Science - Mathematics, Aesthetics and Immoratily

gPOENPtPO, isPF´ÓOdPyPY oPF amPFrPñPL (iSPFXPAMSPF)

ePHPArP tPOAhPFilP çpPOLSLÔP wvPOVPFitPOvhPF pPOLAirP iyP EHP¸PPAinPLrP anPLzAnPLz SPFAKPAbPL nPLA hPFbPL kFÖOEtPOiñPLrP FpOLUrPãFFkPPArP ãO÷PrPìpPOL inPLAiHPlP FpOLUrPãFFkPPArP aAiCPF, gPOENPitPOrP iHPlPAbPL itPOmPFnPL EkPPCUF cPFAlU aAiCPF EkPP? iCPFAWvPFiHPlPAbPL aAmPFrPA sPFHPAvhPF jPLAnPLtPOAmPF inPLAiHPlP çpPOLAvhPFijPLrP tPOAElPkPPAbPL gPOENPtPO EHPXPbPLWvPFA inPLvhPF| ePkPPWvUF HPwxPF hPFHPArP jPLAnPLitPO vhPFi©CPF kPPrPtPO ikPPnPL inPLvhPF! ainPLkPP gPOÜP cPFAlU aAiCPF eP EnPLibPL| isPFgOUElPrP sPFME¾PPâPL sPFArP hPFlP:

aAlPi`çFfPOLwPO inPLAiHPlP nPLAEkPP gPOENPtPO HPA Theoretical Science@ EnPLibPL EHPiSPFXP wvPOðsPFAhPFQ ECPFilPnPL nPLA;
inPLAiHPlP FpOLUrPãFFkPPArP ikPPHPlP mPFAÀeOL` isPFvhPFsPFHP aAEHPúPOArPikPPvhPF yPAidPLrP sPFiËP mPFnFUXPzsPFBPOztPOArP practical@ iyPAgPO aAiCPF;
aAlPi`çFfPOLwPO inPLAiHPlP nPLAEkPP içpPOLimPF HPzTPY hPFibPL gPOENPitPOrP wvPOpPOLrP HPQtPO`çLSPFªPì hPFibPL pPOLiwxPFECPFilPnPL| EtPOEnPL yPAikPP BPOAilPAHPAsPFitPOnPL isPFvhPF imPFibPLEWvPF nPLAEkPP ePkPPjPLnPL gPOENPtPOEHPdPLikPP EHPHPAhPF kPPirPnPL| tPOAvhPF inPLAiHPlP gPOENPtPOikPP FpOLUrPãFFkPPAirPrP tPOAElPkPPArP HPAvhPFirP irPiKPECPFilPnPL|

ePvhPFsPFiHPrP sPFtPOz EmPFTPzA hPFbPLitPOA ikPPAnPL EdPLnPLvhPF yPAcPFAvhPF kPPrPA yPAiHP nPLA, tPOiHP ilPAkPPçpPOLHPAidPLrP pPOLA`ÂlPAbPL tÖOtPOQbPL kPPArPNPWvPFAvhPF BPOArPQ|

aArP ePkPPWvUF HPwxPF hPFibPL jPLAnPLitPO ipPOLirPECPFlPAmPF, iyP, gPOENPtPOSPFAKPAbPL inPLAiHPlP FpOLUrPãFFkPPAirPrP sPFmPFtUOlPz hPFi©CPF Field Medal@ iyPWvPFA International Mathematical Union@-ePrP pPOL¾PP iTPikPP çpPOLEtPO cPFArP HPCPFrP aÙPOrP ePkPP HPA ePkPPAEDPFkPP gPOENPtPO¸PPikPP idPLoPFbPLA hPFbPL tPOÿAidPLrP kFÖOEtPOiñPLrP jPLnPLz|
ePCPFAwxPFAoPF ainPLkPP FpOLUrPãFFkPPArP cPFAlU aAiCPF iyPgOUElP pPOLAoPFbPLA iyPitPO pPOLAirP ikPPAnPL ePkPPWvPFA EHPiSPFXP sPFmPFsPFzA sPFmPFADPFAinPLrP jPLnPLz| yPÿArPA wvPOðsPFAhPFQ tPOÿArPA ePvhPF oPFibPLHPsPFAvhPFiWvPF iKPAÿjPL EnPLitPO pPOLAirPnPL http://www.claymath.org/prizeproblems/@| ePKPAinPL ePkPPWvPFA FpOLUrPãFFkPPAirPrP tPOAElPkPPA idPLoPFbPLA aAiCPF iyPWvPFAikPP HPlPA hPFbPL Clay Institute Millennium Prize Problems@|
sPFmPFsPFzAgOUElPrP mPFiDPFz Reimann Hypothesis-oPF aAiCPF| ePWvPFA HPtPOYmPFAnPL aADFUEnPLkPP sPFBPOztPOArP ePkPPWvPFA EHPiSPFXP aiËPrP (Computer)@ sPFAiTP iyPAgPO rPAiKP HPilP ePikPP aAmPFrPA ePkPPWvUF HPNPYnPLA kPPrPHP| EkPPCUF HPCPFrP pPOLyPYÙPO iyP EtPOnPLiWvPF sPFmPFsPFzA EnPLibPL sPFHPicPFibPL iHPESPF sPFMKPzkPP HPzEÀoPLÝ mPFATPA GPLAEmPFibPLiCPFnPL, isPFgOUElP hPFlP Fermat’s Last Theorem, Reimann Hypothesis@ aArP Goldbach Conjecture| ePrP mPFiDPFz Fermat’s Theorem@ EkPPCUF HPCPFrP aAigPO çpPOLmPFANP kPPirPiCPFnPL azALæÕPFq oPFbPLAvhPFlP²sPF (Andrew Wiles)@| EtPOEnPL ePvhPF sPFmPFsPFzA sPFmPFADPFAinPLrP jPLnPLz ipPOLibPLiCPFnPL Wolfskehl Prize@ - yPArP FpOLUrPãFFkPPAirPrP mFZlPz 100,000 jPLAmPFYAnPL mPFAkPPY| ainPLikPPvhPF jPLAinPLnPL Fermat last Theorem EkPP| ePvhPF EnPLibPL çpPOLcUFrP ilPKPAilPEKP hPFibPLiCPF, EkPPÙUO yPÿArPA BUOilP igPOiCPFnPL tPOÿAidPLrP ePkPPWvUF mPFinPL kPPErPibPL idPLoPFbPLA yPAkPP| idPLKPitPO EkPPÙUO ePvhPF sPFmPFsPFzAWvPFA EnPLtPOAÙPOvhPF sPFrPlP| Fermat-ikPP HPlPA hPFtPO Prince of Ameteurs@, kPPArPNP EtPOEnPL ECPFilPnPL aAdPLitPO ePkPPjPLnPL fPOrPAsPFQ aAvhPFnPL¸PP, EyPEnPL aHPsPFrP sPFmPFibPL aÌPO kPPrPitPOnPL| yPAvhPFihPFAkPP sPFmPFsPFzAWvPFA hPFlP:xⁿ + yⁿ = zⁿ , iyPKPAinPL x, y, z, n sPFHPvhPF DPFnPLAñPLkPP FpOLZNPY sPFMKPzA|
n-ePrP mPFAnPL 2@-ePrP iTPikPP HPwxPF hPFilP(n > 2)@ ePrP nPLAEkPP ikPPAinPLA sPFmPFADPFAnPL inPLvhPF HPA wvPOiÃFWvPFABPOAiHP HPlPitPO igPOilP n > 2@ hPFilP x, y, z-rP pPOLArPãPOpPOLErPkPP sPFÈOLpPOLkPPYWvPFA sPFEtPOz nPLbPL!
idPLKPitPO çpPOLcPFLÕPLvhPF sPFrPlP| EkPPÙUO ePWvPFAvhPF aAmPFAidPLrP 300 HPCPFirPrP iHPSPFQ sPFmPFbPL HPzéPF irPiKPECPFlP| sPFHPAvhPF iBPOiHPECPFlP ePWvPFArP çpPOLmPFANP KLUHPvhPF sPFhPFjPL aArP tPOArP kPPArPNP ECPFlP Fermat@-ePrP EnPLijPLrP ePkPPWvPFA wvPOEÀoPLÝ| tPOÿArP ePkPPWvPFA HPvhPFibPLrP mPFAEjPLYinPL EtPOEnPL ElPiKP irPiKPECPFilPnPL ePrP ePkPPWvPFA cPFmPFðkPPArP sPFmPFADPFAnPL EtPOEnPL ipPOLibPLiCPFnPL, EkPPÙUO jPLAbPLgPOArP aBPOAiHP EtPOEnPL ElPKPitPO pPOLArPiCPFnPL nPLA| tPOAvhPF ePvhPF iCPFAôPO sPFmPFsPFzAWvPFA sPFmPFADPFAnPL kPPrPitPO Wiles EnPLibPLECPFilPnPL çpPOLTPmPFHPArP mPFAÀeOL` 170-180 pPOLAtPOA, aArP ePkPPHPArP sPFMiSPFADPFinPLrP pPOLrP isPFWvPFA dPLÿAEwxPFibPLECPFlP 200-rP kPPACPFAkPPAECPF|
tPOiHP ePvhPF FpOLUrPãFFkPPArP hPFAtPOCPFAwxPFA hPFibPLiCPF HPilP aApPOLEnPL hPFtPOASPF hPFiHPnPL nPLA| kPPArPNP hPFAitPOrP kPPAiCPFvhPF rPibPLiCPF Goldbach conjecture@| ePrP sPFmPFADPFAnPL kPPrPitPO pPOLArPilP $1,000,000@ aAsPFiHP aApPOLnPLArP pPOLikPPiWvPF - aArP tPOACPFAwxPFA ePWvPFA idPLKPitPOoPF iHPSPF sPFhPFjPL| aApPOLnPLAikPP SFUDFU çpPOLmPFANP kPPrPitPO hPFiHP iyP, iyP ikPPAnPL ijPLAwxPF FpOLZNPY sPFMKPzA (even integer)@-ikPP dLUEWvPF imPF´ElPkPP sPFMKPzArP* (Prime number)@ iyPAgPOfPOlP EhPFisPFiHP ilPKPA yPAbPL| iyPmPFnPL,

4 = 2 + 2
6 = 3 + 3
50 = 31 + 19
120 = 79 + 41

ilPigPO pPOLwxPUnPL| SFUDFU mPFinPL rPAKPiHPnPL 1998 sPFAilP kPPEÈOLpPOLwvPOWvPFAirPrP sPFAhPFAiyPz idPLKPAinPLA igPOiCPF sPFÈOLpPOLkPPYWvPFA 400,000,000,000,000 pPOLyPYÙPO sPFEtPOz!

ePHPArP iCPFAôPO kPPirP Reimann Hypothesis@-ePrP aAilPAcPFnPLAWvPFA kPPirP ifPOlPA yPAkPP| ePWvPFA aipPOL¾PPAkFÖOtPO jPLEWvPFlP| yPÿArPA aArPoPF jPLAnPLitPO vhPF©CUFkPP ePrP sPFÈOLpPOLikPPY tPOÿAidPLrP jPLAnPLAvhPF çpPOLcUFrP HPvhPF pPOLAoPFbPLA yPAbPL - SFUDFU lPAvhPFi`çFHPrPQ yPAHPArP aipPOL¾PPA| nPLA iyPitPO cPFAvhPFilP isPFvhPF google.com-eP EfPOirP iyPitPO pPOLAirPnPL| aArP yPÿArPA HPAMlPAbPL pPOLwxPFitPO cPFAnPL tPOÿAidPLrP jPLAnPLAvhPF 2 EkPP 3 HPCPFrP aAigPO FpOLUijPLA-HPAEXPYkPPQ idPLSPF pPOLEÀeOL`kPPAbPL pPOLETPkPP gOUhPF-ePrP ilPKPA 'sFUÓOdPrPQ, sFUDPFApPOLAÀeOL` oPF amPFrPñPL'-itPO ePvhPF EnPLibPL KLUHP sFUÓOdPrP aAilPAcPFnPLA aAiCPF|

imPF´ElPkPP sPFMKPzArP aAcPFrPNP aAmPFAidPLrP dPLQGPLYEdPLnPL EHPEãPFÉPtPO kPPirPiCPF| ePidPLrP aAcPFrPNP EkPP sPFtPOzvhPF asPFMlPgLÔP - nPLAEkPP ePrPAoPF imPFinPL cPFilP SFÖÍPlPA! ainPLikPPvhPF icPFêPLA kPPirP ePisPFiCPFnPL ePmPFnPL ikPPAnPL sFZÀeOL` aAEHPúPOArP kPPrPitPO yPA EdPLibPL imPF´ElPkPP sPFMKPzA sPFÈOLpPOLikPPY FpOLZHPYABPOAsPF kPPrPA yPAbPL! gPOsPF² EnPLijPLoPF icPFêPLA kPPirPECPFilPnPL| ePmPFnPL ikPPAnPL sFZÀeOL` pPOLAoPFbPLA yPAiHP EkPP yPA EdPLibPL aAmPFrPA imPF´ElPkPP sPFMKPzA gPOVPFnPL kPPrPitPO pPOLArPiHPA yPtPO HPwxPF vhPF©CPFA? EkPPMHPA HPlPitPO pPOLArPHP dLUEWvPF EnPLEdPLYêPL sPFMKPzArP mPFiDPFz kPPtPOgOUElP imPF´ElPkPP sPFMKPzA TPAkPPitPO pPOLAirP| tPOA ErPmPFzAnPL ePmPFnPL ePkPPWvPFA sFZiÀeOL`rP sPFÆPFAHPnPLA kPPirPECPFilPnPL yPA EdPLibPL nPLAEkPP imPF´ElPkPP sPFMKPzArP aAcPFrPNP KLUHP GPLEnPLêPL BPOAiHP HPzAKPzA ÀePÝA yPAbPL| isPFvhPF function@ ikPP HPlPA hPFbPL Riemann Zeta Function@| ePWvPFA çpPOLmPFANP kPPrPA igPOilP nPLAEkPP sPFMKPzAidPLrP tUOGPLlPEkPP aAcPFrPNP sPFHP VPFALÕPLA kPPirP idPLoPFbPLA yPAiHP|

tPOA ErPmPFzAnPL hPFAvhPFipPOLAETPEsPFsPF EnPLibPL hPFVPFAð ePtPO ûihPFûicPF kPPrPArP EkPP aAiCPF? aAsPFilP Prime Number@ aArP Cryptography@ pPOLrPãPOpPOLrP EnPLBPOYrPSPFQlP| Cryptography@ nPLAmPFWvPFA aicPFnPLA lPAgPOiCPF? ePWvPFA aArP EkPPCUFvhPF nPLbPL, ePWvPFA ePkPPWvPFA pPOLªPìEtPO yPA EdPLibPL igPOApPOLnPLQbPL tPOiTPzrP aAdPLAnPL çpPOLdPLAnPL kPPrPA hPFbPL| ePHPM SFUDFUmPFAÀeOL` tPOiTPzrP çpPOLApPOLkPPvhPF tPOArP wvPOªPìArP kPPrPitPO pPOLArPiHPnPL| aTPYAð HPAEkPPidPLrP kPPAiCPF ePWvPFA TPAkPPiHP lUkPPinPLA| ePvhPF iyP aAmPFrPA vhPF×FWvPFArPinPLWvPF-eP iÀePÝEwPOtPO kPPAwPOY HPzHPhPFArP kPPErP tPOArP sFUrP¾PPAoPF EnPLBPOYrP kPPirP imPF´ElPkPP sPFMKPzrP wvPOpPOLirP| 1977 sPFAilP EtPOnPLjPLnPL CPFAÀeOL` Ron Rivest, Adi Shamir, @aArP Leonard Adleman ePvhPF vhPF×FWvPFArPinPLWvPF sFUrP¾PPArP jPLnPLz Algorithm aAEHPúPOArP kPPirPECPFilPnPL| ePvhPF pPOLªPìEtPOitPO dLUiWvPFA HÖhPFð imPF´ElPkPP sPFMKPzAikPP gOUNP kPPirP ePkPPWvPFA sPFMKPzA pPOLAoPFbPLA yPAbPL, yPAikPP HPlPA hPFbPL cPFAEHP (Key)@| ePvhPF HPwxPF sPFMKPzAWvPFAvhPF aAmPFrPA vhPF×FWvPFArPinPLWvPF EdPLibPL aAdPLAnPL çpPOLdPLAnPL kPPErP| aArP ePvhPF imPF´ElPkPP sPFMKPzAgOUElP aApPOLnPLArP iÀePÝEwPOWvPF kPPAwPOY HPA anPLz ikPPAinPLA tPOiTPzrP sPFMikPPtPO HPhPFnPL kPPirP| tPOAhPFilP HUJPFitPOvhPF pPOLArPiCPFnPL FpOLUirPA EHPXPbPLEWvPFrP sFUrP¾PPA EnPLBPOYrP kPPirP kPPtPO sPFhPFijPL eý HPwxPF sPFMKPzAWvPFAikPP (Key)@ wvPOðpPOLAdPLikPP EHPi`ÂLSPFXPNP kPPrPA yPAi©CPF| yPtPO HPwxPF sPFMKPzA hPFiHP, tPOArP wvPOðpPOLAdPLkPP EHPi`ÂLSPFXPNP hPFiHP tPOtPO kPPEVPFnPL, aTPYAð aApPOLEnPL tPOtPO sFUrPE¾PPtPO! tPOiHP aAmPFAidPLrP EnPLEåcPFtPO hPFitPO hPFiHP, iyP dLUEWvPF imPF´ElPkPP sPFMKPzA aAmPFrPA çpPOLTPimPF gOUNP kPPirPECPFlPAmPF tPOArPA aAidPL´ imPF´ElPkPP EkPPnPLA! EkPP BPOAiHP pPOLrPQ¾PPA kPPrPHP tPOA? aAmPFAidPLrP gPOiHPYrP EHPXPbPL iyP BPOArPitPOrP Indian Institute of Technology, Kanpur-ePrP çpPOLifPOsPFrP aAgPOrPoPFbPLAlP ePHPM tPOÿArP CPFAÀeOL` nPLQrPjPL aArP nPLQEtPOnPL ePmPFnPL ePkPPWvPFA pPOLªPìEtPO aAEHPúPOArP kPPirPiCPFnPL yPA EdPLibPL ikPPAnPL sPFMKPzA imPF´ElPkPP EkPPnPLA yPAcPFAvhPF kPPrPA yPAiHP| EkPPÙUO mPFinPL rPAKPiHPnPL ePvhPF pPOLªPìEtPOitPO EkPPÙUO imPF´ElPkPP sPFMKPzA ûitPOrPQ kPPrPA yPAiHP nPLA|

ilPKPA HPwxPF hPFibPL yPAi©CPF| tPOAvhPF ePHPArP aAmPFAidPLrP HPAéPFHP jPLQHPinPL gPOENPitPOrP EHPãPFÉPbPLkPPrP HPzHPhPFAirPrP wvPOdPLAhPFrPNP EdPLibPL ilPKP iSPFXP kPPrPHP| yPÿArPA EHPXPdPL jPLAnPLitPO cPFAnPL ePKPAinPL iKPAÿjPL kPPrPitPO pPOLAirPnPL| sPFtPOzvhPF asPFADPFArPNP: http://www.ams.org/mathmoment|

DPFrPqnPL aApPOLEnPL yPKPnPL HPAjPLArP kPPirPnPL, tPOKPnPL ikPPAnPL ædPiHPzrP dPLAmPF ilPKPA TPAikPP tPOAitPO kPPibPLkPPEWvPF sPFAMikPPEtPOkPP dPLÿAEwxPFrP (Bar Code)@ sPFAhPFAiyPz| ePKPAinPL HPzHPhPFArP kPPrPA hPFbPL Modular Arithmatic| tPOArPpPOLrP ePvhPF iyP icPFAKP Scan@ kPPirP HPzEÀoPLÝidPLrP EcPFEþPFtPO kPPrPArP sPFmPFibPLoPF isPFvhPF gPOENPtPO| Probability Theory-rP sPFfPOlP çpPOLibPLAgPO| aAHPArP BPOAHUnPL isPFvhPF Traveling Salesman-ePrP sPFmPFsPFzAEWvPFrP kPPTPA| mPFinPL kPPrPqnPL aApPOLEnPL kPPtPOgOUElP EHPiSPFXP SPFhPFrP ¦mPFNP kPPrPitPO cPFAnPL FpOLÖETPHPQ jULiwxPF| tPOAhPFilP EkPPBPOAiHP ¦mPFNP kPPrPilP aApPOLEnPL sPFHP SPFhPFrPgOUElPitPOvhPF ePkPPHPArP kPPirP yPAiHPnPL, EkPPÙUO sPFHPicPFibPL kPPmPF dLZrPñPL aEtPOÀePÝmPF kPPrPiHPnPL| isPFKPAinPLoPF isPFvhPF gPOENPtPO| mPFAnPLEcPFiÀeOL` kPPtPOoPF rPiÊPFrP HPAhPFArP aAmPFrPA idPLEKP| ePkPPidPLSPF ePkPP rPkPPmPF rPÊPF| tPOAhPFilP kPPtPOgOUElP EHPEBPOnÔP rPÊPF kPPmPFpPOLi¾PP HPzHPhPFArP kPPrPilP pPOLASPFApPOLAESPF dLUEWvPF idPLSPF kPPKPinPLA ePkPP rPiÊPFrP hPFiHP nPLA| aAmPFrPA iyP kPPAgPOjPL EdPLibPL nPLAnPLA EjPLEnPLsPF HPAnPLAvhPF iKPlPArP CPFilP (Origami)@ isPFKPAinPLoPF jPLzAEmPFEtPOkPP BPOÿAijPLrP iKPlPA| mPFhPFAkPPAiSPF EHPSPFAlP aAbPLtPOinPLrP iWvPFElPiãFFkPPApPOL pPOLAVPFAinPLArP sPFmPFibPL EkPPBPOAiHP sPFHPicPFibPL iCPFAWvPF aAbPLtPOinPL BPOÿAjPL kPPrPA yPAiHP - wvPOADPFArPNP EdPLibPL iSPFXP kPPrPA yPAiHP nPLA|
tPOiHP iSPFXP kPPrPA iyPitPOvhPF pPOLAirP ePkPP EHPKPzAtPO HPzEÀoPLÝrP wvPOEÀoPLÝ EdPLibPL| tPOiHP kPPArP wvPOEÀoPLÝ aAEmPF HPlPHP nPLA - ePWvPFA aApPOLnPLArPA BPOAHUnPL - ikPP HPA kPPArPA kPPrPitPO pPOLAirPnPL ePmPFnPL wvPOEÀoPLÝ, Poets do not go mad; but chess players do; mathematicians go mad, and cashiers; but creative artists very seldom. I am not, as will be seen, in any sense attacking logic; I only say that this anger does lie in logic, not in imagination.

sPFMKPzA EdPLibPL iKPlPA kPPrPilPvhPF EkPP gPOENPtPOEHPdPL hPFoPFbPLA yPAbPL? aAmPFrPA sPFHPAvhPF itPOA sPFMKPzA EnPLibPL nPLAwxPFAcPFAwxPFA kPPErP, tPOAhPFilP aAmPFrPA sPFHPAvhPF gPOENPtPO¸PP? tPOA aAEmPF HPlPitPO pPOLArPHP nPLA, tPOiHP aApPOLEnPL EnPLåcPFbPL gPOENPtPO¸PP yPEdPL:

pPOLAvhPF-ePrP (Pi)@ mPFAnPL pPOLÏPOASPF dPLSPFEmPFkPP ëPOAnPL pPOLyPYÙPO aApPOLnPLArP mFUKPëPO TPAikPP|
aApPOLEnPL ikPPAnPL sPFmPFbPL sPFmPFbPL Fermat’s last theorem-ePrP çpPOLmPFAiNPrP icPFêPLA kPPirP TPAikPPnPL|
aApPOLEnPL aÙPOtPOß dPLSPF rPkPPmPF BPOAiHP EpPOLTPAigPOArPAisPFrP wvPOpPOLpPOLAdPLz çpPOLmPFANP kPPrPitPO jPLAinPLnPL|
aApPOLnPLArP iWvPFElPifPOAnPL nPLÈ÷PrP dLUEWvPF imPF´ElPkPP sPFMKPzArP iyPAgPOfPOlP|
yPEdPL aApPOLnPLArP ãFíPLQikPP aApPOLEnPL ikPPAnPL GPLEnPLêPL mFUhUFitPOY HPilPnPL iyP tPOÿArP cUFlPgOUilPA isPFAjPLA ePHPM pPOLrPãPOpPOLrP sPFmPFAÙPOrPAlP|
gPOAEwxPF EkPPnPLitPO EgPOibPL yPEdPL EHPiÀePÝtPOAikPP HPilPnPL, aAEmPF lPAlP gPOAEwxPFWvPFA aTPHPA nPLQlP gPOAEwxPFWvPFA inPLHP| ePHPM tPOArP sPFAiTP iyPAgPO kPPirPnPL, tPOiHP dLUiWvPFA gPOAEwxPF ePkPPsPFAiTP nPLbPL|

sFUkPPAÙPO iGPLAXP

* DPFnPLAñPLkPP pOLZNPY sPFMKPzA, iyPEWvPF 1 HPA isPFvhPF sPFMKPzAEWvPF HPAdPL EdPLibPL anPLz ikPPAinPLA pOLZNPY sPFMKPzA ªPArPA EHPBPOAjPLz nPLbPL|

tPOTPzsFZÀeOL`:
Men and Mathematics – E.T. Bell
Of Men and Numbers: The Story of the Great Mathematicians – Jane Muir
Fermat’s Last Theorem – Amrid Aczel
On the Shoulder of Giants – Stephen Hawking
The Emperor’s New Mind – Roger Penrose
Pi in the Sky – John D, Barrow
The Last Problem – E.T. Bell
Mathematical Scandals
pPOLETPkPP gOUihPFrP ilPKPA aAnPLÓOdPHPAjPLArP oPF idPLiSPF çpPOLkPPAESPFtPO ainPLkPP çpPOLHPÓ÷Pì
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