Muscle pain for the brain - math

I received this letter during the week.

Hi Zac,
I was thrilled by the enthusiasm and clarity of your blogs about mathematics. I got here because of a small quest of mine and maybe you can help me.

Thanks for the kind comment. I'll try to help.

I want to create a "muscle pain for the brain"- package for my best friend (28, architect). She told me she hasn't had a good challenge for her brain for long time. She loves mathematics, would even like to study it, but seems to hesitate to really get into it at the end.

I'm an Artificial Intelligence student and nearly everyday stunned by the beauty of mathematics and the mathematics of beauty. But I don't know any books or other material that shows the connection strongly, clearly and in a visual way. I was thinking about the mathematics behind the architecture of the Moores for instance (Alhambra in Spain), or the mathematics in biological phenomenon. But also books that fulfill the reader with love for the beauty of mathematics as a system would be very good.

Do you have any ideas? I would be grateful beyond words and numbers!!

All the best,
Kiki (from Amsterdam, the Netherlands)

The classic book for brain sprain in the mathematics/art/music realm - and it's fascinating - is Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter. According to the Amazon blurb:

Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought.

So with your A.I. background, I imagine there will be many topics in that book that you will be able to discuss with your friend.

There are myriad possibilities in the art/math realm, like Math and the Mona Lisa: The Art and Science of Leonardo da Vinci.

The history of mathematics can always be a good springboard to inspire further study. How about something like Mathematics and its History. One of the reviews says:

"A beautiful little book, certain to be treasured by several generations of mathematics lovers, by students and teachers so enlightened as to think of mathematics not as a forest of technical details but as the beautiful coherent creation of a richly diverse population of extraordinary people...His writing is so luminous as to engage the interest of utter novices, yet so dense with particulars as to stimulate the imagination of professionals."

Ian Stewart is an inspiring writer of a broad range of mathematics books. One of my favorites is Letters to a Young Mathematician.

Then there are always mathematics puzzles and games - remember Rubik's Cube? There are some interesting mathematical ways to approach solving the cube.

But I still think the best bet is Gödel, Escher, Bach.

Good luck with your quest.

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