Math Consciousness


A Mathematician’s Lament by Paul Lockhart

The first thing to understand is that mathematics is an art. The difference between math and
the other arts, such as music and painting, is that our culture does not recognize it as such.
Everyone understands that poets, painters, and musicians create works of art, and are expressing
themselves in word, image, and sound. In fact, our society is rather generous when it comes to
creative expression; architects, chefs, and even television directors are considered to be working
artists. So why not mathematicians?

Part of the problem is that nobody has the faintest idea what it is that mathematicians do.
The common perception seems to be that mathematicians are somehow connected with
science— perhaps they help the scientists with their formulas, or feed big numbers into
computers for some reason or other. There is no question that if the world had to be divided into
the “poetic dreamers” and the “rational thinkers” most people would place mathematicians in the
latter category.

Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical,
subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or
physics (mathematicians conceived of black holes long before astronomers actually found any),
and allows more freedom of expression than poetry, art, or music (which depend heavily on
properties of the physical universe). Mathematics is the purest of the arts, as well as the most

So let me try to explain what mathematics is, and what mathematicians do...​

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That is a nice video, but she did make one small blunder. Multiplication by (1+i) is not a pure rotation by 45 degrees, which is (1+i)/sqrt(2)!

Maths has certainly acquired an unnecessarily off-putting style, and it is interesting to know what it would be like to learn with some of her approach mixed in. However, I fear I might just get too distracted by her to think about what she was saying!