# Harry Vandiver's comment on the infinitude of Wilson primes

Wilson primes are prime numbers that meet a specific criterion. Only three such numbers are known: 5, 13, and 563.

In Paulo Ribenboim's book "My Numbers, My Friends: Popular Lectures on Number Theory", there is a quote from the mathematician Harry Vandiver:

It is not known if there are infinitely many Wilson primes. This question seems to be of such a character that if I should come to life any time after my death and some mathematician were to tell me that it had definitely been settled, I think I would immediately drop dead again.

What does Vandiver mean by this?

I can think of a few possible interpretations:

1. Vandiver is very curious about the question, and if he became aware of its resolution, he would be happy to die afterward, content in that knowledge.

2. Vandiver finds the question extremely uninteresting, and if he were to be resurrected and told the answer, he would be bored to death.

3. Vandiver thinks that the question is extremely difficult or impossible to answer, and so would be so surprised upon hearing that it had been solved, that he would die of shock.

These correspond to three opinions that Vandiver could be expressing about the question of whether there are infinitely many Wilson primes: an extremely interesting question, an extremely uninteresting question, or an extremely difficult question.

My guess is that 2 is not likely to be what he meant, but I'm not sure which is more plausible between 1 and 3.

• It is a wry comment on the number theory community. The Wilson prime question's being settled would be such big news in the number theory community that they would even be telling zombies about it. The zombie would re-die. "I came back to life -- for this?" (Voting to close as the question seeks opinions on the reasons Vandiver might drop dead in those circumstances.)
– TimR
Commented Jul 8 at 10:26

## 1 Answer

The key phrase is drop dead. Dictionaries may not be helpful, because this informal phrase has here its literal meaning, simply to fall down suddenly lifeless.

However, while it does simply mean that, it implies that there are no other features like dying happy; that would be the informal "die with a smile on my face."

Being bored to death is not a sudden thing, it's a slow process, so drop dead can't imply that.

Thus it is your meaning 3: Vandiver would die of shock, because not only is it "not known if there are infinitely many Wilson primes," but he feels that it cannot be known.

[The reason that we know he feels it cannot be known is that he would drop dead if it became known; but you can't know how he feels without knowing what the description of the problem's character actually means.]

• Yes, sudden overwhelming shock. It always sounds slightly odd to me when people attribute great beauty or attractiveness by saying that someone is 'drop-dead gorgeous'. Commented Jul 8 at 8:11
• Or might the shock be caused by learning that somebody had spent enough time on the problem to solve it? Commented Jul 8 at 10:12