In 2012, the UK government published a list of eight Technologies in which the UK is “set to be a global leader”. In this 2 part series I will detail how maths is essential for ALL these great technologies.

The eight great technologies are:

- big data and energy-efficient computing
- Satellites and commercial applications of space
- robotics and autonomous systems
- synthetic biology
- regenerative medicine
- agri-science
- advanced materials and nanotechnology
- energy and its storage

**Big Data**

Big Data is a term used for data sets that are so large or complex that traditionally processing applications are inadequate.

In the UK, examples of where Big Data arises include data on prescription drugs (connecting origin, location and time of each prescription) and well as joining up data in order to allow authorities to recognise certain patterns and therefore improve public services accordingly.

There is a large challenge in visualising, modelling and understanding Big Data. How do we experiment on the systems that generate it and how do we control these systems? The mathematical challenges behind these questions require automation, which in turn relies on mathematical algorithms.

Mathematical techniques to deal with big data are being developed and researched, including network theory. Network theory describes nodes, that are linked together by edges. When dealing with large networks, it is hard to identify clusters – groups of highly interlinked nodes – or to segment the data into groups that share common features. However, network theory provides algorithms for both these problems.

Furthermore, more obscure areas of maths can aid in the analysis of Big Data, which can also take the form of images:

**Algebraic topology** is concerned with studying shapes using algebra and plays are very useful role in classifying images;
**Category Theory**, which investigates mathematical structures and concepts on an abstract level, can be used to split up an image in order to analyse it and see how the various components fit together.

This can aid machines ‘perceive’ what the images are and hence make decisions about it.

### Satellites and Space

There are many areas in which mathematics can aid in space exploration, including:

- GPS;
- Data compression for transmitting messages;
- Digitising and coding images;
- Correcting errors in codes for accurate transmissions;
- ‘Gravitational boosting’ for optimal trajectories;
- Use of Lagrange points for the strategic placement of satellites;
- Understanding and controlling the dynamics of satellite systems in order to efficiently place orbits.

### Robotics and Autonomous Systems

Numerical methods developed by mathematicians are used to stimulate movement and control robotic systems. Furthermore, mathematics can be applied the field of robotics through machine learning algorithms, pattern recognition techniques, neural networks, which mimic simple nervous systems, and computer vision.

### Genomics and Synthetic Biology

Genomics is a field in biology in which DNA sequencing methods and bioinformatics are used to sequence, assemble, and analyse the function and structure of genomes. Genomes are the complete set of DNA within one cell in an organism.

Genomics has relied on a wide array of mathematical tools, for example hidden Markov chains, pattern recognition, probability and database analysis.

In addition, graph theory, braid theory and knot theory have proved to be invaluable in studying coiled DNA. Differential geometry has also been used to study the relation between writhe, twist, and linking number.

Finally, network theory has been used to study interactions between genes and proteins; the nodes of the networks in this case are genes or proteins and the edges describe allele combinations that control specific phenotypes.

Sources: 1 | 2 | 3 | 4 | 5 | 6

This is just a short summary of how mathematics can play a role in these technologies. Stay tuned for part 2! Hope you enjoyed M x