I “discovered” Ian Stewart both from his writing about mathematics and from his writing with Terry Pratchett and Jack Cohen. Unfortunately, the Science of Discworld books are not (were not) available in the US but I got hold of them, eventually, over several trips home to England. In the US I could get hold of Wheelers which is a science fiction book written with Jack Cohen (ya for the local library). Finally, I read Nature’s Numbers several years ago. So I was keen to read his latest Math book Why Beauty is Truth which was published this April. Stewart also blogs about the book.
I know I am nerdy and odd in that I like reading books on math and physical sciences. I get teased because I think holiday reading is books like “e – the story of a number“. I enjoy well written books about all sciences and as I am a physical scientist, generally prefer books on chemistry and mathematics. They must be vaguely understandable though as I do not want to feel stupid when I read. I want to stretch my scientific ideas and come a way from a book excited about new concepts and new ideas. One of the problems with reading technical books is that is hard for me to explain what they are about as my understanding, especially after a first reading, is very limited. I am going to try.
My latest science reading was “Why Beauty is Truth?“. The title comes from Keats’s poem Ode to a Grecian Urn which Stewart quotes part of on the frontispiece. The book is about how modern mathematics got to where it is today by looking at the history of both mathematic thought and the mathematicians who made the steps forward in understanding. They do seem to have been a bunch of characters. The saddest story is that of Niels Henrik Abel, who could not marry his sweetheart because he did not have enough money as he could not get a job. He published his mathematical proofs but was ignored by the establishment and then died of TB before he was thirty at the same time as being finally offered a position in Berlin.
Symmetry as defined by mathematicians is not quite the same thing that I understood by symmetry. It is to do with how things (numbers, shapes, groups, matrices) can be transformed without changing. According to my science dictionary symmetry (as Stewart refers to it) is:
A function of several variables is symmetric if it is unchanged when any two of the variables are interchanged.
Stewart defines it as:
A symmetry of some mathematical object is a transformation that preserves the object’s structure.
He then goes on to give a great example using an equilateral triangle with has all sides the same length and all three angles the same size.
If you rotate the triangle through 90 o, a corner point is now facing to the left showing that is not a symmetrical transformation of the triangle so you can see that the triangle has been moved. Rotating the triangle through 120 o however does maintain symmetry as you would not be able to tell that the triangle had been moved, unless the corners are marked in some way.
In turns out that mathematicians can transform many objects some of which are very complicated. Some of these concepts and manipulations allow physicists to understand quantum theory and string theory. Stewart is very excited about the link between math and physics. He is also keen on the fact that the mathematics used to do these transformations is beautiful. Ugly maths is false.
The true strength of mathematics lies precisely in this remarkable fusion of the human sense of pattern (“beauty”) with the physical world, which acts as both a reality check (“truth”) and as an inexhaustible source of inspiration. We cannot solve the problems posed by science without new mathematical ideas. But new ideas for their own sake, if carried to extremes, can degenerate into meaningless games. The demands of science keep mathematics running along fruitful lines, and frequently suggest new ones.
I intend to read more of Stewart’s earlier math books. I think I might start with Flatland or Flatterland as these seem interesting as they deal with the idea of hidden dimensions. I remember when my brother was doing his degree in Maths (at the same institution that Stewart is a professor – I don’t know if their paths crossed at all) he told me he was doing problems with multiple dimensions. At time, and even now, I could not concieve of more than four and thought it was some kind of mathematical game. Having read Why beauty is truth? I have a better understanding of what my brother might have been doing. Enough, in fact, to make me slightly envious that I had not realized until now that this could be done and what it all meant.
Not that it matters much. My brother went on to do a PhD in Art History, using his advanced mathematics [snark*] to study JMWTurner’s ideas on perspective.
*Actually bro’ said that anyone with high school math** could do the math needed in his thesis.
**Actually he said O-level maths*** which was the public examination that most English children took then at sixteen years old.
***Why do Americans do math and Brits do maths?