JUNE 7, 1912] 
Wissenschaften by the will of a deceased 
German mathematician named Wolfskehl, 
and it is to remain open for about a cen- 
tury, until 2007, unless some one should 
successfully solve the problem at an earlier 
date. 
It is too early to determine whether the 
balance of the effects of this prize will tend 
towards real progress. One desirable fea- 
ture is the fact that the interest on the 
money is being used from year to year to 
further important mathematical enterprises. 
A certain amount of this has already been 
given to A. Wieferich for results of impor- 
tance towards the solution of Fermat’s 
problem, and other amounts were employed 
to secure at Gottingen courses of lectures 
by Poinearé and Lorentz. 
What appears as a bad effect of this 
offered prize is the fact that many people 
with very meager mathematical training 
and still less ability are wasting their time 
and money by working out and publishing 
supposed proofs. The number of these is 
already much beyond 1,000 and no one can 
foresee the extent to which this kind of 
literature will grow, especially if the com- 
plete solution will not be attained during 
the century. A great part of this waste 
would be eliminated if those who would like 
to test their ability along this line could be 
induced to read, before they offer their 
work for publication, the discussion of 
more than 100 supposed proofs whose er- 
rors are pointed out in a German mathe- 
matical magazine called Archiv der Mathe- 
matik und Physik, published by B. G. 
Teubner, of Leipzig. A very useful 
pamphlet dealing with this question is en- 
titled, ‘‘Ueber das letzte Fermatische The- 
orem, von B. Lind,’’ and was also pub- 
lished by B. G. Teubner, in 1910. 
A possible good effect of the offered prize 
is that it may give rise to new develop- 
ments and to new methods of attack. As 
SCIENCE 
881 
the most successful partial solution of the 
problem was due to the modern theory of 
algebraic numbers, one would naturally 
expect that further progress would be most 
likely to result from a further extension 
of this theory, or, possibly, from a still 
more powerful future theory of numbers. 
If such extensions will result from this 
offer they will go far to offset the bad effect 
noted above, and they may leave a decided 
surplus of good. Such a standing problem 
may also tend to lessen mathematical idol- 
atry, which is one of the most serious bar- 
riers to real progress. We should welcome 
everything which tends to elevate the truth 
above our idols formed by men, institutions 
or books. 
In view of the fact that the offered 
prize is about $25,000 and that lack of 
marginal space in his copy of Diophantus 
was the reason given by Fermat for not 
communicating his proof, one might be 
tempted to wish that one could send credit 
for a dime back through the ages to Fer- 
mat and thus secure this coveted prize and 
the wonderful proof, if it actually existed. 
This might, however, result more seriously 
than one would at first suppose; for if 
Fermat had bought on eredit a dime’s 
worth of paper even during the year of his 
death, 1665, and if this bill had been draw- 
ing compound interest at the rate of six 
per cent. since that time, the bill would 
now amount to more than seven times as 
much as the prize. It would therefore re- 
quire more than $150,000, in addition to 
the amount of the prize, to settle this bill 
now. 
While it is very desirable to be familiar 
with such standing problems as Fermat’s 
theorem, they should generally be used by 
the young investigator as an indirect 
rather than as a direct object of research. 
Unity of purpose can probably not be se- 
cured in any better way than by keeping 
