Omaha daily bee., 1909-06-20

their surroundings, and opens to many an
entirely new world. a world which teaches
that the useful is not necessarily the ugly,
and that environment Is the inspiration Of
action. Beautifying the village or town Is
bound to bring the citizens together IN a
new and more intimate association, and
does much to abolish those dens OF vice
which disfigure not only the aspect but
the moral life Of a town.
OF course this is but one phase Of civic
Improvement; there are many others. In
the factory town especially there Is wide
scope for the colleged-bred woman's ac-
tivity. There is no reason why the factory
town should be unsightly, or why the em-
ployes Of the factory should live in ugly,
unsanitary dwellings; no reason why the
women Of the town should not be reused to
interest in their surroundings, and above
all, to self-respect.
The woman of education owes II to her
less fortunate sister to encourage that feel
ing Of self-respect which lies dormant in
the breasts of so many factory women.
Give them the vision of something broader
and higher than is comprehended in their
own horizon, and they will try to conform
their lives to II. Give them model day
nurseries, and they will give their children
cleaner homes. Awaken in them the con-
seriousness that they have possibilities, and
they will try to realize them.
Solves Fermat TheOrem.
A woman who has taught mathematics
for a decade in New York City is believed
to have worked out the famous fermatian
theorem which has remained undemon-
strated for almost $50 years. As a oonse-
quence she is likely to receive the money
reward offered by the will Of a professor
in Darmstadt university, but the Academy
of Scienc Of Gottingen Is permitted, by
the terms of the bequest, to hold hack the
prize for two years, in the course Of
which period of time the New York teach
er's demonstration will be passed upon by
the leading mathematician Of the world.
This is the theorem:
The sum Of the nth powers Of two posi-
tive integers cannot be IN nth power for
any value OF n except 2.
In the demonstration made by the
woman, who prefers to remain incognito
until Gottingen has crowned her work,
every letter employed represents a posi-
tive integer. Her proof, in the printed
form required by the conditions attached
to the contest, covers eight pages, and has
satisfied Prof. Mcmahon of Cornell uni
versity, Prof. Moore of Chicago university
and Prof. Bchwartz of Berlin that 1t en-
braces at least the most important of the
almost innumerable forms into which the
argument may fail.
For years mathematician of all countries
have labored at it, relates the New York
Evening Post. The difficulty, expressed
crudely, is that It embodies in one step an
indefinitely large number of syllogisms. To
discern in regular progression, and not to
leap irregularly over several intergers, to
compass, In a word, all the vague posi-
bilities Of numbers and their relations and
properties, has fascinated mathematical
students everywhere.
But, in the opinion Of several, and among
them the greatest of our mathematician
the great fermat theorem has been proved
by an American woman. These gentlemen
have Endorsed her demonstration, and five
copies have recently been received by the
academy at Gottingen. She was occupied
the better part Of a year in preparing this
proof, which, 1t is expected, will bear of
the prize. Two years must elapse, how
ever, before the result is positively known
in her case as In that OF any contestant
She was born and educated in New Eng.
land, but took her masters degree from
Cornell. Her work as a teacher has beer
done In Brooklyn and New York.