Deprecated: The each() function is deprecated. This message will be suppressed on further calls in /home/zhenxiangba/zhenxiangba.com/public_html/phproxy-improved-master/index.php on line 456
Why do I bother with all this?

Why do I bother with all this?

From Mathematics: The New Golden Age, by Keith Devlin, Penguin Books, 1990, p. 71

In Gauss's time, nine values of d were known for which the system of numbers a+b*sqrt(-d) (where a and b are half-integers as well as integers and d is some positive integer) has a unique factorization theorem. They are

d = 1, 2, 3, 7, 11, 19, 43, 67, 163.

Are there any more values? Despite considerable efforts by Gauss and others in the decades that followed, no one was able to find any. The next result was the discovery by Heilbronn and Linfoot in 1934 that there could be at most one extra value, and if it existed it would have to be astronomically large. But was there a tenth value?

In 1952 one man knew that there was not. In that year Kurt Heegner, a retired Swiss scientist who did mathematics as a hobby, published what he claimed to be a proof that there was no tenth d, but no one believed him. (His paper was very hard to follow. Even so ... .) The rest of the world had to wait another fifteen years before they knew the truth. In 1967, Harold Stark of Massachusetts Institute of Technology and Alan Baker of the University of Cambridge independently (and using different methods) also proved that there was no tenth d, and this time the mathematical community was convinced. Motivated by their discovery, Stark and Baker set about looking at Heegner's earlier work, and to their amazement found that is was essentially correct! The neglected Swiss had been right after all!


Would the story be any different should Heegner use Mizar to state his pretenses? I believe so.