Iwaniec and Friedlander wrote a short survey article for the notices of the AMS, entitled "What is the Parity Phenomenon?"


At the end of the article they refer to a young mathematician:

"Sometimes it almost seems as though there is a ghost in the House of Prime Numbers. Perhaps that will be ruled out some day. There are suggestions of a youngster who might do this, one who will come from the Automorphic Room of the house."

Does anyone know who this mathematician is?


  • 2
    $\begingroup$ Seems more like a tongue in cheek comment (possibly a reference to someone 'predicting' Hilbert's 10th would be solved by a 'young Russian'?) than a sly reference to someone specific... $\endgroup$ Jun 16, 2010 at 5:04
  • 6
    $\begingroup$ I think that the rooms in their house are populated by ideas rather than people. $\endgroup$ Jun 16, 2010 at 6:32

1 Answer 1


They wrote a mixed technical summary and allegory, something of a prose poem. The allegorical part is concentrated in three paragraphs. These are the second paragraph, the last paragraph, and one in the middle in which people in the "Analytic Room" regard their methods as recent in that Euler is only about three hundred years old. The youngster is evidently anyone from the "Automorphic Room." So the suggestion is that progress is likely to come from automorphic methods, and no specific mathematician is indicated. My best guess on the "ghost" is the possibility of an "exceptional" character whose $L$-function could possess a bad zero. This is from the next to last paragraph, after mention of the "Algebraic Room."

Overnight my impression of the piece clarified a bit, from a pretty vague sense that the inhabitants in the Rooms were not specific people, even from the distant past. I am close to Unreasonable Sin's comment of just an hour ago. I think the inhabitants of the Rooms are ideas more than specific theorems, techniques, particular papers. So the Youngster is an idea. Note Victor Protsak's comment of ten hours ago, I think he got it exactly right. Victor is a smart man. Heed him.

For examples of this style, see the fantasy short story collections of Lord Dunsany,


especially, from 1905, The Gods of Pegana


evidently available online in full, see for instance


  • $\begingroup$ Yes, the ghost is certainly the exceptional characters but it seems by youngster', a certain person is indicated. Otherwise they wouldn't have said youngster', for an old resident of the automorphic room may as well drive the ghost away. It is interesting to note that in keeping with the `spectral' allusions, they bring in the number 666 - the number of of the beast. $\endgroup$
    – Idoneal
    Jun 16, 2010 at 6:12
  • $\begingroup$ +1 Ghost = exceptional zero. The opaque style of this short survey is a striking counterpoint to the praise for their earlier research paper: "Happily, the authors reject the too-widespread notion that mathematics must be written opaquely in order to be considered substantive. (MR1995146)" $\endgroup$ Jun 16, 2010 at 6:22
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    $\begingroup$ Ahhh, I see now. By youngster he meant that the automorphic room is a newer development in mathematics, compared to the elementary and analytic room. Thanks for your replies! $\endgroup$ Jun 16, 2010 at 15:06

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