Negativity

Peter Cameron's Blog 2026-03-04

It is not unusual for a mathematician, having proved a theorem, to devalue the creativity that went into it. Once a theorem is proved, it is obvious, at least to its prover; it is easy to think that anybody could have done that. So this is common among mathematicians, and is sometimes referred to as impostor syndrome.

What is much more unusual is for a mathematician to disown the result. One of the few cases of this was L. E. J. Brouwer; once he was converted to the philosophy of intuitionism, he had to disown some of his best theorems, including the famous “fixed point theorem”, which used proof by contradiction (unacceptable to intuitionists).

Is this more common in other fields? I don’t know, but it is true that in many of Paul Simon’s early songs, he is extremely negative about his own craft of poetry and songwriting. This is someone who, in 59th Street Bridge Song, has to beg a rhyme from a lamp-post. Here are some more examples.

The Sound of Silence My words, like silent raindrops, fell And echoed in the wells of silence

Homeward bound All my words come back to me In shades of mediocrity Like emptiness in harmony

I am a rock I have my books And my poetry to protect me

Kathy’s Song And a song I was writing is left undone I don’t know why I spend my time Writing songs I can’t believe With words that tear and strain to rhyme

Wednesday morning, 3am My life seems unreal, my crime an illusion, A scene badly written, in which I must play

The Dangling Conversation Like a poem poorly written We are verses out of rhythm Couplets out of rhyme In syncopated time

Bleecker Street The poet writes his crooked rhyme Holy, holy is his sacrament Thirty dollars pays your rent On Bleecker Street

Hazy Shade of Winter Funny how my memory skips While looking over manuscripts Of unpublished rhyme Drinking my vodka and lime

Have I mmissed anything?

The amazing thing is that all this negativity gives power to some of Simon’s best songs, and indeed some of the most beautiful songs of that very creative time. Despite what the words say, there are no couplets out of rhyme or words straining.

I have long felt that there is a kinship between “The Sound of Silence” and Hermann Hesse’s novel Steppenwolf. Both involve strange magical messages from neon signs glimpsed from narrow damp streets. But it goes deeper. The book is a life-affirming story about a middle-aged misanthrope, so perhaps it fits the pattern I was trying to draw.

Jorge Luis Borges pointed out in an essay that there is a group of writers for whom we would not have seen any commonality if Franz Kafka had not existed; now we would call their writing “Kafkaesque”. Are there perhaps other examples of literary works that we might call “Simonesque”, because they brew beauty and wonder from negativity?