Invitation to Mathematics

An Invitation to Mathematics

I just finished reading  An Invitation to Mathematics.  As a non-professional, the book was a rewarding and  motivating experience to read. Each of the chapters can be read independently. Each chapter starts with elementary concepts then quickly dives into deeper and more complex mathematics. The diverse connections between different areas of Mathematics, the frequently unexpected relationships discovered and the applications are explored.

I  was frequently (and sadly quite quickly) out of my depth but still both amazed and motivated to learn more. Each chapter has a number of citations and some have appendices to assist the confused reader.

I was particularly captivated by chapter The Lion and the Christian, and Other Pursuit and Evasion Games by Professor Bollobas. The dissection of the Lion and Christian pursuit game was clear and the extension from sequential discrete game to continuous was amazing.

The final chapter, however, gave me particular joy.  I was amazed to the see the Mandelbrot set emerge in the badlands of the space for the iterated (translated and rescaled) cubic polynomial. It inspired to rush out and code in Mathematica to see this for myself. I hope I can do this when time permits.  In addition the exhortation of the author to give up classifying Mathematics into useful and useless for pursuit of “truth” and understanding was a wonderful end to the book.

Finally, the authors expression of the experience in discussion with students of the frequent advice given to young interested people to pursue non-mathematical pursuits rather than useless Mathematics resonated with me.  I was not a star, but I loved Mathematics (still do). However, my father told me, “what good is a Mathematician to the world?…you should do something useful”.  I followed my father’s advice and did not pursue Mathematics. My father’s advice was well intentioned.  I have (I hope) pursued an honorable path (whether it is useful  that is another question).

I hope young people today take up the invitation and that those people like me who are beyond this call can still delight in the wonder that is Mathematics.