Prover’s Block



What to do when afraid to see if what you want is true



Cropped from Canadian Bergler Society source



Edmund Bergler coined the term in 1947, the great writers Francis Fitzgerald—F. Scott to most—and Joseph Conrad among many others suffered from it, as did the great cartoonist Charles Schulz. The problem is writer’s block.

Today Ken and I want to write about something that I wonder if any of you have ever had.



I will call it prover’s block. It is related to, but different from, writer’s block. Of course writer’s block is the condition that makes one unable to write, unable to create new sentences, unable to produce. It is the fear of the blank sheet of paper, which today is more likely the fear of that blank laptop screen in front of you.

There are many suggestions on how to overcome writer’s block. One I like is from the poet William Stafford who offered this advice to poets:

There is no such thing as writer’s block for writers whose standards are low enough.

The point is not to write garbage. The point is to write something: get started and be prepared to throw away lots, but write. Start getting your ideas down and trust that later, with much re-writing and edits, the writing will be okay. Of all the advice I find this one very useful. I certainly use it for GLL. I hope we do enough re-writes and edits so that most of what gets out is not garbage.

Prover’s Block

Some what is prover’s block? Let me explain in a personal way, since am just about over a bad case. I actually hope that writing this piece will help me overcome my block.

I have been working for a long time—let’s not say how long right now—to prove a certain Lemma X. I have thought at least a hundred times I had found a proof of X, but alas each time I started to work out the details the proof failed. After a while I began to doubt that X was true, but I really want X to be true. If it is true I will have proved something quite nice. No not that—not a “breakthrough”—but something that is still quite important.

A few weeks ago I looked at the statement of X from a new angle. How I missed this angle before who knows; somehow I did miss it. A quick rough check showed that this new approach should yield a proof of X. So I ran right off to the computer to write up the LaTeX version of the full details of the proof. Right.

No. I did nothing. I am afraid. I want this new approach to work so very much. I think it will. But the fear is as with all the previous ones this approach will collapse when I start hashing out all the details. This is prover’s block. I am stuck right here.

I have a great new approach to X, but am afraid to work out all the details. Perhaps this is one of the advantages of working with co-authors. On this one, however, I am alone.

Some Observations by Ken

Sometimes I, Ken writing now, find it helps even just to define a few new LaTeX macros in a document header to get rolling. A similar idea definitely works for “programmer’s block”: define a few routines to make the problem smaller.

The “ ” typesetting program which I introduced to Oxford in 1985, and which is still going strong today as “Scientific Word,” had the philosophy that nothing is ever started from scratch. There was no “New Document” menu item—every document had to begin as a modification of another document. I still do that with many LaTeX documents, including solo posts for this blog.

Personality-wise I work better in the mode of modifying and extending over creating ex nihilo. It may not be simplistic to ascribe this trait to the ‘P’ versus ‘J’ component of the Myers-Briggs typology. The ‘P’ stands for “perceiving” but may as well stand for “perfectionistic” or “procrastinating,” whereas those with high ‘J’ (for “judging”) may align with those able to generate content quickly from scratch with less concern over errors or polish.

Specifically with regard to proofs, one thing I’ve noticed is in trying to prove a “simple” lemma on-the-fly while typing. Often the details mill around and cause backtracking to the extent that I’m not even sure the lemma is true anymore. I still find I need to sit with a notebook or sheets of paper to nail it down.

Open Problems

Is Lemma X proved by this new method? I, Dick, am about to find out. This has energized me to delve in to seeing if it works or not. The worst that can happen is I will have a new angle on X and potentially new ideas will emerge. The best that can happen is that I will finally prove X.

I will let you know. Thanks for listening.