Title 4 – KQ 7 In what ways Knowledge production and acquisition require “ suspension of Disbelief” in area of Mathematics?
Mathematician , G H Hardy in his book , ‘ A Mathematician’s Apology ‘ writes that “ A mathematician like a poet or a painter is a maker of patterns . I am interested in mathematics only as a creative art.” In his later years Hardy admitted that his own time as a creative mathematician was finished and that “Exposition, criticism, appreciation, is work for second-rate minds.
In his essay “The Burden of Skepticism,” published in 1987 Carl Sagan posits , “If you are only skeptical, then no new ideas make it through to you. You never learn anything new. But every now and then, maybe once in a hundred cases, a new idea turns out to be on the mark, valid and wonderful. If you are too much in the habit of being skeptical about everything, you are going to miss or resent it, and either way you will be standing in the way of understanding and progress.On the other hand, if you are open to the point of gullibility and have not an ounce of skeptical sense in you, then you cannot distinguish the useful as from the worthless ones.”
Successful Mathematicians balance the two modes of thought of “ Suspension of Disbelief” and “ Skeptism” that direct them further to ideas and possibilities. Mathematicians are driven by very creative and aesthetics instincts. Both for problem solving and Inquiry , mathematicians require creativity . Going beyond ordinary thinking in their work enables them to look for options, to choose, to make judgements on their way to solutions.
Mathematicians are adept at looking and finding the pieces or themes that have nothing to do with each other , and yet when brought together they connect and unite in ways that astonish us. For example Fermat connects the world of primes with the world of squares through his equation. It is sheer “ leap of faith” to see associations in two totally unrelated seemingly disparate groups and come up with a simple and elegant equation that is beautiful, simple , useful and full of pleasant surprise.
In “The Life and Survival of Mathematical Ideas”, the British mathematician Michael F. Barnsley discusses how a specific mathematical topic can be viewed as a “creative system”: The forms emerging from this system are fractals. “The mind of a mathematician”, he argues, “provides a locus for creative systems, a place where mathematical structures live and evolve.” He makes a parallel between biological forms, such as plants, and mathematical forms. An example of mathematical forms are the geometric building blocks of points, lines, and planes; their “DNA” consists of the equations that describe points, lines, and planes. The forms evolve and adapt as they are passed on through generations of mathematicians’ minds.
Creativity in Mathematics and the Arts – Marcus Du Sautoy
Rex Jung – Creativity and the Brain