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

III. Methods and tools
onsidr two ontrasting laims aout
Lt’s
truth. Th first, y Avigad (2018),
mathmatial
that “th truth of a mathmatial
assrts
dos not rly on historial ontxt or
statmnt
irumstans of th spakr”. On th othr
th
Lvy-Eihl argus that mathmatis
hand,
th laim that onsnsus on a proof
Considr
mathmatis forms unontrovrsially.
in
What argumnt an you offr to support
1.
laim? this
How would you onstrut and support a
2.
ountrlaim?
how rahing onsnsus in
Considr
ompars to th pross of
mathmatis
What ar signifiant similaritis and
3.
twn onsnsus in
diffrns
What an you say aout th sours of
4.
similaritis and diffrns?
ths
today, as th standard of rigour in
assum
proof has hangd throughout
mathmatial
Th advnt of omputr proof
history.
and automatd thorm provrs,
assistants
disussd low, has alrady gun to
as
what is mant y mathmatial rigour
hang
vry onpt of ‘asolut’
“Th
rigour is not immutal.
mathmatial
variaility of th onpt of rigour
Th
that somthing ls sids
shows
astration must ntr
mathmatial
th makup of mathmatis.” (von
into
ould this “somthing ls” that von
What
rfrs to?
Numann
11
andproof.
has no timlss standard, dspit what many
Practising skills: Evaluating claims
For reflection
A mathematical “je ne sais quoi”
John von Numann statd th following.
rahing onsnsus in othr AOKs.
and in on othr AOK of
mathmatis
hoi?
your
Numann 1947)
Figure 11.6 Th four-olour thorm. Th four-olour thorm stats that only four olours ar rquird on a map so that no two adjant
rgions hav th sam olour. It was th rst major thorm provd using omputr assistan, in 1976 y Knnth Appl and Wolfgang
Haknand, ut was not aptd y all mathmatiians as no individual human ould hk it. Nw forms of th proof (all of whih hav usd
omputr assistan in som form) hav n asir for humans to vrify.
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