# Maths

In Episode 9 of Ever Wondered?  Series 2, Dr John Watt finds out about the unsung hero of the science world – mathematics. Through a series of discussions with mathematicians, scientists and engineers, John finds out how maths is a fundamental tool to understand the natural world and the man-made world.

## Maths modelling the natural world

At Victoria University of Wellington, mathematician Dr Dillon Mayhew begins by telling John that maths is the most special of sciences. He explains that maths is different to other sciences as it doesn’t rely on experimentation and observation. Maths provides knowledge through logical deduction. Using a whiteboard and marker, Dillon uses a simple example to illustrate this to John. He discusses how the natural world seems to run on maths and, in turn, how maths is useful for modelling the natural world. John and Dillon then head outside with a tape measure, stopwatch and apple to do some basic physics, revisiting Sir Isaac Newton’s theory and seeing a mathematical formula working in action.

Watch Episode 9, Part 1

## Maths, biology and evolution

Mathematics can also be used to understand the complex field of biology. John travels to Auckland Zoo and meets up with Professor Mike Steel, Director of Biomathematics Research Centre, University of Canterbury, who explains how mathematics has become entwined in the field of evolution.

Professor Mike Steel outlines to John how the abundance of genetic data being produced by modern sequencing techniques means that mathematics, computer science and statistics are all required to understand it. Mike is finding ways to use maths to make sense of questions posed by this new genetic data. Using a basic deck of playing cards, Mike explains how two different genetic sequences are compared to establish the level of relatedness between species. He discusses how his ingenious mathematical solution helped answer an unexpected question about the evolutionary tree. Fossil evidence supported that birds evolved from reptiles, but genetic data suggested that birds were more closely related to mammals. Mike explains to John how he used maths to determine that birds were in fact more closely related to reptiles than mammals.

Watch Episode 9, Part 2

## Game theory and the electricity market

Optimisation is all about finding the best way to do things, and it lies behind everything from the sequencing of traffic lights to the price of rugby tickets. Professor Andy Philpott is trying to figure out how optimisation can be used in the New Zealand electricity market. John finds out how this works and explains one of the theories used in optimisation – known as game theory – by playing noughts and crosses. Andy then takes John to the Electric Power Optimisation Centre at Auckland University to play more games – this time, a computer game designed to provide insight into the very complex nature of our electricity market. Fellow gamer Dr Golbon Zakeri uses her mathematical knowledge to investigate whether changes to the market may have undesirable results and whether swapping assets between power companies can actually keep power prices down for the average Kiwi.

Mathematics is a language in its own right, with poetry, beauty and immense powers of problem-solving. It seems it can also be one of the best ways to describe the world around us.

Watch Episode 9, Part 3

### Activity idea

In conjunction with this episode of Ever Wondered?, your students may enjoy these activities that use maths to find out more about our natural world.

In this activity, students use real-time data from Argo scientific floats to study ocean currents.
Using Argo data

In this activity, students explore the transit method of searching for planets. They plot graphs of light measurements from stars, searching for dimming that indicates the presence of a planet, and calculate its size.
Hunt the planet

Your students may also be interested to find out more about DNA sequencing and evolutionary biology. In this video clip, students can see how DNA sequencing is being used to understand fern evolutionary history.
Using DNA analyses for classification

DNA sequencing is now routinely undertaken in a huge range of research projects. In this animation on the Biotechnology Learning Hub, students can watch a step-by-step guide to sequencing DNA in the lab.
www.biotechlearn.org.nz/themes/dna_lab/sequencing_revealing_the_dna_code