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Can Mathematics be a creative pursuit as well as a logical one?

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Following on from his successful TedxGreenwich University talk, Senior Lecturer of Mathematics at the University of Greenwich Neil Saunders expands on how Mathematics can be a creative subject, and how moments he has witnessed over the course of his life and career have supported this idea

Neil Saunders

Daydreaming within the realm of Mathematics

Neil Saunders’ recent TedxGreenwich University talk – Daydreaming, Mathematics and our Creative Future – has received over two thousand views on YouTube.

In his talk, Neil discusses the relationship between Mathematics and a topic that may not usually be associated with the subject – daydreaming. He describes how daydreaming accesses the subconscious, and so can assist with problem-solving. He explains there have been many times where he has found a solution to a problem he has been facing whilst his mind was focused on something else. For Neil, this is how solving a problem can be a creative process.

Many areas of our lives require problem-solving skills. We are at our best problem-solving capacity when our minds are relaxed and free to make connections and creatively find solutions.

He remembers an occasion as an undergraduate student where he struggled with an assignment question until the early hours of the morning, only for the answer to come to him while he was asleep through a dream. Neil says this is just one example of how the brain, or the subconscious, is continually working on problems.

At the University of Greenwich, Neil has witnessed his mathematics students solving mathematical problems in innovative ways, which further leads him to believe the path to the solution is often as important as the solution itself. He says mathematics in general provide people with the ability to see similar things from different perspectives which encourages mathematicians to think in more creative ways.

Pure mathematics is a poetic language

Neil’s research is primarily in pure mathematics – his view is that it underpins almost all of the natural sciences. His particular area of research is in geometric representation theory, which is the study of the ways symmetry manifests in higher dimensional geometric objects and how it can be quantified, and he has recently published a work describing functions between higher dimensional objects, called algebraic varieties. He believes research into pure mathematics can enhance the understanding of the technical and scientific aspects of our world, giving the analogy, what pure mathematics to science is and what creative writing, or poetry, is to language: it allows intricate things to be succinctly and beautifully expressed.

Before commencing his post at Greenwich, Neil held several post-doctoral research fellowships at Bristol University, the École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland and the University of Sydney, where he also completed his PhD.

A powerful subject

Empowering students and cultivating in them capacities to spot patterns and see things from different perspectives is something quite powerful.

In Neil’s experience, students appreciate being taught mathematics by someone who is actively pursuing research into it. His enthusiasm for his subject feeds into his teaching, which he hopes proves inspiring for his students.

Through his work and research, he hopes to play a part in breaking down the conceptions that Mathematics is only a subject accessible to people who are somehow mathematically gifted, and so encourage more people to take up this powerful – and empowering – subject.