{"id":37047,"date":"2019-03-09T11:35:39","date_gmt":"2019-03-09T09:35:39","guid":{"rendered":"http:\/\/omathimatikos.gr\/?p=37047"},"modified":"2019-03-05T07:39:46","modified_gmt":"2019-03-05T05:39:46","slug":"%ce%b7-%ce%b8%ce%b5%cf%89%cf%81%ce%af%ce%b1-%cf%84%cf%89%ce%bd-%cf%87%ce%bf%cf%81%ce%b4%cf%8e%ce%bd-%ce%bf%ce%b9-%ce%bc%ce%b1%cf%8d%cf%81%ce%b5%cf%82-%cf%84%cf%81%cf%8d%cf%80%ce%b5%cf%82-%ce%ba%ce%b1","status":"publish","type":"post","link":"https:\/\/omathimatikos.gr\/?p=37047","title":{"rendered":"\u0397 \u03b8\u03b5\u03c9\u03c1\u03af\u03b1 \u03c4\u03c9\u03bd \u03c7\u03bf\u03c1\u03b4\u03ce\u03bd, \u03bf\u03b9 \u03bc\u03b1\u03cd\u03c1\u03b5\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b5\u03c2 \u03ba\u03b1\u03b9 \u03b7 \u03b9\u03b4\u03b9\u03bf\u03c6\u03c5\u0390\u03b1 \u03c4\u03bf\u03c5 Ramanujan"},"content":{"rendered":"

<\/p>\n

\n

\u039c\u03b9\u03b1 \u03b1\u03c0\u03cc \u03c4\u03b9\u03c2 \u03c0\u03b9\u03bf \u03b5\u03bd\u03c4\u03c5\u03c0\u03c9\u03c3\u03b9\u03b1\u03ba\u03ad\u03c2 \u03bc\u03bf\u03c1\u03c6\u03ad\u03c2 \u03c3\u03c4\u03bf\u03bd \u03c7\u03ce\u03c1\u03bf \u03c4\u03c9\u03bd \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03af \u03bf \u0399\u03bd\u03b4\u03cc\u03c2 \u00ab\u03b1\u03c5\u03c4\u03bf\u03b4\u03af\u03b4\u03b1\u03ba\u03c4\u03bf\u03c2\u00bb \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 Srinivasa Ramanujan (\u03a1\u03b1\u03bc\u03b1\u03bd\u03bf\u03c5\u03c4\u03b6\u03ac\u03bd) (1887 \u2013 1920). \u03a0\u03b1\u03c1\u03ac \u03c4\u03b7 \u03c3\u03cd\u03bd\u03c4\u03bf\u03bc\u03b7 \u03b4\u03b9\u03ac\u03c1\u03ba\u03b5\u03b9\u03b1 \u03c4\u03b7\u03c2 \u00ab\u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae\u03c2\u00bb \u03b6\u03c9\u03ae\u03c2 \u03c4\u03bf\u03c5, \u03ac\u03c6\u03b7\u03c3\u03b5 \u03c0\u03af\u03c3\u03c9 \u03c4\u03bf\u03c5 \u03ad\u03bd\u03b1 \u03ad\u03c1\u03b3\u03bf \u03c0\u03bf\u03c5 \u03b1\u03c0\u03b1\u03c3\u03c7\u03bf\u03bb\u03b5\u03af \u03b1\u03ba\u03cc\u03bc\u03b7 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03ba\u03b1\u03b9 \u03c6\u03c5\u03c3\u03b9\u03ba\u03bf\u03cd\u03c2 \u2013 \u03c0\u03b1\u03c1\u03cc\u03c4\u03b9 \u03c4\u03bf \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf \u03bc\u03ad\u03c1\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03b1\u03bd\u03b1\u03ba\u03b1\u03bb\u03cd\u03c6\u03b8\u03b7\u03ba\u03b5 \u03bc\u03b5 \u03ad\u03bd\u03b1\u03bd \u03b5\u03bd\u03c4\u03b5\u03bb\u03ce\u03c2 \u03b4\u03b9\u03b1\u03b9\u03c3\u03b8\u03b7\u03c4\u03b9\u03ba\u03cc \u03ba\u03b1\u03b9 \u03bc\u03c5\u03c3\u03c4\u03b7\u03c1\u03b9\u03ce\u03b4\u03b7 \u03c4\u03c1\u03cc\u03c0\u03bf.<\/strong><\/h4>\n<\/blockquote>\n

\u039f \u03b2\u03c1\u03b1\u03b2\u03b5\u03c5\u03bc\u03ad\u03bd\u03bf\u03c2 \u03bc\u03b5 \u039d\u03cc\u03bc\u03c0\u03b5\u03bb \u03c6\u03c5\u03c3\u03b9\u03ba\u03cc\u03c2\u00a0Steven Weinberg<\/a>\u00a0\u03b8\u03c5\u03bc\u03ac\u03c4\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03c3\u03c4\u03b9\u03c2 \u03b1\u03c1\u03c7\u03ad\u03c2 \u03c4\u03b7\u03c2 \u03b4\u03b5\u03ba\u03b1\u03b5\u03c4\u03af\u03b1\u03c2 \u03c4\u03bf\u03c5 1970, \u03cc\u03c4\u03b1\u03bd \u03bc\u03b5\u03bb\u03b5\u03c4\u03bf\u03cd\u03c3\u03b5 \u03c4\u03b7 \u2013 \u03b4\u03b7\u03bc\u03bf\u03c6\u03b9\u03bb\u03ae \u03c3\u03ae\u03bc\u03b5\u03c1\u03b1 \u2013 \u03b8\u03b5\u03c9\u03c1\u03af\u03b1 \u03c4\u03c9\u03bd \u03c7\u03bf\u03c1\u03b4\u03ce\u03bd, \u03b1\u03bd\u03c4\u03b9\u03bc\u03b5\u03c4\u03ce\u03c0\u03b9\u03c3\u03b5 \u03c4\u03bf \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1 \u03c4\u03bf\u03c5 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03bf\u03cd \u03c4\u03bf\u03c5 \u03c0\u03bb\u03ae\u03b8\u03bf\u03c5\u03c2 p(n) \u03c4\u03c9\u03bd \u03b1\u03bd\u03b1\u03bb\u03cd\u03c3\u03b5\u03c9\u03bd \u03c3\u03b5 \u03ac\u03b8\u03c1\u03bf\u03b9\u03c3\u03bc\u03b1 \u03c4\u03bf\u03c5 n, \u03cc\u03c4\u03b1\u03bd \u03c4\u03bf n \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03b5\u03b3\u03ac\u03bb\u03bf. \u0391\u03c0\u03bf\u03b4\u03b5\u03af\u03c7\u03b8\u03b7\u03ba\u03b5 \u03cc\u03c4\u03b9 \u03cc\u03bb\u03bf\u03b9 \u03bf\u03b9 \u03c4\u03cd\u03c0\u03bf\u03b9 \u03c0\u03bf\u03c5 \u03c7\u03c1\u03b5\u03b9\u03b1\u03b6\u03cc\u03c4\u03b1\u03bd \u03b5\u03af\u03c7\u03b1\u03bd \u03b1\u03bd\u03b1\u03ba\u03b1\u03bb\u03c5\u03c6\u03b8\u03b5\u03af \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd Ramanujan \u03c4\u03bf 1918!<\/strong>
\n\u03a4\u03bf p(n) \u03b4\u03af\u03bd\u03b5\u03b9 \u03c4\u03bf \u03c0\u03bb\u03ae\u03b8\u03bf\u03c5\u03c2 \u03c4\u03c9\u03bd \u03c4\u03c1\u03cc\u03c0\u03c9\u03bd \u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03bf\u03c0\u03bf\u03af\u03bf\u03c5\u03c2 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bc\u03b5 \u03bd\u03b1 \u03c0\u03b1\u03c1\u03b1\u03c3\u03c4\u03ae\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc n \u03c9\u03c2 \u03ac\u03b8\u03c1\u03bf\u03b9\u03c3\u03bc\u03b1 \u03c6\u03c5\u03c3\u03b9\u03ba\u03ce\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd.
\n\u0393\u03b9\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1, p(4) = 5<\/p>\n

4 = 3 +1 = 2 +2 = 2 + 1 + 1 = 1 + 1 + 1 + 1<\/p>\n

\u0397 \u03b4\u03b9\u03b1\u03b4\u03b9\u03ba\u03b1\u03c3\u03af\u03b1 \u03bc\u03b5 \u03bc\u03b9\u03b1 \u03c0\u03c1\u03ce\u03c4\u03b7 \u03bc\u03b1\u03c4\u03b9\u03ac \u03c6\u03b1\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c0\u03b1\u03bd\u03b5\u03cd\u03ba\u03bf\u03bb\u03b7, \u03cc\u03bc\u03c9\u03c2 \u03cc\u03c4\u03b1\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 n \u03c0\u03bf\u03c5 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b4\u03b9\u03b1\u03bc\u03b5\u03c1\u03af\u03c3\u03bf\u03c5\u03bc\u03b5 \u03b1\u03c5\u03be\u03ac\u03bd\u03b5\u03c4\u03b1\u03b9, \u03b1\u03c5\u03be\u03ac\u03bd\u03b5\u03c4\u03b1\u03b9 \u03ba\u03b1\u03b9 \u03c4\u03bf \u03c0\u03bb\u03ae\u03b8\u03bf\u03c2 \u03c4\u03c9\u03bd \u03b4\u03b9\u03b1\u03bc\u03b5\u03c1\u03af\u03c3\u03b5\u03ce\u03bd p(n).
\n\u0391\u03bd\u00a0n = 10 \u03c4\u03cc\u03c4\u03b5 p(10) = 42<\/a>\u00a0<\/strong>
\n\u0391\u03bd\u00a0n = 30 \u03c4\u03cc\u03c4\u03b5 p(30) = 5604<\/strong><\/a>
\n\u0391\u03bd\u00a0n = 40 \u03c4\u03cc\u03c4\u03b5 p(40) = 37338<\/strong><\/a>
\n\"\"<\/a>\u0391\u03bd\u00a0n = 50 \u03c4\u03cc\u03c4\u03b5 p(50) = 204226<\/strong><\/a>
\n\u03ba\u03b1\u03b9 \u03b1\u03bd
\n\u0391\u03bd\u00a0n = 100 \u03c4\u03cc\u03c4\u03b5 p(100) = 190569292<\/strong><\/a>
\nTo p(n) (\u03b3\u03b9\u03b1 \u03c0\u03bf\u03bb\u03cd \u03bc\u03b5\u03b3\u03ac\u03bb\u03b1 n) \u03c0\u03c1\u03bf\u03c3\u03b5\u03b3\u03b3\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03c4\u03cd\u03c0\u03bf
\n\"\"<\/a><\/p>\n

\u039c\u03b9\u03b1 \u03b2\u03b5\u03bb\u03c4\u03b9\u03c9\u03bc\u03ad\u03bd\u03b7 \u03c0\u03c1\u03bf\u03c3\u03ad\u03b3\u03b3\u03b9\u03c3\u03b7 \u03c4\u03bf\u03c5 p(n) \u03c0\u03c1\u03bf\u03ad\u03ba\u03c5\u03c8\u03b5 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03b4\u03b9\u03cc\u03c1\u03b8\u03c9\u03c3\u03b7 \u03c0\u03bf\u03c5 \u00ab\u03bf\u03c1\u03b1\u03bc\u03b1\u03c4\u03af\u03c3\u03c4\u03b7\u03ba\u03b5\u00bb \u03bf Ramanujan:
\n\"\"<\/a><\/p>\n

\u03cc\u03c0\u03bf\u03c5 \u03bf \u03c0\u03b1\u03c1\u03ac\u03b3\u03bf\u03bd\u03c4\u03b1\u03c2<\/p>\n

\"\"<\/a>\u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \u03c4\u03bf\u03c5 n.<\/p>\n

To \u03b5\u03bd\u03c4\u03c5\u03c0\u03c9\u03c3\u03b9\u03b1\u03ba\u03cc \u03bc\u03b5 \u03c4\u03bf\u03bd \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9 \u03c4\u03cd\u03c0\u03bf \u03b5\u03af\u03bd\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03b5\u03bd\u03ce \u03b5\u03af\u03bd\u03b1\u03b9 \u00ab\u03c0\u03c1\u03bf\u03c3\u03b5\u03b3\u03b3\u03b9\u03c3\u03c4\u03b9\u03ba\u03cc\u03c2\u00bb,<\/strong><\/p>\n

\u03b3\u03b9\u03b1 n= 200 \u03b4\u03af\u03bd\u03b5\u03b9 p(n)=3972999029388<\/strong><\/p>\n

\u03c0\u03bf\u03c5 \u03c4\u03b1\u03c5\u03c4\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03c4\u03b9\u03bc\u03ae!<\/strong><\/p>\n

\u03a4\u03bf \u03b1\u03ba\u03cc\u03bc\u03b1 \u03c0\u03b9\u03bf \u03bc\u03c5\u03c3\u03c4\u03b7\u03c1\u03b9\u03ce\u03b4\u03b5\u03c2 \u03c3\u03c4\u03b7\u03bd \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03bc\u03b9\u03ba\u03c1\u03ae \u03b4\u03b9\u03cc\u03c1\u03b8\u03c9\u03c3\u03b7 (-1\/24) \u03c0\u03bf\u03c5 \u03b5\u03af\u03c7\u03b5 \u03c0\u03c1\u03bf\u03c4\u03b5\u03af\u03bd\u03b5\u03b9 \u03bf Ramanujan. \u039a\u03b1\u03bd\u03b5\u03af\u03c2, \u03bf\u03cd\u03c4\u03b5 \u03ba\u03b1\u03bd \u03bf Ramanujan, \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03c3\u03b5 \u03bd\u03b1 \u03b5\u03be\u03b7\u03b3\u03ae\u03c3\u03b5\u03b9 \u03b3\u03b9\u03b1\u03c4\u03af \u03b5\u03bc\u03c6\u03b1\u03bd\u03af\u03b6\u03b5\u03c4\u03b1\u03b9. \u03a0\u03ac\u03bd\u03c4\u03c9\u03c2, \u03b1\u03c5\u03c4\u03ae \u03b7 \u03bc\u03c5\u03c3\u03c4\u03ae\u03c1\u03b9\u03b1 \u03b4\u03b9\u03cc\u03c1\u03b8\u03c9\u03c3\u03b7 \u03ad\u03ba\u03b1\u03bd\u03b5 \u03c4\u03bf\u03bd \u03c4\u03cd\u03c0\u03bf \u03bd\u03b1 \u03b4\u03bf\u03c5\u03bb\u03b5\u03cd\u03b5\u03b9. \u039f Hardy \u03ba\u03b1\u03b9 \u03bf Ramanujan \u03b4\u03b5\u03bd \u03c3\u03c4\u03b1\u03bc\u03ac\u03c4\u03b7\u03c3\u03b1\u03bd \u03c3\u03c4\u03bf\u03bd \u03c0\u03c1\u03bf\u03c3\u03b5\u03b3\u03b3\u03b9\u03c3\u03c4\u03b9\u03ba\u03cc \u03c4\u03cd\u03c0\u03bf. \u0391\u03c1\u03b3\u03cc\u03c4\u03b5\u03c1\u03b1 \u03b1\u03bd\u03b1\u03ba\u03ac\u03bb\u03c5\u03c8\u03b1\u03bd\u00a0\u03bc\u03b9\u03b1 \u03b1\u03ba\u03c1\u03b9\u03b2\u03ae \u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1 \u03b3\u03b9\u03b1 \u03c4\u03bf p(n)<\/a>.<\/p>\n

\u03a3\u03cd\u03bc\u03c6\u03c9\u03bd\u03b1 \u03bc\u03b5 \u03c4\u03bf\u00a0newscientist<\/a><\/strong>\u00a0\u03ad\u03bd\u03b1\u03c2 \u03bd\u03ad\u03bf\u03c2 \u03c4\u03cd\u03c0\u03bf\u03c2 \u03b2\u03b3\u03b1\u03bb\u03bc\u03ad\u03bd\u03bf\u03c2 \u03b1\u03c0\u03cc \u03c4\u03b9\u03c2 \u00ab\u03bc\u03c5\u03c3\u03c4\u03b7\u03c1\u03b9\u03ce\u03b4\u03b5\u03b9\u03c2\u00bb \u03b5\u03bc\u03c0\u03bd\u03b5\u03cd\u03c3\u03b5\u03b9\u03c2 \u03c4\u03bf\u03c5 Srinivasa Ramanujan, \u03b8\u03b1 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03c3\u03b5 \u03bd\u03b1 \u03b2\u03b5\u03bb\u03c4\u03b9\u03ce\u03c3\u03b5\u03b9 \u03c4\u03b7\u03bd \u03ba\u03b1\u03c4\u03b1\u03bd\u03cc\u03b7\u03c3\u03ae \u03bc\u03b1\u03c2 \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ac \u03bc\u03b5 \u03c4\u03b9\u03c2 \u03bc\u03b1\u03cd\u03c1\u03b5\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b5\u03c2.
\n\u0395\u03c0\u2019 \u03b5\u03c5\u03ba\u03b1\u03b9\u03c1\u03af\u03b1\u03c2 \u03c4\u03b7\u03c2\u00a0125\u03b7\u03c2 \u03b5\u03c0\u03b5\u03c4\u03b5\u03af\u03bf\u03c5<\/strong>\u00a0\u03b1\u03c0\u03cc \u03c4\u03b7 \u03b3\u03ad\u03bd\u03bd\u03b7\u03c3\u03b7 \u03c4\u03bf\u03c5 , \u03bf Ken Ono \u03c4\u03bf\u03c5 \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03af\u03bf\u03c5 Emory \u03c3\u03c4\u03b7\u03bd \u0391\u03c4\u03bb\u03ac\u03bd\u03c4\u03b1, \u03bf \u03bf\u03c0\u03bf\u03af\u03bf\u03c2 \u03c0\u03b1\u03bb\u03b9\u03cc\u03c4\u03b5\u03c1\u03b1 \u03b5\u03af\u03c7\u03b5 \u03b1\u03bd\u03b1\u03ba\u03b1\u03bb\u03cd\u03c8\u03b5\u03b9 \u03c4\u03b1 \u03bc\u03c5\u03c3\u03c4\u03b7\u03c1\u03b9\u03ce\u03b4\u03b7 \u03b2\u03ae\u03bc\u03b1\u03c4\u03b1 \u03c3\u03c4\u03b7 \u03c3\u03ba\u03ad\u03c8\u03b7 \u03c4\u03bf\u03c5 Ramanujan, \u03b5\u03be\u03ad\u03c4\u03b1\u03c3\u03b5 \u03b3\u03b9\u03b1 \u03ac\u03bb\u03bb\u03b7 \u03bc\u03b9\u03b1 \u03c6\u03bf\u03c1\u03ac \u03c4\u03b9\u03c2 \u03c3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b9\u03c2 \u03b5\u03c0\u03b9\u03c3\u03c4\u03bf\u03bb\u03ad\u03c2 \u03c4\u03bf\u03c5 (\u03ad\u03bd\u03b1 \u03c0\u03b9\u03bf \u03c4\u03b5\u03c7\u03bd\u03b9\u03ba\u03cc \u03ac\u03c1\u03b8\u03c1\u03bf \u03bc\u03c0\u03bf\u03c1\u03b5\u03af\u03c4\u03b5 \u03bd\u03b1 \u03b4\u03b9\u03b1\u03b2\u03ac\u03c3\u03b5\u03c4\u03b5\u00a0\u0395\u0394\u03a9: mathcs.emory.edu<\/strong><\/a>). \u039f Ken Ono \u03b5\u03c0\u03b9\u03ba\u03ad\u03bd\u03c4\u03c1\u03c9\u03c3\u03b5 \u03c4\u03bf \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03bd \u03c4\u03bf\u03c5, \u03c3\u03c4\u03b7\u03bd \u03c4\u03b5\u03bb\u03b5\u03c5\u03c4\u03b1\u03af\u03b1 \u03b3\u03bd\u03c9\u03c3\u03c4\u03ae \u03b5\u03c0\u03b9\u03c3\u03c4\u03bf\u03bb\u03ae \u03c0\u03bf\u03c5 \u03ad\u03b3\u03c1\u03b1\u03c8\u03b5 \u03bf Ramanujan \u03c0\u03c1\u03bf\u03c2 \u03c4\u03bf\u03bd Hardy, \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ac \u03bc\u03b5 \u03ad\u03bd\u03b1 \u03b5\u03af\u03b4\u03bf\u03c2 \u03c3\u03c5\u03bd\u03b1\u03c1\u03c4\u03ae\u03c3\u03b5\u03c9\u03bd \u03c0\u03bf\u03c5 \u03b1\u03c0\u03bf\u03ba\u03b1\u03bb\u03bf\u03cd\u03bd\u03c4\u03b1\u03b9 modular \u03bc\u03bf\u03c1\u03c6\u03ad\u03c2.\u00a0A\u03c5\u03c4\u03ad\u03c2 \u03bf\u03b9 \u03c3\u03c5\u03bd\u03b1\u03c1\u03c4\u03ae\u03c3\u03b5\u03b9\u03c2 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03bf\u03cd\u03bd\u03c4\u03b1\u03b9 \u03c3\u03ae\u03bc\u03b5\u03c1\u03b1 \u03c3\u03c4\u03bf\u03bd \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc \u03c4\u03b7\u03c2 \u03b5\u03bd\u03c4\u03c1\u03bf\u03c0\u03af\u03b1\u03c2 \u03c4\u03c9\u03bd \u03bc\u03b1\u03cd\u03c1\u03c9\u03bd \u03c4\u03c1\u03c5\u03c0\u03ce\u03bd<\/strong>.\u00a0\u0397 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u03b1\u03c5\u03c4\u03ae \u03c3\u03c5\u03bd\u03b4\u03ad\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03b5\u03ba\u03c0\u03bb\u03b7\u03ba\u03c4\u03b9\u03ba\u03ae \u03c0\u03c1\u03cc\u03b2\u03bb\u03b5\u03c8\u03b7 \u03c4\u03bf\u03c5 Stephen Hawking \u03cc\u03c4\u03b9 \u03bf\u03b9 \u03bc\u03b1\u03cd\u03c1\u03b5\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b5\u03c2 \u03b5\u03ba\u03c0\u03ad\u03bc\u03c0\u03bf\u03c5\u03bd \u03b1\u03ba\u03c4\u03b9\u03bd\u03bf\u03b2\u03bf\u03bb\u03af\u03b1.<\/strong>
\n\u0393\u03b9\u03b1 \u03c4\u03bf\u03bd \u03b1\u03bd\u03b1\u03b3\u03bd\u03ce\u03c3\u03c4\u03b7 \u03c0\u03bf\u03c5 \u03b4\u03b5\u03bd \u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03b5\u03b9 \u03c4\u03bf \u03c6\u03b1\u03b9\u03bd\u03cc\u03bc\u03b5\u03bd\u03bf Ramanujan, \u03c0\u03b1\u03c1\u03b1\u03b8\u03ad\u03c4\u03bf\u03c5\u03bc\u03b5 \u03c3\u03c4\u03b7 \u03c3\u03c5\u03bd\u03ad\u03c7\u03b5\u03b9\u03b1 \u03ad\u03bd\u03b1 \u03b1\u03c0\u03cc\u03c3\u03c0\u03b1\u03c3\u03bc\u03b1 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03c0\u03c1\u03cc\u03bb\u03bf\u03b3\u03bf \u03c0\u03bf\u03c5 \u03ad\u03b3\u03c1\u03b1\u03c8\u03b5 \u03bf \u0393\u03b9\u03ce\u03c1\u03b3\u03bf\u03c2 \u039b. \u0395\u03c5\u03b1\u03b3\u03b3\u03b5\u03bb\u03cc\u03c0\u03bf\u03c5\u03bb\u03bf\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03b5\u03bb\u03bb\u03b7\u03bd\u03b9\u03ba\u03ae \u03ad\u03ba\u03b4\u03bf\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03b2\u03b9\u03b2\u03bb\u03af\u03bf\u03c5 \u00ab\u03a1\u0391\u039c\u0391\u039d\u039f\u03a5\u03a4\u0396\u0391\u039d, \u039f \u0399\u03bd\u03b4\u03cc\u03c2 \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2<\/strong>, Robert Kanigel, \u03b5\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u03a4\u03c1\u03b1\u03c5\u03bb\u03cc\u03c2\u00bb<\/p>\n

(\u2026.)\u0397 \u03c0\u03b5\u03c1\u03af\u03c0\u03c4\u03c9\u03c3\u03b7 \u03c4\u03bf\u03c5 \u0392\u03c1\u03b1\u03c7\u03bc\u03ac\u03bd\u03bf\u03c5 \u0399\u03bd\u03b4\u03bf\u03cd, Srinivasa Ramanujan (1887 \u2013 1920), \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03af \u03bc\u03b9\u03b1 \u03b1\u03c0\u03cc \u03c4\u03b9\u03c2 \u03c0\u03b9\u03bf \u03c3\u03c0\u03ac\u03bd\u03b9\u03b5\u03c2 \u03c0\u03b5\u03c1\u03b9\u03c0\u03c4\u03ce\u03c3\u03b5\u03b9\u03c2 \u03b5\u03be\u03b1\u03af\u03c1\u03b5\u03c4\u03b7\u03c2 \u03b4\u03b7\u03bc\u03b9\u03bf\u03c5\u03c1\u03b3\u03b9\u03ba\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 \u03c3\u03c4\u03b7\u03bd \u03b9\u03c3\u03c4\u03bf\u03c1\u03af\u03b1 \u03c4\u03b7\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae\u03c2 \u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b7\u03c2. \u038a\u03c3\u03c9\u03c2 \u03c4\u03b7\u03bd \u03c0\u03b9\u03bf \u03b1\u03be\u03b9\u03bf\u03c3\u03b7\u03bc\u03b5\u03af\u03c9\u03c4\u03b7, \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03ac\u03c0\u03bf\u03c8\u03b7 \u03c4\u03b7\u03c2 \u03c0\u03c1\u03c9\u03c4\u03bf\u03c4\u03c5\u03c0\u03af\u03b1\u03c2 \u03c4\u03bf\u03c5 \u03ad\u03c1\u03b3\u03bf\u03c5 \u03c0\u03bf\u03c5 \u03c0\u03b1\u03c1\u03ae\u03b3\u03b1\u03b3\u03b5 \u03c9\u03c2 \u03b1\u03c5\u03c4\u03bf\u03b4\u03af\u03b4\u03b1\u03ba\u03c4\u03bf\u03c2 \u2013 \u03bc\u03ad\u03c7\u03c1\u03b9 \u03c4\u03b1 \u03b5\u03af\u03ba\u03bf\u03c3\u03b9 \u03ad\u03be\u03b9 \u03c4\u03bf\u03c5 \u03c7\u03c1\u03cc\u03bd\u03b9\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2!
\n\u039c\u03b5\u03c4\u03ac \u03c4\u03b7\u03bd \u03b5\u03c0\u03b9\u03c4\u03c5\u03c7\u03ae \u03bf\u03bb\u03bf\u03ba\u03bb\u03ae\u03c1\u03c9\u03c3\u03b7 \u03c4\u03c9\u03bd \u03b3\u03c5\u03bc\u03bd\u03b1\u03c3\u03b9\u03b1\u03ba\u03ce\u03bd \u03c4\u03bf\u03c5 \u03c3\u03c0\u03bf\u03c5\u03b4\u03ce\u03bd, \u03b1\u03c6\u03bf\u03c3\u03b9\u03ce\u03b8\u03b7\u03ba\u03b5 \u03c0\u03bb\u03ae\u03c1\u03c9\u03c2 \u03c3\u03c4\u03b7 \u03bc\u03b5\u03bb\u03ad\u03c4\u03b7 \u03c4\u03c9\u03bd \u03bc\u03b1\u03b8\u03b7\u03bc\u03ac\u03c4\u03c9\u03bd \u03c0\u03bf\u03c5 \u03b1\u03c0\u03b1\u03b9\u03c4\u03bf\u03cd\u03bd\u03c4\u03b1\u03bd \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03ba\u03c4\u03b7\u03c3\u03b7 \u03c0\u03c4\u03c5\u03c7\u03af\u03bf\u03c5 \u03c0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03b9\u03b1\u03ba\u03bf\u03cd \u03ba\u03bf\u03bb\u03b5\u03b3\u03af\u03bf\u03c5. \u0395\u03bc\u03c0\u03bd\u03b5\u03cc\u03bc\u03b5\u03bd\u03bf\u03c2 \u03b1\u03c0\u03cc \u03c4\u03b7 \u03bc\u03b5\u03bb\u03ad\u03c4\u03b7 \u03b5\u03bd\u03cc\u03c2 \u03b5\u03b3\u03c7\u03b5\u03b9\u03c1\u03b9\u03b4\u03af\u03bf\u03c5, \u03b4\u03bf\u03cd\u03bb\u03b5\u03c8\u03b5 \u03bc\u03cc\u03bd\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03c0\u03b1\u03c1\u03ae\u03b3\u03b1\u03b3\u03b5 \u03bc\u03b9\u03b1 \u03c3\u03b5\u03b9\u03c1\u03ac \u03b1\u03c0\u03cc \u03b8\u03b5\u03c9\u03c1\u03ae\u03bc\u03b1\u03c4\u03b1 \u03ba\u03b1\u03b9 \u03ac\u03bb\u03bb\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03b1, \u03ba\u03c5\u03c1\u03af\u03c9\u03c2 \u03c3\u03c4\u03b7 \u03b8\u03b5\u03c9\u03c1\u03af\u03b1 \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd. \u0397 \u03b1\u03c0\u03bf\u03c4\u03c5\u03c7\u03af\u03b1 \u03c4\u03bf\u03c5, \u03cc\u03bc\u03c9\u03c2, \u03bd\u03b1 \u03b1\u03c0\u03bf\u03ba\u03c4\u03ae\u03c3\u03b5\u03b9 \u03c0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03b9\u03b1\u03ba\u03cc \u03c4\u03af\u03c4\u03bb\u03bf \u03c3\u03c0\u03bf\u03c5\u03b4\u03ce\u03bd, \u03c0\u03bf\u03c5 \u03b4\u03c5\u03c3\u03c7\u03ad\u03c1\u03b1\u03b9\u03bd\u03b5 \u03c0\u03bf\u03bb\u03cd \u03c4\u03b7\u03bd \u03c0\u03c1\u03bf\u03c3\u03c0\u03ac\u03b8\u03b5\u03b9\u03b1 \u03b1\u03bd\u03b5\u03cd\u03c1\u03b5\u03c3\u03b7\u03c2 \u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b1\u03c2, \u03b1\u03bb\u03bb\u03ac \u03ba\u03c5\u03c1\u03af\u03c9\u03c2 \u03b7 \u03b5\u03c0\u03b9\u03c6\u03c5\u03bb\u03b1\u03ba\u03c4\u03b9\u03ba\u03cc\u03c4\u03b7\u03c4\u03b1 \u03ad\u03c9\u03c2 \u03b1\u03c0\u03cc\u03c1\u03c1\u03b9\u03c8\u03b7 \u03c0\u03bf\u03c5 \u03b3\u03bd\u03ce\u03c1\u03b9\u03c3\u03b5 \u03c3\u03c4\u03b7\u03bd \u03c0\u03c1\u03bf\u03c3\u03c0\u03ac\u03b8\u03b5\u03b9\u03ac \u03c4\u03bf\u03c5 \u03bd\u03b1 \u03c0\u03b5\u03c4\u03cd\u03c7\u03b5\u03b9 \u03b1\u03bd\u03b1\u03b3\u03bd\u03ce\u03c1\u03b9\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03b1\u03be\u03af\u03b1\u03c2 \u03c4\u03bf\u03c5 \u03ad\u03c1\u03b3\u03bf\u03c5 \u03c4\u03bf\u03c5 \u03b1\u03c0\u03cc \u03c3\u03c5\u03bc\u03c0\u03b1\u03c4\u03c1\u03b9\u03ce\u03c4\u03b5\u03c2 \u03c4\u03bf\u03c5 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 (\u03bc\u03b5 \u03c4\u03b7\u03bd \u03b5\u03c5\u03c7\u03ac\u03c1\u03b9\u03c3\u03c4\u03b7 \u03ad\u03ba\u03c0\u03bb\u03b7\u03be\u03b7 \u03b5\u03bb\u03ac\u03c7\u03b9\u03c3\u03c4\u03c9\u03bd \u03b5\u03be\u03b1\u03b9\u03c1\u03ad\u03c3\u03b5\u03c9\u03bd), \u03c0\u03b1\u03c1\u2019 \u03bf\u03bb\u03af\u03b3\u03bf \u03bd\u03b1 \u03bf\u03b4\u03b7\u03b3\u03ae\u03c3\u03bf\u03c5\u03bd \u03c3\u03b5 \u03ac\u03b4\u03bf\u03be\u03bf \u03c4\u03ad\u03bb\u03bf\u03c2 \u03c4\u03b7 \u03c3\u03c4\u03b1\u03b4\u03b9\u03bf\u03b4\u03c1\u03bf\u03bc\u03af\u03b1 \u03c4\u03bf\u03c5.
\n\u038c\u03bb\u03b1 \u03ac\u03bb\u03bb\u03b1\u03be\u03b1\u03bd, \u03cc\u03c4\u03b1\u03bd \u03bf G. H. Hardy (1877 \u2013 1947), \u03ad\u03bd\u03b1\u03c2 \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03b4\u03c5\u03bf \u03c0\u03b9\u03bf \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u0386\u03b3\u03b3\u03bb\u03bf\u03c5\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03c0\u03bf\u03c7\u03ae\u03c2 \u03c4\u03bf\u03c5 \u2013 \u03bf \u03ac\u03bb\u03bb\u03bf\u03c2 \u03ae\u03c4\u03b1\u03bd \u03bf \u03c6\u03af\u03bb\u03bf\u03c2 \u03ba\u03b1\u03b9 \u03c3\u03c5\u03bd\u03b5\u03c1\u03b3\u03ac\u03c4\u03b7\u03c2 \u03c4\u03bf\u03c5 \u03c3\u03b5 \u03c3\u03b5\u03b9\u03c1\u03ac \u03ba\u03bf\u03b9\u03bd\u03ce\u03bd \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03b4\u03b7\u03bc\u03bf\u03c3\u03b9\u03b5\u03cd\u03c3\u03b5\u03c9\u03bd, J. E. Littlewood, \u03b5\u03c4\u03b1\u03af\u03c1\u03bf\u03c2 \u03ba\u03b9 \u03b1\u03c5\u03c4\u03cc\u03c2, \u03cc\u03c0\u03c9\u03c2 \u03ba\u03b1\u03b9 \u03bf hardy, \u03c4\u03cc\u03c3\u03bf \u03c4\u03bf\u03c5 \u039a\u03bf\u03bb\u03b5\u03b3\u03af\u03bf\u03c5 \u03a4\u03c1\u03af\u03bd\u03b9\u03c4\u03b9 \u03c4\u03bf\u03c5 \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03af\u03bf\u03c5 \u03c4\u03bf\u03c5 \u039a\u03ad\u03bc\u03c0\u03c1\u03b9\u03c4\u03b6, \u03cc\u03c3\u03bf \u03ba\u03b1\u03b9 \u03c4\u03b7\u03c2 \u0392\u03b1\u03c3\u03b9\u03bb\u03b9\u03ba\u03ae\u03c2 \u0395\u03c4\u03b1\u03b9\u03c1\u03b5\u03af\u03b1\u03c2 \u03c4\u03bf\u03c5 \u039b\u03bf\u03bd\u03b4\u03af\u03bd\u03bf\u03c5 \u2013 \u03ad\u03bb\u03b1\u03b2\u03b5 \u03bc\u03b9\u03b1 \u03b5\u03c0\u03b9\u03c3\u03c4\u03bf\u03bb\u03ae \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd Ramanujan \u03c0\u03bf\u03c5 \u03c3\u03c5\u03bd\u03bf\u03b4\u03b5\u03c5\u03cc\u03c4\u03b1\u03bd \u03b1\u03c0\u03cc \u03c0\u03bf\u03bb\u03bb\u03ad\u03c2 \u03c3\u03b5\u03bb\u03af\u03b4\u03b5\u03c2 \u03bc\u03b5 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03b8\u03b5\u03c9\u03c1\u03ae\u03bc\u03b1\u03c4\u03b1.
\n\u039f Hardy \u03c3\u03b5 \u03b1\u03bd\u03c4\u03af\u03b8\u03b5\u03c3\u03b7 \u03bc\u03b5 \u03b4\u03c5\u03bf \u03b5\u03ba\u03bb\u03b5\u03ba\u03c4\u03bf\u03cd\u03c2 \u03c3\u03c5\u03bd\u03b1\u03b4\u03ad\u03bb\u03c6\u03bf\u03c5\u03c2 \u03c4\u03bf\u03c5 \u03c0\u03bf\u03c5 \u03ad\u03bb\u03b1\u03b2\u03b1\u03bd \u03b1\u03bd\u03ac\u03bb\u03bf\u03b3\u03bf\u03c5 \u03c0\u03b5\u03c1\u03b9\u03b5\u03c7\u03bf\u03bc\u03ad\u03bd\u03bf\u03c5 \u03b5\u03c0\u03b9\u03c3\u03c4\u03bf\u03bb\u03ad\u03c2 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd Ramanujan \u03ba\u03b1\u03b9 \u03c0\u03c1\u03bf\u03c6\u03b1\u03bd\u03ce\u03c2 \u03b1\u03b4\u03b9\u03b1\u03c6\u03cc\u03c1\u03b7\u03c3\u03b1\u03bd, \u03ba\u03b1\u03c4\u03b1\u03c0\u03b9\u03ac\u03c3\u03c4\u03b7\u03ba\u03b5 (\u03b1\u03c0\u03cc \u03ba\u03bf\u03b9\u03bd\u03bf\u03cd \u03bc\u03b5 \u03c4\u03bf\u03bd Littlewood, \u03c4\u03bf\u03c5 \u03bf\u03c0\u03bf\u03af\u03bf\u03c5 \u03b6\u03ae\u03c4\u03b7\u03c3\u03b5 \u03ba\u03b1\u03b9 \u03ad\u03bb\u03b1\u03b2\u03b5 \u03c4\u03b7 \u03b2\u03bf\u03ae\u03b8\u03b5\u03b9\u03b1) \u03bc\u03b5 \u03c4\u03b7 \u03bc\u03b5\u03bb\u03ad\u03c4\u03b7 \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u03ba\u03b1\u03c4\u03b1\u03bd\u03cc\u03b7\u03c3\u03b7 \u03c4\u03c9\u03bd \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03c3\u03bc\u03ac\u03c4\u03c9\u03bd \u03c0\u03bf\u03c5 \u03c0\u03b5\u03c1\u03b9\u03b5\u03af\u03c7\u03b5 \u03b7 \u03b5\u03c0\u03b9\u03c3\u03c4\u03bf\u03bb\u03ae. \u0391\u03c1\u03ba\u03b5\u03c4\u03ac \u03b1\u03c0\u03cc \u03b1\u03c5\u03c4\u03ac \u03c4\u03b1 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03b1 \u03ae\u03c4\u03b1\u03bd \u03bd\u03ad\u03b1, \u03b5\u03bd\u03ce \u03c3\u03c5\u03c7\u03bd\u03ac \u03ad\u03bc\u03bf\u03b9\u03b1\u03b6\u03b1\u03bd \u03ba\u03b1\u03b9 \u03b1\u03c0\u03bf\u03bb\u03cd\u03c4\u03c9\u03c2 \u03b4\u03c5\u03c3\u03bd\u03cc\u03b7\u03c4\u03b1, \u03c4\u03bf\u03c5\u03bb\u03ac\u03c7\u03b9\u03c3\u03c4\u03bf\u03bd \u03c9\u03c2 \u03c0\u03c1\u03bf\u03c2 \u03c4\u03bf\u03bd \u00ab\u03b1\u03c0\u03bf\u03b4\u03b5\u03b9\u03ba\u03c4\u03b9\u03ba\u03cc\u00bb \u03c3\u03c5\u03bb\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc \u03c0\u03bf\u03c5 \u03c4\u03b1 \u03c3\u03c4\u03ae\u03c1\u03b9\u03b6\u03b5. \u0397 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7, \u03bc\u03b5 \u03c4\u03b7\u03bd \u03b1\u03c5\u03c3\u03c4\u03b7\u03c1\u03ae \u03ad\u03bd\u03bd\u03bf\u03b9\u03b1 \u03c4\u03bf\u03c5 \u03cc\u03c1\u03bf\u03c5 (\u03b1\u03c5\u03c4\u03ae \u03c0\u03bf\u03c5 \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03b5 \u03c4\u03b7 \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03b7 \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03ae \u03c4\u03b7\u03c2 \u03b1\u03c1\u03c7\u03b1\u03af\u03b1\u03c2 \u03b5\u03bb\u03bb\u03b7\u03bd\u03b9\u03ba\u03ae\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae\u03c2 \u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b7\u03c2 \u03c3\u03c4\u03bf\u03bd \u03c4\u03c1\u03cc\u03c0\u03bf \u03bc\u03b5 \u03c4\u03bf\u03bd \u03bf\u03c0\u03bf\u03af\u03bf \u03ba\u03ac\u03bd\u03bf\u03c5\u03bc\u03b5 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03c3\u03ae\u03bc\u03b5\u03c1\u03b1), \u03ae\u03c4\u03b1\u03bd \u03ac\u03b3\u03bd\u03c9\u03c3\u03c4\u03b7 \u03c3\u03c4\u03bf\u03bd Ramanujan. \u039f\u03b9 \u00ab\u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03b9\u03c2\u00bb \u03c4\u03bf\u03c5 \u03ae\u03c4\u03b1\u03bd \u03b1\u03c0\u03bf\u03bb\u03cd\u03c4\u03c9\u03c2 \u03b9\u03b4\u03b9\u03cc\u03bc\u03bf\u03c1\u03c6\u03b7\u03c2 \u03c6\u03cd\u03c3\u03b5\u03c9\u03c2 \u03ba\u03b1\u03b9 \u03c3\u03c4\u03b7\u03c1\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03bd \u03ba\u03c5\u03c1\u03af\u03c9\u03c2 \u03c3\u03c4\u03b7 \u03b4\u03b9\u03b1\u03af\u03c3\u03b8\u03b7\u03c3\u03ae \u03c4\u03bf\u03c5, \u03c0\u03bf\u03c5 \u03c4\u03bf\u03bd \u03bf\u03b4\u03b7\u03b3\u03bf\u03cd\u03c3\u03b5 \u03c0\u03ac\u03bd\u03c4\u03bf\u03c4\u03b5 \u03c3\u03b5 \u03bc\u03b9\u03b1 \u03c3\u03b5\u03b9\u03c1\u03ac \u00ab\u03c0\u03b5\u03c1\u03af\u03b5\u03c1\u03b3\u03c9\u03bd\u00bb \u03b2\u03b7\u03bc\u03ac\u03c4\u03c9\u03bd \u03c3\u03c4\u03bf \u03c0\u03bb\u03b1\u03af\u03c3\u03b9\u03bf \u03bc\u03b9\u03b1\u03c2 \u03b5\u03bd\u03c4\u03b5\u03bb\u03ce\u03c2 \u03b4\u03b9\u03ba\u03ae\u03c2 \u03c4\u03bf\u03c5 \u03c3\u03c5\u03bb\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03b9\u03ba\u03ae\u03c2. \u0391\u03bb\u03bb\u03ac \u03ba\u03b1\u03b9 \u03cc\u03c3\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03b1 \u03ae\u03c4\u03b1\u03bd \u03b3\u03bd\u03c9\u03c3\u03c4\u03ac, \u03c0\u03c1\u03bf\u03ba\u03ac\u03bb\u03b5\u03c3\u03b1\u03bd \u03ba\u03b9 \u03b1\u03c5\u03c4\u03ac \u03c4\u03b7\u03bd \u03ad\u03ba\u03c0\u03bb\u03b7\u03be\u03b7 \u03ba\u03b1\u03b9 \u03c4\u03bf \u03b8\u03b1\u03c5\u03bc\u03b1\u03c3\u03bc\u03cc \u03c4\u03bf\u03c5 Hardy, \u03b4\u03b9\u03cc\u03c4\u03b9 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03bf\u03cd\u03c3\u03b1\u03bd \u03b5\u03ba \u03bd\u03ad\u03bf\u03c5 \u03b1\u03bd\u03b1\u03ba\u03b1\u03bb\u03cd\u03c8\u03b5\u03b9\u03c2 \u03b3\u03bd\u03c9\u03c3\u03c4\u03ce\u03bd \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03c3\u03bc\u03ac\u03c4\u03c9\u03bd \u03c0\u03bf\u03c5 \u03c0\u03b1\u03c1\u03ae\u03b3\u03b1\u03b3\u03b1\u03bd \u03bc\u03b5\u03b3\u03ac\u03bb\u03bf\u03b9 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03af \u03c4\u03bf\u03c5 \u03c0\u03b1\u03c1\u03b5\u03bb\u03b8\u03cc\u03bd\u03c4\u03bf\u03c2 (\u03b3\u03b9\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 \u03bf Euler).
\nO\u03b9 Hardy \u03ba\u03b1\u03b9 Littlewood \u03b1\u03bd\u03c4\u03b9\u03bb\u03ae\u03c6\u03b8\u03b7\u03ba\u03b1\u03bd \u03b1\u03bc\u03ad\u03c3\u03c9\u03c2 \u03cc\u03c4\u03b9 \u03bf \u03bd\u03b5\u03b1\u03c1\u03cc\u03c2 \u0399\u03bd\u03b4\u03cc\u03c2 \u03b5\u03c0\u03b9\u03c3\u03c4\u03bf\u03bb\u03bf\u03b3\u03c1\u03ac\u03c6\u03bf\u03c2 \u03c3\u03c5\u03bd\u03b9\u03c3\u03c4\u03bf\u03cd\u03c3\u03b5 \u03ac\u03ba\u03c1\u03c9\u03c2 \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03c5\u03c3\u03b1 \u03c0\u03b5\u03c1\u03af\u03c0\u03c4\u03c9\u03c3\u03b7 \u03c0\u03c1\u03c9\u03c4\u03cc\u03c4\u03c5\u03c0\u03b7\u03c2 \u03b9\u03b4\u03b9\u03bf\u03c6\u03c5\u03af\u03b1\u03c2. \u039c\u03ac\u03bb\u03b9\u03c3\u03c4\u03b1, \u03ad\u03c0\u03b5\u03b9\u03c4\u03b1 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03b1\u03bd\u03c4\u03b1\u03bb\u03bb\u03b1\u03b3\u03ae \u03ba\u03ac\u03c0\u03bf\u03b9\u03c9\u03bd \u03b1\u03ba\u03cc\u03bc\u03b7 \u03b5\u03c0\u03b9\u03c3\u03c4\u03bf\u03bb\u03ce\u03bd \u03bc\u03b1\u03b6\u03af \u03c4\u03bf\u03c5, \u03bf Hardy \u03bf\u03c1\u03b3\u03ac\u03bd\u03c9\u03c3\u03b5 \u03ba\u03b1\u03b9 \u03bc\u03b5\u03b8\u03cc\u03b4\u03b5\u03c5\u03c3\u03b5 \u2013 \u03bc\u03ad\u03c3\u03c9 \u03c4\u03b7\u03c2 \u03b1\u03c0\u03bf\u03c3\u03c4\u03bf\u03bb\u03ae\u03c2 \u03c4\u03bf\u03c5 \u03c3\u03c5\u03bd\u03b1\u03b4\u03ad\u03bb\u03c6\u03bf\u03c5 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd, E. H. Neville, \u03c3\u03c4\u03b7\u03bd \u0399\u03bd\u03b4\u03af\u03b1 \u03b3\u03b9\u2019 \u03b1\u03c5\u03c4\u03cc\u03bd \u03b1\u03ba\u03c1\u03b9\u03b2\u03ce\u03c2 \u03c4\u03bf \u03c3\u03ba\u03bf\u03c0\u03cc \u2013 \u03c4\u03b7\u03bd \u03c0\u03c1\u03cc\u03c3\u03ba\u03bb\u03b7\u03c3\u03b7 \u03c4\u03bf\u03c5 Ramanujan \u03c3\u03c4\u03bf \u039a\u03bf\u03bb\u03ad\u03b3\u03b9\u03bf \u03a4\u03c1\u03af\u03bd\u03b9\u03c4\u03b9 \u03c4\u03bf\u03c5 \u039a\u03ad\u03bc\u03c0\u03c1\u03b9\u03c4\u03b6. \u038e\u03c3\u03c4\u03b5\u03c1\u03b1 \u03b1\u03c0\u03cc \u03bc\u03b9\u03b1 \u03c0\u03c1\u03ce\u03c4\u03b7, \u03c0\u03c1\u03cc\u03c3\u03ba\u03b1\u03b9\u03c1\u03b7 \u03ac\u03c1\u03bd\u03b7\u03c3\u03b7, \u03bf Ramanujan \u03b4\u03ad\u03c7\u03c4\u03b7\u03ba\u03b5 \u03bd\u03b1 \u03c0\u03ac\u03b5\u03b9 \u03c3\u03c4\u03bf \u039a\u03ad\u03bc\u03c0\u03c1\u03b9\u03c4\u03b6, \u03cc\u03c0\u03bf\u03c5 \u03ad\u03c6\u03c4\u03b1\u03c3\u03b5 \u03c4\u03bf\u03bd \u0391\u03c0\u03c1\u03af\u03bb\u03b9\u03bf \u03c4\u03bf\u03c5 1914. \u0395\u03ba\u03b5\u03af, \u03c3\u03cd\u03bc\u03c6\u03c9\u03bd\u03b1 \u03bc\u03b5 \u03c4\u03bf \u03c0\u03c1\u03cc\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1 \u03c0\u03bf\u03c5 \u03c4\u03bf\u03c5 \u03b5\u03af\u03c7\u03b5 \u03b5\u03c4\u03bf\u03b9\u03bc\u03ac\u03c3\u03b5\u03b9 \u03bf Hardy, o Ramanujan \u03c0\u03b1\u03c1\u03b1\u03ba\u03bf\u03bb\u03bf\u03cd\u03b8\u03b7\u03c3\u03b5 \u03ba\u03ac\u03c0\u03bf\u03b9\u03b5\u03c2 \u03b4\u03b9\u03b1\u03bb\u03ad\u03be\u03b5\u03b9\u03c2 \u03c3\u03c4\u03b7\u03bd \u0391\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7 (\u03c0\u03c1\u03bf\u03cb\u03c0\u03cc\u03b8\u03b5\u03c3\u03b7 \u03b1\u03c0\u03b1\u03c1\u03b1\u03af\u03c4\u03b7\u03c4\u03b7 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03bc\u03c0\u03bf\u03c1\u03ad\u03c3\u03b5\u03b9 \u03bd\u03b1 \u03ba\u03b1\u03c4\u03b1\u03bd\u03bf\u03ae\u03c3\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03bb\u03c5\u03c4\u03b9\u03ba\u03ae \u03b8\u03b5\u03c9\u03c1\u03af\u03b1 \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd) \u03ba\u03b1\u03b9, \u03b4\u03b5\u03c5\u03c4\u03b5\u03c1\u03b5\u03c5\u03cc\u03bd\u03c4\u03c9\u03c2, \u03c3\u03c4\u03b7\u03bd \u03ac\u03bb\u03b3\u03b5\u03b2\u03c1\u03b1, \u03ce\u03c3\u03c4\u03b5 \u03bd\u03b1 \u03bc\u03c0\u03bf\u03c1\u03ad\u03c3\u03b5\u03b9 \u03ba\u03b1\u03c4\u03cc\u03c0\u03b9\u03bd \u03bd\u03b1 \u03c3\u03c5\u03bd\u03b5\u03c1\u03b3\u03b1\u03c3\u03c4\u03b5\u03af \u2013 \u03b5\u03c0\u03af \u03af\u03c3\u03bf\u03b9\u03c2 \u03cc\u03c1\u03bf\u03b9\u03c2 \u2013 \u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 Littlewood \u03ba\u03b1\u03b9 Hardy. \u0395\u03c0\u03b9\u03c0\u03bb\u03ad\u03bf\u03bd, \u03b1\u03c1\u03ba\u03b5\u03c4\u03ac \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03c4\u03bf\u03c5 \u03c4\u03b1 \u03b4\u03af\u03b4\u03b1\u03be\u03b5 \u03ba\u03b1\u03c4\u2019 \u03b9\u03b4\u03af\u03b1\u03bd \u03bf Hardy \u03c3\u03c4\u03b7 \u03b4\u03b9\u03ac\u03c1\u03ba\u03b5\u03b9\u03b1 \u03c4\u03c9\u03bd \u03c3\u03c5\u03bd\u03b1\u03bd\u03c4\u03ae\u03c3\u03b5\u03ce\u03bd \u03c4\u03bf\u03c5\u03c2. \u0393\u03b5\u03bd\u03bd\u03b1\u03b9\u03cc\u03b4\u03c9\u03c1\u03bf\u03c2, \u03cc\u03bc\u03c9\u03c2, \u03ba\u03b1\u03b9 \u03b5\u03b9\u03bb\u03b9\u03ba\u03c1\u03b9\u03bd\u03ae\u03c2, \u03ba\u03b1\u03b8\u03ce\u03c2 \u03ae\u03c4\u03b1\u03bd, \u03c0\u03b1\u03c1\u03b1\u03b4\u03ad\u03c7\u03b8\u03b7\u03ba\u03b5 \u03cc\u03c4\u03b9 \u00ab\u03c0\u03c1\u03bf\u03c6\u03b1\u03bd\u03ce\u03c2 \u03b5\u03b3\u03ce \u03b4\u03b9\u03b4\u03ac\u03c7\u03b8\u03b7\u03ba\u03b1 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b1 \u03b1\u03c0\u03cc \u03b5\u03ba\u03b5\u03af\u03bd\u03bf\u03bd \u03b1\u03c0\u0384\u03cc\u03c3\u03b1 \u03b1\u03c5\u03c4\u03cc\u03c2 [\u03bf Ramanujan] \u03b1\u03c0\u03cc \u03b5\u03bc\u03ad\u03bd\u03b1\u00bb.
\n\u03a4\u03b1 \u03c7\u03c1\u03cc\u03bd\u03b9\u03b1 \u03c4\u03bf\u03c5 \u039a\u03ad\u03bc\u03c0\u03c1\u03b9\u03c4\u03b6 \u03c5\u03c0\u03ae\u03c1\u03be\u03b1\u03bd \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03b9\u03ba\u03ac \u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd Ramanujan, \u03b1\u03bb\u03bb\u03ac \u03b4\u03b5\u03bd \u03b4\u03b9\u03ae\u03c1\u03ba\u03b5\u03c3\u03b1\u03bd \u03c0\u03bf\u03bb\u03cd. \u03a4\u03b7\u03bd \u03ac\u03bd\u03bf\u03b9\u03be\u03b7 \u03c4\u03bf\u03c5 1917 \u03b1\u03c1\u03c1\u03ce\u03c3\u03c4\u03b7\u03c3\u03b5 \u03ba\u03b1\u03b9 \u03bd\u03c9\u03c1\u03af\u03c2 \u03c4\u03bf \u03ba\u03b1\u03bb\u03bf\u03ba\u03b1\u03af\u03c1\u03b9 \u03bc\u03c0\u03ae\u03ba\u03b5 \u03c3\u03c4\u03bf \u03bd\u03bf\u03c3\u03bf\u03ba\u03bf\u03bc\u03b5\u03af\u03bf. \u0391\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03ce\u03bd\u03c4\u03b1\u03c2 \u03b9\u03b1\u03c4\u03c1\u03b9\u03ba\u03ae \u03c3\u03cd\u03c3\u03c4\u03b1\u03c3\u03b7, \u03b5\u03c0\u03ad\u03c3\u03c4\u03c1\u03b5\u03c8\u03b5 \u03c3\u03c4\u03b7\u03bd \u0399\u03bd\u03b4\u03af\u03b1 \u03c3\u03c4\u03b9\u03c2 \u03b1\u03c1\u03c7\u03ad\u03c2 \u03c4\u03bf\u03c5 1919, \u03ba\u03b1\u03b9 \u03c0\u03ad\u03b8\u03b1\u03bd\u03b5 \u03b5\u03ba\u03b5\u03af \u03c4\u03bf\u03bd \u0391\u03c0\u03c1\u03af\u03bb\u03b9\u03bf \u03c4\u03bf\u03c5 1920. \u03a0\u03ad\u03c1\u03b1\u03c3\u03b5 \u03c4\u03b1 \u03c4\u03c1\u03af\u03b1 \u03c4\u03b5\u03bb\u03b5\u03c5\u03c4\u03b1\u03af\u03b1 \u03c7\u03c1\u03cc\u03bd\u03b9\u03b1 \u03c4\u03b7\u03c2 \u03b6\u03c9\u03ae\u03c2 \u03c4\u03bf\u03c5 \u03c3\u03b5 \u03c3\u03b1\u03bd\u03b1\u03c4\u03cc\u03c1\u03b9\u03b1, \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c5\u03b3\u03b5\u03af\u03b1 \u03c4\u03bf\u03c5 \u03c3\u03b5 \u03ba\u03b1\u03ba\u03ae \u03ba\u03b1\u03c4\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7. \u03a0\u03b1\u03c1\u2019 \u03cc\u03bb\u03b1 \u03b1\u03c5\u03c4\u03ac, \u03ae\u03c4\u03b1\u03bd \u03bc\u03cc\u03bb\u03b9\u03c2 \u03c4\u03bf 1918 \u03c0\u03bf\u03c5 \u03b1\u03bd\u03b1\u03ba\u03ac\u03bb\u03c5\u03c8\u03b5 \u03bc\u03b5\u03c1\u03b9\u03ba\u03ac \u03b1\u03c0\u03cc \u03c4\u03b1 \u03c0\u03b9\u03bf \u03c9\u03c1\u03b1\u03af\u03b1 \u03c4\u03bf\u03c5 \u03b8\u03b5\u03c9\u03c1\u03ae\u03bc\u03b1\u03c4\u03b1, \u03c4\u03b7\u03bd \u03b5\u03c0\u03bf\u03c7\u03ae \u03c0\u03b5\u03c1\u03af\u03c0\u03bf\u03c5 \u03c0\u03bf\u03c5 \u03b5\u03ba\u03bb\u03ad\u03c7\u03c4\u03b7\u03ba\u03b5 \u03b5\u03c4\u03b1\u03af\u03c1\u03bf\u03c2 \u03c4\u03b7\u03c2 \u0392\u03b1\u03c3\u03b9\u03bb\u03b9\u03ba\u03ae\u03c2 \u0395\u03c4\u03b1\u03b9\u03c1\u03b5\u03af\u03b1\u03c2 \u03c4\u03bf\u03c5 \u039b\u03bf\u03bd\u03b4\u03af\u03bd\u03bf\u03c5.
\n\u03a4\u03bf \u03b4\u03b9\u03ac\u03c3\u03c4\u03b7\u03bc\u03b1 \u03c0\u03bf\u03c5 \u03bf Ramanujan \u03b4\u03b9\u03ad\u03b8\u03b5\u03c4\u03b5 \u03c4\u03b7 \u03c7\u03c1\u03bf\u03bd\u03b9\u03ba\u03ae \u03ac\u03bd\u03b5\u03c3\u03b7 \u03ba\u03b1\u03b9 \u03ae\u03c4\u03b1\u03bd \u03c5\u03b3\u03b9\u03ae\u03c2, \u03ce\u03c3\u03c4\u03b5 \u03bd\u03b1 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b1\u03c3\u03c7\u03bf\u03bb\u03b5\u03af\u03c4\u03b1\u03b9 \u03b1\u03bd\u03b5\u03bc\u03c0\u03cc\u03b4\u03b9\u03c3\u03c4\u03b1 \u03bc\u03b5 \u03c4\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac, \u03b4\u03b5\u03bd \u03c5\u03c0\u03b5\u03c1\u03ad\u03b2\u03b7 \u03c4\u03b5\u03bb\u03b9\u03ba\u03ce\u03c2 \u03c4\u03b1 \u03c4\u03ad\u03c3\u03c3\u03b5\u03c1\u03b1 \u03c7\u03c1\u03cc\u03bd\u03b9\u03b1, \u03b5\u03bd\u03ce \u03b7 \u03c3\u03c5\u03bd\u03bf\u03bb\u03b9\u03ba\u03ae \u03b4\u03b9\u03ac\u03c1\u03ba\u03b5\u03b9\u03b1 \u03c4\u03b7\u03c2 \u03b6\u03c9\u03ae\u03c2 \u03c4\u03bf\u03c5 \u03c9\u03c2 \u00ab\u03b5\u03c0\u03b1\u03b3\u03b3\u03b5\u03bb\u03bc\u03b1\u03c4\u03af\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u00bb \u03ae\u03c4\u03b1\u03bd \u03b5\u03c0\u03c4\u03ac \u03c0\u03b5\u03c1\u03af\u03c0\u03bf\u03c5 \u03ad\u03c4\u03b7 (\u03b1\u03c1\u03c7\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03b1\u03c0\u03cc \u03c4\u03b7 \u03bc\u03b5\u03c4\u03ac\u03b2\u03b1\u03c3\u03ae \u03c4\u03bf\u03c5 \u03c3\u03c4\u03bf \u039a\u03ad\u03bc\u03c0\u03c1\u03b9\u03c4\u03b6).
\n\u03a3\u03c4\u03b1 \u03c0\u03c1\u03bf\u03c3\u03ba\u03cc\u03bc\u03bc\u03b1\u03c4\u03b1 \u03c0\u03bf\u03c5 \u03b1\u03bd\u03c4\u03b9\u03bc\u03b5\u03c4\u03ce\u03c0\u03b9\u03c3\u03b5 \u03c3\u2019 \u03b1\u03c5\u03c4\u03ac \u03c4\u03b1 \u03c7\u03c1\u03cc\u03bd\u03b9\u03b1 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03c3\u03c5\u03bd\u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03bf\u03cd\u03bd \u03ba\u03b1\u03b9 \u03bf\u03b9 \u03b4\u03c5\u03c3\u03ba\u03bf\u03bb\u03af\u03b5\u03c2 \u03c0\u03bf\u03c5 \u03b5\u03c0\u03ad\u03c6\u03b5\u03c1\u03b5 \u03c3\u03c4\u03b7 \u03b4\u03b9\u03b5\u03be\u03b1\u03b3\u03c9\u03b3\u03ae \u03c4\u03b7\u03c2 \u03ad\u03c1\u03b5\u03c5\u03bd\u03ac\u03c2 \u03c4\u03bf\u03c5, \u03bf \u03a0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03a0\u03b1\u03b3\u03ba\u03cc\u03c3\u03bc\u03b9\u03bf\u03c2 \u03a0\u03cc\u03bb\u03b5\u03bc\u03bf\u03c2, \u03bc\u03b5 \u03ba\u03c5\u03c1\u03b9\u03cc\u03c4\u03b5\u03c1\u03b7 \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03b3\u03ba\u03b1\u03c3\u03c4\u03b9\u03ba\u03ae \u03c0\u03c1\u03bf\u03c3\u03c9\u03c1\u03b9\u03bd\u03ae \u03b4\u03b9\u03b1\u03ba\u03bf\u03c0\u03ae \u03c4\u03b7\u03c2 \u03c3\u03c5\u03bd\u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b1\u03c2 \u03c4\u03bf\u03c5 \u03bc\u03b5 \u03c4\u03bf\u03bd Littlewood, \u03bf \u03bf\u03c0\u03bf\u03af\u03bf\u03c2 \u03ac\u03c6\u03b7\u03c3\u03b5 \u03c4\u03bf \u039a\u03ad\u03bc\u03c0\u03c1\u03b9\u03c4\u03b6, \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03c0\u03c1\u03bf\u03c3\u03c6\u03ad\u03c1\u03b5\u03b9 \u03c4\u03b9\u03c2 \u03ba\u03b1\u03bb\u03ad\u03c2 \u03c4\u03bf\u03c5 \u03c5\u03c0\u03b7\u03c1\u03b5\u03c3\u03af\u03b5\u03c2 \u03c3\u03c4\u03bf\u03bd \u03b1\u03b3\u03b3\u03bb\u03b9\u03ba\u03cc \u03c3\u03c4\u03c1\u03b1\u03c4\u03cc.
\n\u03a4\u03bf \u03b5\u03c1\u03ce\u03c4\u03b7\u03bc\u03b1 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03c0\u03cc\u03c3\u03bf \u03bc\u03b5\u03b3\u03ac\u03bb\u03bf\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 \u03c5\u03c0\u03ae\u03c1\u03be\u03b5 \u03c0\u03c1\u03ac\u03b3\u03bc\u03b1\u03c4\u03b9 \u03bf Ramanujan \u03ae \u03c0\u03cc\u03c3\u03bf \u03bc\u03b5\u03b3\u03ac\u03bb\u03bf\u03c2 \u03b8\u03b1 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03c3\u03b5 \u03bd\u03b1 \u03b5\u03af\u03c7\u03b5 \u03b3\u03af\u03bd\u03b5\u03b9, \u03b5\u03ac\u03bd \u03b5\u03af\u03c7\u03b5 \u03c4\u03b7\u03bd \u03c4\u03cd\u03c7\u03b7 \u03bd\u03b1 \u03bb\u03ac\u03b2\u03b5\u03b9 \u03bf\u03c1\u03b3\u03b1\u03bd\u03c9\u03bc\u03ad\u03bd\u03b7 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03b5\u03ba\u03c0\u03b1\u03af\u03b4\u03b5\u03c5\u03c3\u03b7, \u03ad\u03c7\u03b5\u03b9 \u03c4\u03b5\u03b8\u03b5\u03af \u03b5\u03c0\u03b1\u03bd\u03b5\u03b9\u03bb\u03b7\u03bc\u03bc\u03ad\u03bd\u03b1 \u03b1\u03c0\u03cc \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03ba\u03b1\u03b9 \u03b9\u03c3\u03c4\u03bf\u03c1\u03b9\u03ba\u03bf\u03cd\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b7\u03c2, \u03b1\u03c0\u03cc \u03c4\u03bf \u03b8\u03ac\u03bd\u03b1\u03c4\u03cc \u03c4\u03bf\u03c5 \u03bc\u03ad\u03c7\u03c1\u03b9 \u03c3\u03ae\u03bc\u03b5\u03c1\u03b1, \u03b5\u03bd \u03cc\u03c8\u03b5\u03b9 \u03bc\u03ac\u03bb\u03b9\u03c3\u03c4\u03b1 \u03c4\u03c9\u03bd \u03c3\u03c5\u03bd\u03b5\u03c7\u03ce\u03bd \u03b5\u03c0\u03b1\u03bd\u03b1\u03be\u03b9\u03bf\u03bb\u03bf\u03b3\u03ae\u03c3\u03b5\u03c9\u03bd \u03c4\u03bf\u03c5 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd \u03ad\u03c1\u03b3\u03bf\u03c5.
\n\u039f C. P. Snow \u03c3\u03c4\u03bf\u03bd \u03c0\u03c1\u03cc\u03bb\u03bf\u03b3\u03cc \u03c4\u03bf\u03c5 \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03cc \u03b2\u03b9\u03b2\u03bb\u03af\u03bf \u03c4\u03bf\u03c5 G. H. Hardy, \u00ab\u0397 \u03b1\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03b1 \u03b5\u03bd\u03cc\u03c2 \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u00bb, \u03c3\u03b7\u03bc\u03b5\u03b9\u03ce\u03bd\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03bf\u03b9 Hardy \u03ba\u03b1\u03b9 Littlewood, \u03bc\u03b5\u03bb\u03b5\u03c4\u03ce\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b9\u03c2 \u03b5\u03c0\u03b9\u03c3\u03c4\u03bf\u03bb\u03ad\u03c2 \u03c4\u03bf\u03c5 Ramanujan, \u03ba\u03b1\u03c4\u03ad\u03bb\u03b7\u03be\u03b1\u03bd \u03c3\u03c4\u03bf \u03c3\u03c5\u03bc\u03c0\u03ad\u03c1\u03b1\u03c3\u03bc\u03b1 \u03cc\u03c4\u03b9 \u00ab\u03bf \u03c3\u03c5\u03b3\u03b3\u03c1\u03b1\u03c6\u03ad\u03b1\u03c2 \u03c4\u03c9\u03bd \u03c7\u03b5\u03b9\u03c1\u03bf\u03b3\u03c1\u03ac\u03c6\u03c9\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03b9\u03b4\u03b9\u03bf\u03c6\u03c5\u03ae\u03c2\u00bb. \u039a\u03b1\u03b9 \u03c3\u03c5\u03bd\u03b5\u03c7\u03af\u03b6\u03b5\u03b9: \u00ab\u0389\u03c4\u03b1\u03bd \u03bc\u03cc\u03bd\u03bf \u03b1\u03c1\u03b3\u03cc\u03c4\u03b5\u03c1\u03b1 \u03c0\u03bf\u03c5 \u03bf Hardy \u03b1\u03c0\u03bf\u03c6\u03ac\u03c3\u03b9\u03c3\u03b5 \u03cc\u03c4\u03b9 \u03bf Ramanujan \u03b1\u03bd\u03ae\u03ba\u03b5, \u03cc\u03c3\u03bf\u03bd \u03b1\u03c6\u03bf\u03c1\u03ac \u03c3\u03c4\u03b7\u03bd \u03ad\u03bc\u03c6\u03c5\u03c4\u03b7 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03c4\u03bf\u03c5 \u03b9\u03b4\u03b9\u03bf\u03c6\u03c5\u03af\u03b1, \u03c3\u03c4\u03b7\u03bd \u03ba\u03bb\u03ac\u03c3\u03b7 \u03c4\u03bf\u03c5 Gauss \u03ba\u03b1\u03b9 \u03c4\u03bf\u03c5 Euler, \u03bc\u03b5 \u03c4\u03b7 \u03bc\u03cc\u03bd\u03b7 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03ac \u03cc\u03c4\u03b9 \u03b4\u03b5\u03bd \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03c3\u03b5 \u03bd\u03b1 \u03b1\u03bd\u03b1\u03bc\u03ad\u03bd\u03b5\u03b9, \u03bb\u03cc\u03b3\u03c9 \u03c4\u03c9\u03bd \u03ba\u03b5\u03bd\u03ce\u03bd \u03c3\u03c4\u03b7\u03bd \u03b5\u03ba\u03c0\u03b1\u03af\u03b4\u03b5\u03c5\u03c3\u03ae \u03c4\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03b5\u03c0\u03b5\u03b9\u03b4\u03ae \u03b5\u03bc\u03c6\u03b1\u03bd\u03af\u03c3\u03c4\u03b7\u03ba\u03b5 \u03c0\u03bf\u03bb\u03cd \u03b1\u03c1\u03b3\u03ac \u03c3\u03c4\u03bf \u03c0\u03c1\u03bf\u03c3\u03ba\u03ae\u03bd\u03b9\u03bf \u03c4\u03b7\u03c2 \u03b9\u03c3\u03c4\u03bf\u03c1\u03af\u03b1\u03c2 \u03c4\u03c9\u03bd \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd, \u03bd\u03b1 \u03c3\u03c5\u03bc\u03b2\u03ac\u03bb\u03bb\u03b5\u03b9 \u03c3\u03b5 \u03af\u03c3\u03b7 \u03ba\u03bb\u03af\u03bc\u03b1\u03ba\u03b1\u00bb.
\n\u03a4\u03b7\u03bd \u03ac\u03c0\u03bf\u03c8\u03b7 \u03b1\u03c5\u03c4\u03ae \u03b1\u03bc\u03c6\u03b9\u03c3\u03b2\u03ae\u03c4\u03b7\u03c3\u03b5 \u03bf \u0399. J. Mordell, \u03c5\u03c0\u03bf\u03c3\u03c4\u03b7\u03c1\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03cc\u03c4\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ba\u03ac\u03c0\u03c9\u03c2 \u03b4\u03cd\u03c3\u03ba\u03bf\u03bb\u03bf \u03bd\u03b1 \u03b4\u03b5\u03c7\u03b8\u03bf\u03cd\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03bf Hardy \u03ad\u03ba\u03b1\u03bd\u03b5 \u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9 \u03b4\u03ae\u03bb\u03c9\u03c3\u03b7 \u03c0\u03bf\u03c5 \u03bf Snow \u03c4\u03bf\u03c5 \u03b1\u03c0\u03bf\u03b4\u03af\u03b4\u03b5\u03b9. \u039a\u03b1\u03b9 \u03b1\u03c5\u03c4\u03cc \u03b4\u03b9\u03cc\u03c4\u03b9 \u03bf Ramanujan \u03b4\u03b9\u03b1\u03ba\u03c1\u03af\u03b8\u03b7\u03ba\u03b5 \u03c3\u03b5 \u03bf\u03c1\u03b9\u03c3\u03bc\u03ad\u03bd\u03bf\u03c5\u03c2 \u03c4\u03bf\u03bc\u03b5\u03af\u03c2 \u03c4\u03c9\u03bd \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03ba\u03b1\u03b9 \u03b5\u03af\u03c7\u03b5 \u03b1\u03bd\u03b1\u03bd\u03c4\u03af\u03c1\u03c1\u03b7\u03c4\u03b1, \u03b1\u03c0\u03af\u03c3\u03c4\u03b5\u03c5\u03c4\u03bf \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03c4\u03b1\u03bb\u03ad\u03bd\u03c4\u03bf, \u03c0\u03bb\u03b7\u03bd \u03cc\u03bc\u03c9\u03c2 \u03b7 \u03c3\u03cd\u03b3\u03ba\u03c1\u03b9\u03c3\u03ae \u03c4\u03bf\u03c5 \u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 Gauss \u03ba\u03b1\u03b9 Euler \u03b5\u03af\u03bd\u03b1\u03b9 \u03c5\u03c0\u03b5\u03c1\u03b2\u03bf\u03bb\u03b9\u03ba\u03ae, \u03b1\u03bd \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03bf\u03cd\u03bc\u03b5 \u03c4\u03b7\u03bd \u03c0\u03bf\u03bb\u03cd\u03c0\u03bb\u03b5\u03c5\u03c1\u03b7 \u03ba\u03b1\u03b9 \u03ba\u03b1\u03b8\u03bf\u03c1\u03b9\u03c3\u03c4\u03b9\u03ba\u03ae \u03c3\u03c5\u03bd\u03b5\u03b9\u03c3\u03c6\u03bf\u03c1\u03ac \u03c4\u03c9\u03bd \u03c4\u03b5\u03bb\u03b5\u03c5\u03c4\u03b1\u03af\u03c9\u03bd \u03c3\u03b5 \u03c0\u03bf\u03bb\u03bb\u03bf\u03cd\u03c2 \u03ba\u03bb\u03ac\u03b4\u03bf\u03c5\u03c2 \u03c4\u03b7\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae\u03c2 \u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b7\u03c2. \u03a4\u03bf\u03cd\u03c4\u03bf \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03bb\u03b7\u03b8\u03ad\u03c2 \u03b5\u03ac\u03bd \u03c3\u03ba\u03b5\u03c6\u03c4\u03bf\u03cd\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03bf\u03b9 \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03ad\u03c2 \u03c4\u03bf\u03c5 Ramanujan \u03c3\u03c4\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03b1\u03c6\u03bf\u03c1\u03bf\u03cd\u03bd \u03c3\u03c4\u03b7 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u0391\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7, \u03c4\u03b7 \u03b8\u03b5\u03c9\u03c1\u03af\u03b1 \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd, \u03c4\u03b9\u03c2 \u03b1\u03c0\u03b5\u03b9\u03c1\u03bf\u03c3\u03b5\u03b9\u03c1\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b1 \u03c3\u03c5\u03bd\u03b5\u03c7\u03ae \u03ba\u03bb\u03ac\u03c3\u03bc\u03b1\u03c4\u03b1.
\n\u0398\u03b5\u03c9\u03c1\u03ce, \u03cc\u03bc\u03c9\u03c2, \u03bb\u03b9\u03b3\u03cc\u03c4\u03b5\u03c1\u03bf \u03b1\u03c6\u03bf\u03c1\u03b9\u03c3\u03c4\u03b9\u03ba\u03ae \u03b1\u03c0\u03cc \u03c4\u03b9\u03c2 \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03b5\u03c2 \u03ba\u03b1\u03b9, \u03c4\u03b1\u03c5\u03c4\u03bf\u03c7\u03c1\u03cc\u03bd\u03c9\u03c2, \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03bf \u03b5\u03ba\u03bb\u03b5\u03c0\u03c4\u03c5\u03c3\u03bc\u03ad\u03bd\u03b7 \u03c3\u03c4\u03b9\u03c2 \u03b4\u03b9\u03b1\u03ba\u03c1\u03af\u03c3\u03b5\u03b9\u03c2 \u03c0\u03bf\u03c5 \u03b5\u03c0\u03b9\u03c7\u03b5\u03b9\u03c1\u03b5\u03af \u2013 \u03ac\u03c1\u03b1 \u03ba\u03b1\u03b9 \u03c0\u03b9\u03bf \u03b1\u03ba\u03c1\u03b9\u03b2\u03bf\u03b4\u03af\u03ba\u03b1\u03b9\u03b7 \u2013 \u03c4\u03b7 \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ae \u03ba\u03c1\u03af\u03c3\u03b7 \u03c4\u03bf\u03c5 Hardy \u03c0\u03bf\u03c5 \u03c0\u03b5\u03c1\u03b9\u03ad\u03c7\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c4\u03bf \u03b1\u03ba\u03cc\u03bb\u03bf\u03c5\u03b8\u03bf \u03b1\u03c0\u03cc\u03c3\u03c0\u03b1\u03c3\u03bc\u03b1 \u03b1\u03c0\u03cc \u03bf\u03bc\u03b9\u03bb\u03af\u03b1 \u03c4\u03bf\u03c5 \u03c3\u03c4\u03bf \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b9\u03bf \u03c4\u03bf\u03c5 \u03a7\u03ac\u03c1\u03b2\u03b1\u03c1\u03bd\u03c4, \u03c3\u03c4\u03b9\u03c2 31 \u0391\u03c5\u03b3\u03bf\u03cd\u03c3\u03c4\u03bf\u03c5 1936: \u00ab\u039f\u03b9 \u03b3\u03bd\u03ce\u03bc\u03b5\u03c2 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03c5\u03bd \u03cc\u03c3\u03bf\u03bd \u03b1\u03c6\u03bf\u03c1\u03ac \u03c3\u03c4\u03b7 \u03c3\u03c0\u03bf\u03c5\u03b4\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03bf\u03c5 \u03ad\u03c1\u03b3\u03bf\u03c5 \u03c4\u03bf\u03c5 Ramanujan, \u03c4\u03bf \u03b5\u03af\u03b4\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03ba\u03c1\u03b9\u03c4\u03b7\u03c1\u03af\u03bf\u03c5 \u03bc\u03b5 \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03b8\u03b1 \u03b1\u03be\u03b9\u03bf\u03bb\u03bf\u03b3\u03b7\u03b8\u03b5\u03af, \u03ba\u03b1\u03b8\u03ce\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u03b5\u03c0\u03b9\u03c1\u03c1\u03bf\u03ae \u03c0\u03bf\u03c5 \u03b5\u03bd\u03b4\u03ad\u03c7\u03b5\u03c4\u03b1\u03b9 \u03bd\u03b1 \u03b1\u03c3\u03ba\u03ae\u03c3\u03b5\u03b9 \u03c3\u03c4\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03c3\u03c4\u03bf \u03bc\u03ad\u03bb\u03bb\u03bf\u03bd. \u0394\u03b5\u03bd \u03ad\u03c7\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b1\u03c0\u03bb\u03cc\u03c4\u03b7\u03c4\u03b1 \u03ba\u03b1\u03b9 \u03c4\u03b7 \u00ab\u03bc\u03bf\u03bd\u03b9\u03bc\u03cc\u03c4\u03b7\u03c4\u03b1\u00bb(inevitableness) \u03c4\u03bf\u03c5 \u03ba\u03b1\u03c4\u2019 \u03b5\u03be\u03bf\u03c7\u03ae\u03bd \u03bc\u03ad\u03b3\u03b9\u03c3\u03c4\u03bf\u03c5 \u03ad\u03c1\u03b3\u03bf\u03c5. \u0398\u03b1 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03c3\u03b5 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf, \u03b5\u03ac\u03bd \u03ae\u03c4\u03b1\u03bd \u03bb\u03b9\u03b3\u03cc\u03c4\u03b5\u03c1\u03bf \u03c0\u03b1\u03c1\u03ac\u03be\u03b5\u03bd\u03bf. \u03a4\u03bf \u03c7\u03ac\u03c1\u03b9\u03c3\u03bc\u03b1 \u03c0\u03bf\u03c5 \u03b4\u03b9\u03b1\u03b8\u03ad\u03c4\u03b5\u03b9 \u03ba\u03b1\u03b9 \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03ba\u03b1\u03bd\u03b5\u03af\u03c2 \u03b4\u03b5\u03bd \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b1\u03c1\u03bd\u03b7\u03b8\u03b5\u03af, \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b2\u03b1\u03b8\u03b9\u03ac \u03ba\u03b1\u03b9 \u00ab\u03b1\u03ba\u03b1\u03c4\u03b1\u03bd\u03af\u03ba\u03b7\u03c4\u03b7\u00bb \u03c0\u03c1\u03c9\u03c4\u03bf\u03c4\u03c5\u03c0\u03af\u03b1. \u03b8\u03b1 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03c3\u03b5 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03bd \u03bd\u03b1 \u03b5\u03af\u03c7\u03b5 \u03b3\u03af\u03bd\u03b5\u03b9 \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2, \u03b5\u03ac\u03bd \u03ae\u03c4\u03b1\u03bd \u03b4\u03c5\u03bd\u03b1\u03c4\u03cc\u03bd \u03bd\u03b1 \u00ab\u03c3\u03c5\u03bb\u03bb\u03b7\u03c6\u03b8\u03b5\u03af\u00bb \u03ba\u03b1\u03b9 \u03bd\u03b1 \u00ab\u03b4\u03b1\u03bc\u03b1\u03c3\u03c4\u03b5\u03af\u00bb \u03bb\u03af\u03b3\u03bf \u03ba\u03b1\u03c4\u03ac \u03c4\u03b7 \u03bd\u03b5\u03cc\u03c4\u03b7\u03c4\u03ac \u03c4\u03bf\u03c5. \u0398\u03b1 \u03b5\u03af\u03c7\u03b5 \u03b1\u03bd\u03b1\u03ba\u03b1\u03bb\u03cd\u03c8\u03b5\u03b9 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b1 \u03c4\u03b1 \u03bf\u03c0\u03bf\u03af\u03b1 \u03b8\u03b1 \u03ae\u03c4\u03b1\u03bd \u03ba\u03b1\u03b9\u03bd\u03bf\u03cd\u03c1\u03b9\u03b1, \u03ba\u03b1\u03b9 \u03b1\u03bd\u03b1\u03bc\u03c6\u03af\u03b2\u03bf\u03bb\u03b1, \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03b7\u03c2 \u03c3\u03c0\u03bf\u03c5\u03b4\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2. \u0391\u03c0\u03cc \u03c4\u03b7\u03bd \u03ac\u03bb\u03bb\u03b7, \u03b8\u03b1 \u03ae\u03c4\u03b1\u03bd \u03bb\u03b9\u03b3\u03cc\u03c4\u03b5\u03c1\u03bf \u201c\u03bf Ramanujan\u201d, \u03b5\u03bd\u03ce \u03b8\u03b1 \u03ad\u03bc\u03bf\u03b9\u03b1\u03b6\u03b5 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03bf \u03c3\u03b5 \u0395\u03c5\u03c1\u03c9\u03c0\u03b1\u03af\u03bf \u039a\u03b1\u03b8\u03b7\u03b3\u03b7\u03c4\u03ae, \u03ba\u03b1\u03b9 \u03b1\u03c5\u03c4\u03cc \u03c0\u03bf\u03c5 \u03b8\u03b1 \u03c7\u03ac\u03bd\u03b1\u03bc\u03b5 \u03b8\u03b1 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03c3\u03b5 \u03bd\u03b1 \u03ae\u03c4\u03b1\u03bd \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf \u03b1\u03c0\u03cc \u03b1\u03c5\u03c4\u03cc \u03c0\u03bf\u03c5 \u03b8\u03b1 \u03ba\u03b5\u03c1\u03b4\u03af\u03b6\u03b1\u03bc\u03b5\u2026\u00bb.
\n\u0395\u03c0\u03b5\u03b9\u03b4\u03ae \u03ad\u03c7\u03b5\u03b9 \u03ae\u03b4\u03b7 \u03b3\u03af\u03bd\u03b5\u03b9 \u03bb\u03cc\u03b3\u03bf\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03b9\u03c2 \u03c3\u03c5\u03bd\u03b5\u03c7\u03b5\u03af\u03c2 \u03b5\u03c0\u03b1\u03bd\u03b1\u03be\u03b9\u03bf\u03bb\u03bf\u03b3\u03ae\u03c3\u03b5\u03b9\u03c2 \u03c4\u03bf\u03c5 \u03ad\u03c1\u03b3\u03bf\u03c5 \u03c4\u03bf\u03c5 Ramanujan, \u03ba\u03bb\u03b5\u03af\u03bd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b7 \u03c3\u03c5\u03b6\u03ae\u03c4\u03b7\u03c3\u03b7 \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03b1\u03c0\u03bf\u03c4\u03af\u03bc\u03b7\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03ae\u03c2 \u03c4\u03bf\u03c5 \u03c3\u03c4\u03b7 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b7, \u03b1\u03be\u03af\u03b6\u03b5\u03b9 \u03bd\u03b1 \u03c0\u03b1\u03c1\u03b1\u03b8\u03ad\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf\u03bd \u03b1\u03ba\u03cc\u03bb\u03bf\u03c5\u03b8\u03bf \u00ab\u0395\u03c0\u03af\u03bb\u03bf\u03b3\u03bf\u00bb \u03b1\u03c0\u03cc \u03ac\u03c1\u03b8\u03c1\u03bf \u03c4\u03bf\u03c5 Bruce C. Bernt, \u03b4\u03b9\u03cc\u03c4\u03b9 \u03b1\u03c0\u03b1\u03bd\u03c4\u03ac \u03c3\u03c4\u03b9\u03c2 \u03b5\u03c0\u03b9\u03c6\u03c5\u03bb\u03ac\u03be\u03b5\u03b9\u03c2 \u03c4\u03bf\u03c5 Hardy \u03cc\u03c3\u03bf\u03bd \u03b1\u03c6\u03bf\u03c1\u03ac \u03c3\u03c4\u03b7 \u00ab\u03bc\u03bf\u03bd\u03b9\u03bc\u03cc\u03c4\u03b7\u03c4\u03b1\u00bb \u03c4\u03b7\u03c2 \u03b8\u03ad\u03c3\u03b7\u03c2 \u03c4\u03c9\u03bd \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03c4\u03bf\u03c5 Ramanujan \u03c3\u03c4\u03b7 \u03c3\u03cd\u03b3\u03c7\u03c1\u03bf\u03bd\u03b7 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b7: \u00ab\u03a3\u03b5 \u03c3\u03c5\u03b6\u03b7\u03c4\u03ae\u03c3\u03b5\u03b9\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd Ramanujan, \u03b5\u03b3\u03b5\u03af\u03c1\u03b5\u03c4\u03b1\u03b9 \u03b1\u03bd\u03b1\u03c0\u03cc\u03c6\u03b5\u03c5\u03ba\u03c4\u03b1 \u03c4\u03bf \u03b5\u03c1\u03ce\u03c4\u03b7\u03bc\u03b1 \u201c\u03a0\u03cc\u03c3\u03bf \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03bc\u03b5\u03b3\u03ac\u03bb\u03bf\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 \u03c5\u03c0\u03ae\u03c1\u03be\u03b5;\u201d \u03a3\u03c4\u03b9\u03c2 \u03c0\u03b5\u03c1\u03b9\u03bf\u03c7\u03ad\u03c2 \u03c4\u03c9\u03bd \u03b1\u03c0\u03b5\u03b9\u03c1\u03bf\u03c3\u03b5\u03b9\u03c1\u03ce\u03bd, \u03c4\u03c9\u03bd \u03b5\u03bb\u03bb\u03b5\u03b9\u03c0\u03c4\u03b9\u03ba\u03ce\u03bd \u03c3\u03c5\u03bd\u03b1\u03c1\u03c4\u03ae\u03c3\u03b5\u03c9\u03bd \u03ba\u03b1\u03b9 \u03c4\u03c9\u03bd \u03c3\u03c5\u03bd\u03b5\u03c7\u03ce\u03bd \u03ba\u03bb\u03b1\u03c3\u03bc\u03ac\u03c4\u03c9\u03bd, \u03c0\u03bf\u03bb\u03cd \u03bb\u03af\u03b3\u03bf\u03b9 \u03c3\u03c4\u03b7\u03bd \u03b9\u03c3\u03c4\u03bf\u03c1\u03af\u03b1 \u03c4\u03c9\u03bd \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03c5\u03c0\u03ae\u03c1\u03be\u03b1\u03bd \u03b9\u03c3\u03ac\u03be\u03b9\u03bf\u03af \u03c4\u03bf\u03c5. \u0397 \u03ba\u03c1\u03af\u03c3\u03b7 \u03bc\u03b1\u03c2, \u03c9\u03c3\u03c4\u03cc\u03c3\u03bf, \u03ba\u03ac\u03c0\u03c9\u03c2 \u201c\u03b8\u03b1\u03bc\u03c0\u03ce\u03bd\u03b5\u03b9\u201d, \u03bb\u03cc\u03b3\u03c9 \u03c4\u03b7\u03c2 \u03c0\u03b1\u03c1\u03ac\u03be\u03b5\u03bd\u03b7\u03c2 \u03c6\u03cd\u03c3\u03b7\u03c2 \u03c4\u03c9\u03bd \u201c\u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03ce\u03bd\u201d \u03c4\u03bf\u03c5. \u039f Hardy \u03b8\u03b5\u03ce\u03c1\u03b7\u03c3\u03b5 \u03cc\u03c4\u03b9 \u201c\u201d\u0391\u03c5\u03c4\u03cc (\u03c4\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03c4\u03bf\u03c5 Ramanujan) \u03b4\u03b5\u03bd \u03ad\u03c7\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b1\u03c0\u03bb\u03cc\u03c4\u03b7\u03c4\u03b1 \u03ba\u03b1\u03b9 \u03c4\u03b7 \u2018\u03bc\u03bf\u03bd\u03b9\u03bc\u03cc\u03c4\u03b7\u03c4\u03b1\u2019 (inevitableness) \u03c4\u03bf\u03c5 \u03ba\u03b1\u03c4\u2019 \u03b5\u03be\u03bf\u03c7\u03ae\u03bd \u03bc\u03ad\u03b3\u03b9\u03c3\u03c4\u03bf\u03c5 \u03ad\u03c1\u03b3\u03bf\u03c5. \u0398\u03b1 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03c3\u03b5 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf, \u03b5\u03ac\u03bd \u03ae\u03c4\u03b1\u03bd \u03bb\u03b9\u03b3\u03cc\u03c4\u03b5\u03c1\u03bf \u03c0\u03b1\u03c1\u03ac\u03be\u03b5\u03bd\u03bf\u201d. \u039c\u03b5\u03b3\u03ac\u03bb\u03bf \u03bc\u03ad\u03c1\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03ad\u03c1\u03b3\u03bf\u03c5 \u03c4\u03bf\u03c5 Ramanujan \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03b4\u03b5\u03bd \u03c6\u03b1\u03b9\u03bd\u03cc\u03c4\u03b1\u03bd \u201c\u03bc\u03cc\u03bd\u03b9\u03bc\u03bf\u201d (inevitable) \u03c4\u03bf\u03bd \u03ba\u03b1\u03b9\u03c1\u03cc \u03c0\u03bf\u03c5 \u03b1\u03bd\u03b1\u03ba\u03b1\u03bb\u03cd\u03c6\u03b8\u03b7\u03ba\u03b5 \u03ad\u03c7\u03b5\u03b9 \u03c4\u03ce\u03c1\u03b1 \u03ba\u03b1\u03c4\u03b1\u03c3\u03c4\u03b5\u03af \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03bf \u201c\u03bc\u03cc\u03bd\u03b9\u03bc\u03bf\u201d, \u03ba\u03b1\u03b8\u03ce\u03c2 \u03b2\u03bb\u03ad\u03c0\u03bf\u03c5\u03bc\u03b5 \u03c0\u03cc\u03c3\u03bf \u201c\u03b4\u03ad\u03bd\u03b5\u03b9\u201d \u03bc\u03b5 \u03c4\u03b1 \u03c5\u03c0\u03cc\u03bb\u03bf\u03b9\u03c0\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac. \u0388\u03c4\u03c3\u03b9, \u03b7 \u03ce\u03c1\u03b1 \u03c4\u03b7\u03c2 \u03c4\u03b5\u03bb\u03b9\u03ba\u03ae\u03c2 \u03ba\u03c1\u03af\u03c3\u03b7\u03c2 \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03ba\u03cc\u03bc\u03b7 \u03ba\u03bf\u03bd\u03c4\u03ac. \u0391\u03bb\u03bb\u03ac, \u03cc\u03c3\u03bf\u03bd \u03b1\u03c6\u03bf\u03c1\u03ac \u03c3\u03c4\u03b7\u03bd \u03b1\u03b3\u03ac\u03c0\u03b7 \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u03b1\u03c6\u03bf\u03c3\u03af\u03c9\u03c3\u03b7 \u03c4\u03bf\u03c5 Ramanujan \u03c3\u03c4\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac, \u03b4\u03b5\u03bd \u03c5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03ba\u03b1\u03bc\u03b9\u03ac \u03b1\u03bc\u03c6\u03b9\u03b2\u03bf\u03bb\u03af\u03b1\u2026\u00bb.
\n\u0395\u03bd \u03ba\u03b1\u03c4\u03b1\u03ba\u03bb\u03b5\u03af\u03b4\u03b9, \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd, \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03af\u03b4\u03b9\u03b1 \u03b7 \u03b5\u03be\u03ad\u03bb\u03b9\u03be\u03b7 \u03c4\u03b7\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae\u03c2 \u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b7\u03c2 \u03c0\u03bf\u03c5 \u03b8\u03b1 \u03b1\u03bd\u03b1\u03b4\u03b5\u03af\u03be\u03b5\u03b9 \u03c4\u03bf \u03bc\u03ad\u03b3\u03b5\u03b8\u03bf\u03c2 \u03c4\u03b7\u03c2 \u03c3\u03c5\u03bd\u03b5\u03b9\u03c3\u03c6\u03bf\u03c1\u03ac\u03c2 \u03c4\u03bf\u03c5 Ramanujan \u03c3\u2019 \u03b1\u03c5\u03c4\u03ae\u03bd (\u2026)<\/p>\n

\u03a0\u0397\u0393\u0395\u03a3
\n1.<\/strong>\u00a0www.wolframalpha.com<\/a>
\n2.<\/strong>\u00a0\u03a1\u0391\u039c\u0391\u039d\u039f\u03a5\u03a4\u0396\u0391\u039d, \u039f \u0399\u03bd\u03b4\u03cc\u03c2 \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2, Robert Kanigel, \u03b5\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u03a4\u03c1\u03b1\u03c5\u03bb\u03cc\u03c2
\n3.<\/strong>\u00a0\u03a0\u03b5\u03c1\u03b9\u03bf\u03b4\u03b9\u03ba\u03cc QUANTUM, \u039c\u03ac\u03b9\u03bf\u03c2\/\u0399\u03bf\u03cd\u03bd\u03b9\u03bf\u03c2 1998, \u03a4\u039f\u039c\u039f\u03a3 5\/ \u03a4\u0395\u03a5\u03a7\u039f\u03a3 3
\n4.<\/strong>\u00a0Mathematical proof reveals magic of Ramanujan\u2019s genius, newscientist.com<\/a>\u00a0\u2013 Jacob Aron
\n5.<\/strong>\u00a0ADDITION AND COUNTING: THE ARITHMETIC OF PARTITIONS,
\nScott Ahlgren and Ken Ono<\/a><\/p>\n

<\/p>\n

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