Look at this beautiful video almost 50 years old. Thinking and learning in mathematics!
This is a bit of a longer article I found in + Plus Magazine:
Where were your most creative experiences at school? In art class? In music? English? In your maths lesson? That last one might not be the obvious choice for many of us, unless you were lucky enough to have a really inspiring maths teacher. But that is exactly the type of opportunity we are hoping to create for maths students aged 7-16 as part of the project, Developing Mathematical Creativity, with our sister site, NRICH.
One aspect of the project that we are particularly excited about is highlighting the role of creativity in mathematics research. All mathematicians tell us that doing original mathematics is highly creative – but what exactly do they mean by that? We asked some researchers from a range of subjects about the role of creativity in their work.
Working within constraints
We started with David Berman who has a very interesting perspective on creativity. As well as being a theoretical physicist at Queen Mary, University of London, he also has a long standing collaboration with the Turner prize winning artist, Grenville Davey. Deconstructing the artistic idea of creativity, Berman told us that rather than an unbridled release of ideas where anything is possible, beauty comes from creating work withing very tight syntactic constraints. “Think of music: the tight system of key and chord makes music very constrained and yet capable of amazing emotional power,” he said. For example Schoenberg’s* experiments with atonal music, though completely new and boundary breaking, were far from unconstrained. “Maths is like this. There are enormous syntactic constrains but still enough freedom to say something new. The beauty lies in between the constraints of syntax and the freedom of meaning.”
How the ancient Greeks shaped modern mathematics – video animation
Chapter 1: The language of the universe
Chapter 2: The genius of the east
Chapter 3: The forntiers of space
Chapter 4: To infinity and beyond
Chandler Davis’s chapter. Part of the book The best writings on mathematics (William P. Thurston and Mircea Pitici)
World of Mathematics
Dive into a colourful and engaging world, discovering some of the most exciting and curious mathematical ideas. Using interactive games, animations and countless illustrations, advanced mathematics becomes accessible to both children and adults.
Topics range from fractals to infinity, prime numbers, game theory, group theory and quantum mechanics.
2013 Lovie Awards Gold Winner: Best Education Website
Inspirational for my idea
In 2010 Taschen republished the work in a facsimile edition. (Wikipedia)
See more here
“The fact that we have never read an endless book, or counted to infinity (and beyond!) or made contact with an extraterrestrial civilisation (all subjects of essays in the book) should not prevent us from wondering: what if? … Literature adds a further dimension to the exploration of those pure possibilities. As Nemirovsky and Ferrara suggest, there are numerous similarities in the patterns of thinking and creating shared by writers and mathematicians (two vocations often considered incomparable.)”
Daniel Tammet: Thinking in Numbers
From the extraordinary blog: brainpicker and her 13 must read books on science and technology books 2013