Teachers of mathematics should be enthusiastic about the subject and it is sure to get transmitted to students, said Robert L. Devaney, professor of mathematics, Boston University, who is striving to get more and more students interested in mathematics.
High school students, who see his work at his mathematical laboratory in the U.S., wonder whether the beautiful images that he has created have anything to do with mathematics, he said. Math Field Days, a workshop that he started about 20 years ago, brings in 1,000 students a year to his department. “We have to tell the students what is happening in mathematics”, he said.
In Kochi as guest faculty member at the International Conference and Workshop on Fractals and Wavelets organised by Rajagiri School of Engineering and Technology,
Prof. Devaney, who is the president of the Mathematical Association of America, said that even though students spend 12 years learning mathematics, they are usually unaware of the latest developments in the field.
Students learn mathematics that is centuries old and have little exposure to the present day systems. The curriculum demands that they learn all that, but teachers must give them an insight into the new world, he said.
Prof. Devaney, who has spent most of his time researching dynamical systems (a mathematical concept that describes how one state develops into another state over the course of time), said it was the arrival of computers that revolutionised this system. Earlier, few mathematicians could carry out the infinite number of calculations needed to be done.
Any process that evolves in time can be chaotic. “Our research helps create a model out of the data and sometimes even predict how the process will behave, except in some highly unpredictable situations like climatic changes or a stock market”. More variables that affect these systems make it unpredictable, he said.
Mathematics is part of everything in nature, but people fail to recognise it. It builds the framework of many physical, biological and social systems.
Differential equations are related to biological rhythms, he said. For several centuries, scientists believed that chemical reactions always ended in a steady state of equilibrium, till chaos was found to be very much a part of these reactions.
Prof. Devaney, who has written and edited many books for undergraduate students of mathematics and has been awarded for his teaching abilities, says pure mathematicians do not normally pursue the application of the subject.
Though associated with some theatre productions as Chaos Consultant and also as mathematics consultant for a Kevin Spacey film Twenty One, he brushes aside these projects as not being really rooted in mathematics. Most of what we see around in nature is deeply rooted in dynamics and students should be able to see the beauty of it.