ssieo-h-Xv¡-c-W-¯nsâ ^e-ambn KWn-X-im-kv{X-h-Xv¡-cn-¡-s¸«
kt¦-X-§-fn-te¡p aS-§n-h-cmw. Gähpw IrXy-am-bn-cn-¡p-I, ka-{K-am-bn-cn-¡p-I,
]qÀW-am-bn-cn-¡pI F¶Xv HcÀ°-¯n ssZhn-IX-sb-¡p-dn-¡p-¶p.
Iem-kr-jvSn-bpsS A\p-]m-X-s¯bpw ebm-ß-I-X-sbbpw Ipdn-¨pÅ k¦-ev]-\-§sf
{]]-©-kr-jvSn-bpsS {Iaw, A\p-]mXw F¶n-h-bp-ambn tNÀ¯p hbv¡m-hp-¶-Xm-Wv.
C{µn-b-§Ä¡p ta _p²n-sbbpw C{µn-b-_-²hpw hymPhp-amb Iem-ku-µ-cy-¯n\p
ta _u²n-Ihpw bYmÀ°-hp-amb Pyma-Xo-b-cq-]-§-sfbpw {]Xn-jvTn-¡p¶
t¹täm-bpsS ZÀi\w Dw_ÀtSm Ft¡m kw{K-ln-¡p¶p:
‘Since in Plato’s view the body is a
dark cavern that imprisons the soul, the sight of the senses must
be overcome by intellectual sight, which requers a knowledge of
the dialectical arts, in other words philosophy. and so not every
one is able to grasp true Beauty. By way of compensation, art in
the proper sense of the term is a false copy of true Beauty and as
such is morally harmful to youth: better therefore to ban it from
the schools, and substitute it with the Beauty of
geometrical forms, based on proportion and a mathematical
consept of the universe’ (On Beauty)
IrXy-amb A\p-]m-X-§-fn cq]-s¸« H¶ns\ kpµ-c-am-bn-¡m-Wp¶ kmam-\y-t_m-[-¯nÂ\n-¶mWv
temIs¯ Hscmä \nb-a-¯m `cn-¡-s¸-Sp¶ {Ia-_-²-amb ka-{K-X-bm-bn-¡m-Wp¶
{]mNo-\-{Ko¡v ZÀi\w cq]-s¸-«-sX¶v tkm{I-«o-kn\pw ap³]pÅ Nn´-I-·msc
]cm-aÀin-¨p-sImWvSv Dw_ÀtSm Ft¡m ]d-bp-¶p.
CuPn-]vjy³ KWn-X-im-kv{X-hp-ambn k¼À¡-ap-WvSm-bn-cp¶ ss]X-tKm-dkv
{]]-©-¯nsâ AkvXn-Xz-s¯-¡p-dn¨v kuµ-cy-im-kv{X-s¯bpw
KWn-X-im-kv{X-s¯bpw ka-\z-bn¨v cq]-s¸-Sp-¯nb ZÀi-\s¯ Ft¡m C§s\
]cm-aÀin-¡p¶p:
‘...all things exist because they are
ordered and they are ordered because they are the
realisation of mathematical laws, which are at once a condition of
existence and of Beauty.’(On Beauty)
tÚb-amb Hmtcm hkvXphn\pw
Hmtcm kwJy-bp-WvsS¶pw kwJy-bn-ÃmsX B hkvXp-hn-s\-¡p-dn¨v Adn-bm-t\m
Nn´n-¡mt\m km[y-a-söpw ^ntem-em-thmkv (_n. kn. A©mw \qäm-v) ]d-bp-¶p.
kwJy-bn-eqsS {]Xn-\n-[o-I-cn-¡m-hp¶ IrXyX, Ah-bpsS A\p-]m-X-¯n-eq-sS-bpÅ
ebw, AXnsâ ssZhn-IX C¯-c-¯n _Ôn-¸n-¡m-hp¶ Nne I®n-IÄ hnip-²-I-e
(-hym-P-amb euIn-I-I-e-bnÂ\n¶p `n¶w)sb¡p-dn-¨pÅ hnNm-c-§-fn¡m-Wmw.
]mÝmXy ¢mÊn-¡Â kwkvImc¯nsâ
kmÀÆ-Im-en-I-X, kmÀÆ-eu-In-IX F¶o t_m[y-§-fn \n¶p-sImv Ønc-Xbpw
KWn-Xhpw X½n-epÅ _Ô-s¯-¡p-dn¨p kzcq-]n¨ [mc-W-bmWv Pn. F¨v. lmÀUn
F¶ KWn-X-im-kv{X-Ú-s\-s¡mWvSv C§s\ ]d-bn-¡p-¶Xv:
‘Archimedes will be remembered when
Aeschylus is forgotten, because languages die and mathematical
ideas do not. ‘ Immortality ’ may be a silly word, but probably a
mathematician has the best chance of whatever it may mean’ ( A
Mathematition’s Apology )
`mc-X-¯n ¢mÊn-¡Â
Iem-Nn-´-IÄ GXmWvSp ]qÀW-am-bn-¯s¶ KWn-X-im-kv{X-t¯mSpw
Bßo-b-hm-Z-t¯mSpw KmV-ambn _Ôn-¡-s¸-«n-cn-¡p-¶p. hm¡p-I-fpsS
D¨m-c-W-t`Zw EtKz-Z-¯nÂ\n¶pw KoXw kma-th-Z-¯nÂ\n¶pw A`n-\bw
bPpÀth-Z-¯nÂ\n¶pw ck-§Ä AYÀh-th-Z-¯nÂ\n¶pw kzoI-cn¨p \nÀ½n-¡-s¸«
A©m-aXp thZ-amb \mSy-thZw Nm£p-j-b-Ú-am-Wv. kwKo-X-Zm-tam-Z-c-¯nÂ
]c-a-in-hsâ ktZym-Pm-Xw, kma-tZ-hw, AtLm-cw, XXv]p-cp-jw, Cuim\w
F¶o ]©-ap-J-§-fnÂ\n¶v \nÀ½n-¡-s¸-«-XmWv kwKo-X-sa¶p ]d-bp-¶p.
kwKo-X-c-Xv\m-I-c-¯n {_Òmhv kma-th-Z-¯nÂ\n-¶p hmÀs¯-Sp-¯-XmWv
kwKoXw F¶p ]cm-aÀin-¡p-¶p.
hoWm-hm-Z-\-X-XzÚ:
{ipXn-im-kv{X-hn-im-cZ:
Xmf-Úm-Ým-{]-bm-tk\
tam£-amÀ¤w \nb-ÑXn
F¶n-§s\ kwKo-X-Im-c\p
Iev]n-¡-s¸« tam£-s¯-¸än tam£-ap-K-e-Zm, kzc-cm-K-kp[ XpS-§nb IoÀ¯-\-§-fn-eqsS
XymK-cm-P\pw BhÀ¯n-¡p-¶p. kwKo-X-Im-c³ sNs¶-¯p¶ tam£-]Zw
HmwIm-c-kz-cq-]-amb \mZ-{_-Ò-am-Wv. \mZs¯ Bl-Xw, A\m-lXw F¶p
cWvSmbn Xncn-¡p-¶-Xn A\m-lXw tbmKn-IÄ¡p am{Xw Adn-bm³ Ign-bp-¶Xpw
BlXw euIn-I-hp-am-Wv. Cu \mZ-hn-`-P-\-¯n Bt]-£n-I-ambn
AaqÀ¯-am-b-Xn\p {]m[m\yw \ÂIp¶ Bßo-b-hm-Z-kv]Ài-apWvSv-.
tam£-{]m-]vXn-sb-¶mÂ
tIh-e-amb {_Ò-¯n ebn-¡p-I-bm-Wv. {_Òw ]qÀW-am-Wv. F´mWp ]qÀW-sa¶v
D]-\n-j-¯n ]d-bp-¶p:
]qÀW-aZ: ]qÀW-anZw
]qÀWm ]qÀW-ap-Z-NytX
]qÀWky ]qÀW-am-Zmb
]qÀW-ta-hm-h-in-jy-tX.
]qÀW-t¯mSp ]qÀWs¯
Iq«n-t¨À¯mepw ]qÀW-¯nÂ\n¶p ]qÀW-sa-Sp-¯mepw ]qÀWw. KWn-X-im-kv{X-{]-Imcw
CXv ]qPy-¯n-sâtbm A\-´-X-bp-sStbm kz`m-h-am-Wv. ]qPy-sa¶ t]cpw
AXnsâ NnÓhpw al-Xzw, tIh-e-X, Ønc-X, A\-iz-c-X, AaqÀ¯X F¶o
Bßo-b-hm-Z-k-¦-ev]-\-§-tfmSp _Ô-s¸-«n-cn-¡p-¶p.
Iem-Nn-´-bn Bßo-b-hm-Z-¯nsâ kzm[o\w D¯-ahpw hnip-²hpw Ønc-hp-sa¶p
k¦-ev]n-¡-s¸-Sp¶ Iebv¡v taÂss¡ t\Sn-s¡m-Sp-¡pI am{X-aÃ
kmaq-ln-I-amb PmXn-hy-hØbn hsc \nÀWm-b-I-Øm\w hln-¡p-Ibpw sN¿p-¶p-WvSvv.
EtKz-Z-¯nse ]pcp-j-kq-à-¯n hncm-Sv]p-cp-jsâ apJ-¯p-\n¶p {_mÒ-W\pw
_mlp-¡-fnÂ\n¶p £{Xn-b\pw XpS-bnÂ\n¶p sshiy\pw ]mZ-¯nÂ\n¶p iq{Z\pw
P\n-¨-Xmbn ]d-bp-¶p. apJ-¯n\p aäw-K-§-sf-¡mÄ {]m[m\yw
Iev]n-¡m-dpWvSv-. AXv D¯-amw-K-am-Wv. A`n-\-b-I-e-bn apJw kmXzn-Im-`n-\-b-¯n-\pÅ
am[y-a-am-Wv. kmXzn-Im-`n-\-b-am-Is«
ckm-`n-\-b-hpw. ckw Ie-bpsS Bßm-hm-Wv. AaqÀ¯-amb Cu Bßmhns\ Hcp ]cn-[n-h-scsb¦nepw
{]Xy-£o-I-cn-¡p-¶Xv apJ-am-Wv. A§s\
ico-c-tI-{µn-X-amb \r¯-s¯-¡mÄ
apJ-tI-{µn-X-amb \mSy-¯n\v {]m[m-\y-ap-WvSm-Ip-¶p. ico-cs¯ apJ-¯n\p
Xmsg-bm-¡p-¶-Xnse LS-\m-t_m[w Ie-I-fp-sSbpw kaq-l-¯n-sâbpw L\m-t_m-[s¯
\nÀW-bn-¡p-¶pWvSv.-
NmXpÀhÀWy-hy-h-Øbpw
Iem-k-t¦-X-§fpw X½n-epÅ _Ô-\nÀW-b-¯n\v Bßo-b-hm-Z-¯nsâbpw
KWn-X-im-kv{X-¯n-sâbpw kw_-Ô-¯n ]nd¶ Iem-{K-Ù-§-fn thWvSp-thmfw
DZm-l-c-W-§-fp-WvSvv. Xmf-im-kv{X-{]-Imcw Xmf-¯n\p {][m-\-ambpw \mep
PmXn-I-fp-WvSv. NXp-c-{iw, {Xy{iw, an{iw, JWvUw F¶o \mep PmXn-IÄ
bYm-{Iaw 4, 3, 7, 5 F¶o kwJy-I-fp-ambn _Ô-s¸-«n-cn-¡p-¶p.
Xmf-k-ap-{Z-sa¶ Xangv{KÙ-¯n Cu \mep PmXn-I-fn NXp-c{iw {_mÒ-W\pw
{Xy{iw £{Xn-b\pw an{iw sshiy\pw JWvUw iq{Z-\p-am-Wv. CXnÂ
NXp-c-{ihpw {Xy{ihpw Xmf-im-kv{X-¯nsâXs¶ ASn-Øm-\-k-t¦-X-§-fp-ambn
_Ô-s¸-«n-cn-¡p-¶p. NXp-c-{i-amb N©-Xv]pSw, {Xy{i-amb NmN-]pSw
F¶n-§s\ Xmf-s¯-¯s¶ cWvSmbn Xncn-¡p¶ \mSy-imkv{Xw aäp
Xmf-§-fp-sS-sbÃmw ASnØm-\-ambn Chsb IcpXp¶p. AXm-bXv NXp-c-{ihpw {Xy{ihpw
ip²hpw aäpÅ Xmf-§Ä IeÀ¸p-I-fp-am-Ip-¶p.
ip²hpw Aip-²hpw thÀXncn¡p¶-XnÂ
ip²-am-b-XnÂ\n¶v Ai-p²-ambXns\ AI-än-\nÀ¯p¶ {]{In-b-IqSn AS-§n-bn-cn-¡p-¶p.
Iem-h-kvXphpw ImgvN-¡m-c\pw X½n-epÅ AIew \nÀW-bn-¡-ens\ D¼ÀtSm
Ft¡m ]uc-kvXy-I-em-Nn-´-bnÂ\n¶p hyXy-kvX-amb {Ko¡v
ImgvN-¸m-Sm-bmWv ImWp-¶-Xv. F¶m At±lw \ÂIp¶ DZm-l-c-W-§Ä s]mXpth
Pm¸-\okv, Sn_-ä³ kwkv¡m-c-§-fp-ambn _Ô-s¸-«-h-bm-Wv. C´y-bnÂ, {]tXy-In¨p
tIc-f-¯n CXv kmaq-ln-I-amb D¨-\o-N-Xz-§-fp-ambnhsc _Ô-s¸«
Imcy-am-Wv. {iotIm-hn-e-Iw, tkm]m-\w, aWvU-]w, \me-¼ew, Iq¯-¼-ew,
aXn¡Iw F¶n-§s\ t£{X-Øm-\-§-tfm-tcm¶nepw PmXn-t{i-Wn-bn-epÅ Øm\-a-\p-k-cn-¨mWv
{]th-i\w \nÀW-bn-¡-s¸-«n-cn-¡p-¶-Xv.
hn{K-l-hp-am-bpÅ ASp¸w/AIew,
hmkvXp-\nÀ½n-Xn-bmb t£{X-¯nsâ Øm\-§Ä F¶n-h Cu {]th-i-\-\n-b-{´-Ws¯
kzm[o-\n-¡p-¶pWvSv-. {iotIm-hn-en-\p-Ånse a{´w sNmÃÂ, tkm]m-\-¯nse
Km\m-em-]-\w, \me-¼-e-¯nse hmZy-ta-fw, Iq¯-¼-e-¯nse
IqSn-bm-«-kw-KoXw, t£{X-a-Xn-en-\-It¯m ]pdt¯m Bbn IY-I-fn-kw-KoXw
F¶n-§s\ KoX-¯nepw, {iotIm-hn-en-\p-Ån ip²-amb hn{K-lw, {iotIm-hn-en\p
Npänepw aWvU-]-¯n-ep-ambn CX-c-in-ev]-§Ä F¶p inev]-I-e-bnepw {iotIm-hn-en-\p-ÅnÂ
Xm{´n-I-ap-{Z-IÄ, Iq¯-¼-e-¯n IqSn-bm-«-ap-{Z-IÄ, AXn-\p-a-¸p-d¯v
IY-I-fn-ap-{Z-IÄ F¶v BwKn-I-I-e-bnepsaÃmw Cu ASp¸w/AIew {]hÀ¯n-¡p-¶p.
XoWvSÂ, sXmSo XpS§n Abn-¯m-N-cWwXs¶ CXn-t\mSp _Ô-s¸-«-Xm-sW-¶-Xn-\mÂ
k¦oÀW-amb Cu hyhØ khn-ti-j-]-T-\-am-h-iy-s¸-Sp-¶p.
t£{X-tI-{µn-Xhpw
Bßo-b-hm-Z-]-chpw ssieo-_-²hpamb ¢mÊn-¡ÂI-e-I-fpsS
KWn-X-im-kv{X-]-c-amb hymI-cWw ewLn-¡-s¸-Sp-¶Xv
Fhn-sS-sbm-s¡-bm-sW¶v Btem-Nn-¡p-¶Xv IuXp-I-I-c-am-Wv. kwkvIr-X-\m-S-Im-`n-\-b-amb
IqSn-bm-«-¯nÂþ\mS-I-]mTs¯-¯s¶ ASn-Øm-\-am-¡nþ\mb-I-I-Ym-]m-{X-§Ä¡p
hn[n-¨n-«pÅ kwkvIr-X-¯nÂ\n¶p `n¶-ambn {]mIr-X-`m-j-kw-km-cn-¡p-¶Xv
kv{XoI-Ym-]m-{X-§fpw A[-a-I-Ym-]m-{X-§-fp-am-Wv.
ssieo-h-XvIr-X-amb {_mÒ-W-a-t{´m-¨m-cW(kz-cn¨p sNmÃÂ-þ-Hm-¯v)¯nÂ\n¶p
hyXy-kvX-amWv IqSn-bm-«-¯nse kzcn-¨p-sNm-ÃÂ. Hm¯p ]ng-¨m Iq¯mbn
F¶ {_mÒ-W-]-cn-lm-k-¯n kvamÀ¯-hn-Nm-c-¯n {`jvS-cm-¡-s¸«hsc
kzoI-cn-¡p¶ NmIymÀk-ap-Zm-b-t¯m-SpÅ \ne-]mSpw AS-§n-bn-«p-v.
IqSn-bm-«-¯nse hnZq-j-I³ kwkvIr-X-\m-S-I-¯nse {]mIr-X-¯nsâ Øm\¯v
khÀW-co-Xn-bn-epÅ ae-bmfw kwkm-cn-¡p-t¼mÄ iqÀ¸-W-J-bpsS kwkm-c-hpw
(Ft¶ XpIta! F{Xbpw XpI-ap-m-tb, Xmt\ XpI-sa¶p sNmÃn-bmepw
t]mcm-tb, XpIw XpIw XpI-sa¶p ]e-h«w sNmÃn-bmte aXnbm-th, AsX-s´-¶Ão?...)- DÂL-«-\hpw
(Xe-h-enb X¼n-cm³ cmh-W-¨³
]mXm-f-¯nÂs¨¶p Np¯w sh«n
Np¯-¯n¨-¯mt\ hn«n-¨n-§³) -AhÀW-`m-j-tbm-S-Sp-¸-apÅ
ae-bm-f-¯n-em-Wv.
IY-I-fn-bnÂ
Blm-cy-¯nsâ ka-{K-Xsb ewLn-¡p¶ thj-a-Wn-bp-¶Xpw IqSn-bm-«-¯nse
iqÀ¸-W-J-bp-tS-Xp-t]m-epÅ kwkmcw ]n³Xp-S-cp-¶Xpw `ocp-th-j-§Ä(-\-c-Im-kp-c-h-[w,
cpKvan-Wo-kz-bw-h-cw, IoN-I-h-[w), B\-¡m-c³(-Iw-k-h-[w),
am¸n-f(-cp-Kvamw-K-Z-N-cn-Xw) F¶n-h-cm-Wv. IY-I-fn-bnse ico-c-hn-\ym-k-¯nsâ
ebm-ß-I-XbpÅ Iem-k-t¦-X-§sf kt¦-X-§-fn-eq-sS-¯s¶ ewLn-¡p¶ thjw
Bim-cn-(_-I-h-[w)bm-Wv. CsXms¡ IY-I-fn-¨n-«-bnÂ
A\p-h-Z-\o-b-am-b-þ-A-Xp-sImWvSp-Xs¶ t_m[-]qÀÆ-amb ewL-\-§-fm-Ip-¶p.AXm-bXv
ssieo-h-XvI-cn-¡-s¸« ¢mÊn-¡ÂI-e-I-fpsS KWn-X-im-kv{X-]-c-amb
ka-{K-X-bn krjvSn-¡-s¸-Sp¶ Nne hnÅ-ep-IÄ t_m[-]qÀÆw \nÀh-ln-¡-s¸-Sp-¶-Xm-Wv.
Cu {]{In-b-bn PmXn-t{i-Wn-bpsS Øm\-§Ä¡p kam-´-c-ambn
ssieo-h-XvI-c-W-¯nsâ ]cn-Wm-a-Øm-\-§fpw AS-bm-f-s¸-«n-cn-¡p-¶p.
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