Easy Recipes for Understanding Complex Maths

Source: Times Higher Education, Jun 2015

“mathematics is there to make difficult things easy”

Cheng touches on many challenges faced when learning maths: thinking that you’re stupid because you don’t understand something; feeling demoralised when you keep getting the wrong answer but don’t know why; and (as I frequently tell my students) the importance of understanding the principle behind the process rather than simply memorising the process.

Written by a successful young woman who openly admits that there were times when she did not “get it”, and who uses examples that girls, in particular, can relate to (such as discussions about relationships), this is as girl-friendly as maths gets. Importantly, however, the maths is not watered down. Category theory is an advanced topic in mathematics that is more often encountered in graduate than undergraduate studies, and it is a remarkable achievement to be able to present it so accessibly for a lay and student readership.

The final chapter, “What category theory is”, brings it all together. It begins with a Venn diagram that links belief, knowledge and understanding – which makes your brain ache as you try to work out whether it is possible to believe something without knowing or understanding it – and concludes with a short discourse on mathematics education in which

Cheng laments that only up to a point do we encourage schoolchildren to ask why mathematics works. She urges us not to stifle young people’s quest for the illumination of mathematical principles, but rather to seek to explain and demystify, helping to lay the groundwork for future mathematical discoveries to occur.

What gives her hope? “Small children: their natural compassion, openness, excitement and curiosity. We expect children to learn from us, but I think we have a lot to learn from them, too.”

 

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