Written specifically for those working in the mathematical sciences, this book provides a proven process for idea generation and a wide range of mathematically oriented examples. In this interview with Higham and Sherwood, they discuss creativity, their techniques, and how they relate to the mathematical sciences.
Q: What is the history of your partnership? How did you meet and decide to start working together?
A: We met at a creativity workshop in 2011, sponsored by the Creativity@home initiative of the Engineering and Physical Sciences Research Council (EPSRC). The workshop was for a cross-disciplinary EPSRC-funded research group that Nick was part of. We have since collaborated on five more creativity workshops: four on mathematics and computer science, and one for the SIAM leadership on formulating SIAM's strategy for the next few years.
A couple of years ago, we decided to collaborate on a book on creativity. Dennis's previous books on the topic are over 20 years old and we felt that a book building on our experiences and containing mathematically oriented examples would be useful.
Q: How did you develop the six-step process?
A: I (Dennis) had read Arthur Koestler’s “The Act of Creation” and his description of creativity as the formation of new patterns from existing elements. I found that to be very powerful with regards to understanding ideas that had already been discovered, but I couldn’t see how to use that insight to generate ideas, until December 1998. I wanted to get a Christmas present for my elder son – a board game called Tri-Tactics, in which the skill is in how each player places the pieces at the start of the game. I went to a game shop and saw a chess set in the window. In chess, the pieces are in fixed initial positions; in Tri-Tactics, a player can choose. That was it!
The conventional placing of chess pieces is a feature of chess as we know it. How might this be different? Suppose you could put the bishop where the knight usually is? That’s a new pattern, which according to Koestler, represents a new idea. By bringing together Tri-Tactics and chess—a process Koestler calls bisociation —I solved the problem of designing a process to generate ideas! The “how might this be different?” part of the process can be applied in many situations, even without following the full process, and we used it many times in developing the content and structure of the book.
Q: Has holding workshops led to any changes to the process?
A: The fundamental six-step process has stood the test of time remarkably well. It has resulted in the generation of great ideas by teams of people from organizations of all types and sizes. And it works for young people at school, too!
Q: How do you counter the objection that “creativity is a wonderful gift—and you can’t reduce it to a process!”?
A: Yes, we encounter that a lot. Our approach is ‘both/and’ rather than ‘either/or’. Some people can run faster than others, some have a greater aptitude for music than others. Those natural abilities are indeed wonderful gifts. But even the fastest runners benefit from training and coaching; even the tone deaf can, with diligence and practice, learn how to play a musical instrument.
So, with creativity: Yes, some people are full of ideas, others less so. What our process does is provide an intellectually sound basis to increase the likelihood that a process of well-directed search will result in an interesting idea. That doesn’t replace or exclude the magic. Rather, it supplements it.
Q: The process you describe emphasizes the importance of teamwork. Is it relevant to mathematicians who work by themselves?
A: We talk in the book about the myth of the lone genius. In fact, it is extremely rare for great ideas to be produced in isolation. Creativity is not only far more common but also much richer when people speak to each other, ask questions of one another, and share knowledge with one another. Even the mathematician working alone reads other people's papers, talks to colleagues at conferences, and references papers and proposals; and all these activities provide different perspectives that feed into the creativity process.
Q: How specific is the book to the mathematical sciences?
A: The principles of creativity are general, as are four of the five chapters in the book. The other chapter provides 19 notable examples of how creative mathematical ideas were generated, or might have been generated, using the techniques described in the book. The protagonists include Carl Friedrich Gauss, Henri Poincaré, Olga Taussky-Todd, and James Wilkinson, as well as some contemporary mathematicians.
Q: Briefly describe the theory behind your techniques.
A: If, with hindsight, any idea can be decomposed into pre-existing elements—which is what Koestler stated—then it must be possible to combine existing elements in many different ways, each of which is in principle a new pattern and a new idea.
In practice, of course, there are two big problems. Every fragment of knowledge is, in this sense, an element. Most of the huge number of combinations of these many elements will be of no interest. So, the search for the new pattern needs to be intelligent— selecting the elements with some care, then identifying the patterns that are good and eliminating the bad. And that identification is all about the process of evaluation, which requires balanced, bias-free judgment, as discussed in the last chapter of the book.
Q: What advice would you give to leaders who wish to encourage creativity in their teams?
A: We believe that a key role of a leader, at any level, is to build a local environment in which everyone’s creativity can flourish. For that to happen, two things need to be in place. First, everyone must be familiar with, and confident in using, the creativity processes we describe, for that ensures that all the team are equipped with the right tools and techniques. But there’s something else too. Throughout the book, we emphasize that although individuals can be creative by themselves, creativity is far more effective and productive within teams. That’s all about how individuals interact with each other, about the team culture—a subject we address in the book’s last chapter. So perhaps the best advice we can give a leader in this regard is to read the book—and then act on it!
How to Be Creative: A Practical Guide for the Mathematical Sciences is available for order here.