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

III. Methods and tools
proofs wr ritiizd as
Computr-assistd
rquiring too many logial
non-survyal,
to vrifial y humans. Tymozko
stps
that suh proofs wr hanging th
argud
of mathmatial proof, rplaing
natur
ddution with trust in an empirical
logial
pross. Apting th four-
omputational
thorm, for instan, rquirs hanging
olour
non-survyal or diffiult-to-survy proof
A
onvining and yt fail to nlightn
may
th link to this artil aout Doron
Follow
a mathmatiian at Rutgrs
Zilrgr,
trms: Quanta
Sarh
In omputrs
Magazin
Do you agr that omputr programs
1.
rditd as authors whn thy
should
or hlp prov, a mathmatial
prov,
thorm?
to stion I for a rmindr of Gödl’s
Rfr
thorm, thn onsidr ths
inompltnss
mathmatial proofs, thnology is
Byond
allowing mathmatiians to ollaorat
also
ral tim on onlin platforms, solvingprolms
in
togthr and vrifying thir
work. But it is th potntial
ollagus’
omputr mathmatiians, working
of
or for thir human ollagus, that
alongsid
xits many osrvrs, and prompts
most
argumnt ut as an osrvation,
mathmatial
this xposs mathmatis to a muh highr
and
do mathmatiians did whthr a
How
is survyal or not? Paul Tllr (1980)
proof
that this is ontingnt on tim and pla,
argus
th ailitis and tools of th ommunity of
on
attmpting to vrify it. It is a
mathmatiians
pross ontingnt on th mathmatial
soial
Survyaility may not an
ommunity.
quality of a proof, ut mor a rfltion
inhrnt
is rtainly not th last to hav
Hals
this prolm. Shinihi Mohizuki
nountrd
a 500-pag proof of th ABC
sumittd
in 2012, ut as of 2020 no on has
onjtur
For somthing to ount as mathmatial
2.
should humans al to
knowldg,
Do you think that in th futur ATPs ould
1.
th thorm?
ovrom
What would nd to happn for ATPs to
2.
th thorm?
ovrom
xampl, what ar mathmatial proofs
For
Thr is valu in oth knowing that
for?
is tru as wll as in how it was
somthing
Th st proofs rval dpr
solvd.
into mathmatis, xplaining “why”
insights
ar tru. What would it man to hav
things
don y omputr that no human
proofs
ould undrstand? What would w
ing
11
potntial for rror.
our undrstanding of “thorm” and “proof”.
th radr as to why it is tru; srving not as a
of th mathmatiians of th tim.
Box 11.2: “In computers we trust?”
Univrsity.
wtrust?
Considr th following qustion.
n al to vrify whthr it is orrt.
it, or is proof y omputr
undrstand
nough?
For reflection
Overcoming the limitations of
mathematics
qustions.
partiularly maningful TOK qustions.
los and gain?
340