrous.”