A Mathematician’s Lament by Paul Lockhart

https://www.maa.org/external_archive/devlin/LockhartsLament.pdf

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

misunderstood.

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

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

misunderstood.

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

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