Dr Toft, who received his Mathematics doctoral degree at Te Whare Wānanga o Waitaha | University of Canterbury’s (UC), is already training AI in his specialty of matroid theory, which is concerned with the dimensions of a mathematical structure.
“Text produced by AI often sounds good but is incorrect. It is especially bad at producing correct mathematics,” Dr Toft says. “Since AI is only as good as the data that is fed into it, we provide that data. Essentially, we are given the AI's response to a maths question and correct it whenever it has made errors.”
Dr Toft has returned to live in Ōtautahi Christchurch after a short stint back in his hometown of Nelson following his doctoral thesis. He’s now working remotely for US platform Outlier, which uses experts such as him to help train AI in various disciplines.
“The reason I studied mathematics is that there are so many beautiful, surprising connections and patterns that show up in matroid theory, and in other areas of maths. I find it really awe inspiring that the universe has all these patterns buried in it, waiting to be discovered.”
For the uninitiated, matroids appear in many different areas of mathematics. Dr Toft cites linear algebra and graph theory as examples.
“This is a very fundamental field of mathematics and is used everywhere from ecological modelling to computer graphics and graph theory, which is concerned with the structure of networks, both of which have matroids underlying them.”
Dr Toft says understanding more about matroids can lead to deeper understanding of the connections between these fields. In simple terms, he describes matroids as all about dimensions.
“In general, given a set of points, a matroid describes the structure of these points by describing the dimension of any subset of the points. As you add more points, the number of ways that they can be arranged grows exponentially. There are around 380,000 possible matroids with nine points, and trillions of possible matroids with 10 points although the exact number is not known.”
Before enrolling at UC as a full-time student, Dr Toft became familiar with the University as a teenager taking a STAR course in mathematics during his final year of high school in 2015. The STAR programme is available for Year 13 secondary school students to try their hand at first-year degree-level university courses. Both on-campus and distance courses are offered, and completed STAR courses can normally be credited towards a university degree later. He went on to tutor STAR mathematics while studying at UC.
“It was a fantastic opportunity to engage with students who are just starting out on their journey in mathematics,” he says. “It was also a great way to deepen my own understanding – trying to figure out how to teach something is one of the best ways to learn it yourself.”
Sustainable Development Goal (SDG) 4 - Quality Education.
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