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

apparnt timlssnss of knowldg in
Th
may lad on to th assumption
mathmatis
mathmatial knowldg is produd in a
that
way. In rality, th prati of mathmatis
timlss
mddd in ultural ontxts and has hangd
is
ovr tim.
markdly
18th-ntury Europ th ida of mathmatis
In
th hiddn languag of th univrs was
as
aptd, and mathmatiians fashiond
widly
as “natural mn” (Alxandr
thmslvs
Prsptivs on mathmatis shift, along
2010).
th norms and valus of mathmatial
with
Rvaling this “hiddn ordr“ in
ommunitis.
mathmatial strutur of rality may attrat
th
partiular kind of mathmatiian: somon al
a
grappl with astrat thoris whil groundd
to
th ral world. Ths Enlightnmnt-ra
in
wr dsrid as unorruptd
mathmatiians
th formalitis, sptals, rivalris and
y
of soity; and thir ontmporaris
jalousis
iographrs praisd th “simpliity” and
and
of thir pursuit. Ths dpitions,
“purity”
ontrast, th prsptiv that mathmatis
In
onrnd with th rlationships twn
is
onpts may hav attratd a vry
astrat
prsonality. Historian of mathmatis
diffrnt
Alxandr xamins how, at th ginning
Amir
th 19th ntury, th Enlightnmnt’s
of
mn” gav way to a nw gnration
“natural
ofmathmatiians:
prsptiv of mathmatis, Alxandr
This
has haratrizd th disiplin sin th
argus,
of th 19th ntury: it has “lgitimizd
ginning
allowd for a nw typ of mathmatial
and
impratial, slf-rfrntial,
knowldg:
to worldly lif, and judgd only y its
irrlvant
TOK w oftn sarh for disagrmnts to
In
a light on diffrnt prsptivs. Howvr,
shin
aout mathmatis appars to mak
somthing
asir to rsolv; w do not oftn
disagrmnts
of mathmatial ontrovrsis. Could it
har
mathmatis has lss sop for disagrmnt?
that
that th prati of mathmatis, or th
Or
of mathmatiians, is partiularly
ommunity
in avoiding, silning or rsolving
fftiv
prsptivs? Kp ths qustions in
onfliting
thorms and onjturs in
Many
arry th nams of individuals.
mathmatis
Do individuals hav an aility to mak
1.
disproportionat impat in th fild
a
mathmatis as ompard to othr
of
disiplins?
How has th rol and influn of
2.
in mathmatis hangd ovr
individuals
Is th fild of mathmatis lss or mor
3.
ompard to othr disiplins?
ollaorativ
Has mathmatis n disproportionatly
4.
y partiular ulturs? If so, dos
shapd
II. Perspectives
II. Perspectives
II.2 Individuals and the mathematical
community
purity, its truth, and its auty” (2010).
mind as you rad through Box 11.1.
For discussion
The humans of mathematics
turn, shapd soial idals and idas aout
in
and mathmatiians, with long-
mathmatis
lasting ffts.
tim?
it ontinu to ?
mathematics . . . was a wondrous alternative
reality governed solely by the eternal laws of pure
mathematics, unsullied by the crass realities of
the world around us. Unlike their elders, the new
mathematicians were not so much interested in
acquiring new and useful results as they were
focused on the internal architecture of mathematics
itself, its interconnections, and the precise meaning
of its statements. Mathematics, for them, was its
own self-contained world and could be judged by
mathematical standards alone.
(Alexander 2010)
327