Theory of Knowledge - Course Companion for Students Marija Uzunova Dang Arvin Singh Uzunov Dang

10 reports that articial intelligence has
Chapter
in a very short period of time, succeeded
already,
producing music and poetry that appeals to
in
tastes. In the arts the question of intent is
human
from aesthetics and metaphysics—we
inseparable
yet escape the doubt about whether software
cannot
to make art. To what extent does this
“intends”
of intent apply in the case of ATPs producing
concern
are numbers beautiful? It’s like asking why is
Why
Ninth Symphony beautiful. If you don’t
Beethoven’s
why, someone can’t tell you. I know numbers are
see
If they aren’t beautiful, nothing is.
beautiful.
of mathmatis hav somtims
Philosophrs
that mathmatial asthtis ar
ommntd
statd. What maks a proof autiful,
vaguly
lgant, spially in omparison to anothr
or
is also logially tru? At th sam tim, to
that
xtnt is auty any mor or lss tightly
what
in th othr AOKs, and should w xpt
dfind
to diffrnt?
mathmatis
auty is sujtiv and
Mathmatial
do not always agr, ut many
mathmatiians
know a autiful proof or rsult whn thy
will
it. Nahin (2006) laorats as follows.
s
a Shakespearean sonnet that captures the very
Like
of love, or a painting that brings out the
essence
of the human form that is far more than just
beauty
deep, Euler’s equation reaches down into the
skin
formula (e iπ + 1 = 0) is itd as an
Eulr’s
of dp mathmatial auty. Fynman
xampl
alld it “our jwl” and “th most
(1977)
formula in mathmatis”. It ontains
rmarkal
of th asi arithmti oprations, ah
thr
xatly on, and links togthr fiv
ourring
mathmatial onstants: 0, 1, π,
fundamntal
i. , π and i ar ompliatd and smingly
and
numrs, so som mathmatiians
unrlatd
rmarkd that it is “amazing that thy ar
hav
y this onis formula” (Pry quotd in
linkd
2014).
Gallaghr
in 2014 usd funtional magnti
Rsarhrs
imaging (fMRI) to osrv th ativity in
rsonan
rains of 15 mathmatiians whn thy viwd
th
formula thy had individually ratd
mathmatial
autiful, indiffrnt or ugly. Th xprimnt
as
that xprining mathmatial auty
showd
with motional ativity in th rain in th
orrlats
way as th xprin of auty from othr
sam
(Zki et al 2014). Davis and Hrsh hav
sours
that an asthti sns is univrsal
ommntd
pratising mathmatiians. But to what
among
is mathmatial auty assil only to
xtnt
auty is said to rfr to a rsult or
Dp
that ontains unxptd insights into
mthod
struturs. Trivial thorms lak
mathmatial
as do proofs or rsults drivd in an
auty,
or rptitiv way, or whih apply only to
ovious
ass. Hardy (1940) suggstd that auty
spial
from th “invitaility”, “unxptdnss”
oms
“onomy” of a work. H also argud that
and
mathmatis is inhrntly suprior in auty
pur
applid mathmatis aus it annot
to
for ommon or violnt human amitions.
usd
and auty hav n asrid to proofs
Elgan
ar unusually suint, asd on original
that
hav an lmnt of surpris, us a
insight,
of assumptions and an gnralizd
minimum
solv similar prolms.
to
appliations of mathmatis to sin,
Th
and nginring ar widly
thnology
ut thr is also a dimnsion of
disussd,
as joy, as art and as litratur.
mathmatis
for xampl, has ompild
Shinrman,
autiful” thorms and proofs in The
“joyful,
Lover’s Companion (2017), arrivd
Mathematics
“through th swat of intlltual play that,
at
th st poms, ontain prftly xprssd
lik
aout th world” (Lvy-Eihl 2018).
truths
III. Methods and tools
III. Methods and tools
Making connections
Exploring the question of intent
”elegant” mathematics?
III.2 Beauty
mathmatiians?
(Devlin 2000)
very depths of existence.
(Nahin 2006)
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