यह एक सर्वविदित अनुभव है कि गणित को सीखने का एकमात्र सही मायनों में आनंददायक और लाभदायक तरीका अपने खुद के प्रयासों से "बारीकियों को भरना" है।
It is a well-known experience that the only truly enjoyable and profitable way of studying mathematics is the method of "filling in details" by one's own efforts.
It is a well-known experience that the only truly enjoyable and profitable way of studying mathematics is the method of "filling in details" by one's own efforts.
अधिकांश कलाएं, जैसे चित्रकला, मूर्तिकला और संगीत, आम जनता को भावनात्मक रूप से आकर्षित करती हैं। ऐसा इसलिए है क्योंकि इन कलाओं को हमारी किसी न किसी इंद्री (संवेदी अंग) के जरिए अनुभव किया जा सकता है। गणित की कला के साथ ऐसा नहीं है; इस कला को केवल गणितज्ञ ही समझ सकते हैं, और गणितज्ञ बनने के लिए लंबे समय तक गहन प्रशिक्षण की आवश्यकता होती है। गणितज्ञों का समुदाय संगीतकारों के एक ऐसे काल्पनिक समुदाय के समान है जिनकी एकमात्र संतुष्टि उनके द्वारा रचे गए संगीत के स्कोर को आपस में एक-दूसरे के साथ आदान-प्रदान करने से मिलती है।
Most of the arts, as painting, sculpture, and music, have emotional appeal to the general public. This is because these arts can be experienced by some one or more of our senses. Such is not true of the art of mathematics; this art can be appreciated only by mathematicians, and to become a mathematician requires a long period of intensive training. The community of mathematicians is similar to an imaginary community of musical composers whose only satisfaction is obtained by the interchange among themselves of the musical scores they compose.
Most of the arts, as painting, sculpture, and music, have emotional appeal to the general public. This is because these arts can be experienced by some one or more of our senses. Such is not true of the art of mathematics; this art can be appreciated only by mathematicians, and to become a mathematician requires a long period of intensive training. The community of mathematicians is similar to an imaginary community of musical composers whose only satisfaction is obtained by the interchange among themselves of the musical scores they compose.
गणितज्ञों का समुदाय संगीतकारों के एक ऐसे काल्पनिक समुदाय के समान है जिनकी एकमात्र संतुष्टि उनके द्वारा रचे गए संगीत के स्कोर को आपस में एक-दूसरे के साथ आदान-प्रदान करने से मिलती है।
The community of mathematicians is similar to an imaginary community of musical composers whose only satisfaction is obtained by the interchange among themselves of the musical scores they compose.
The community of mathematicians is similar to an imaginary community of musical composers whose only satisfaction is obtained by the interchange among themselves of the musical scores they compose.
खगोल विज्ञान प्राकृतिक विज्ञानों का पालना और ज्यामितीय सिद्धांतों का शुरुआती बिंदु था।
Astronomy was the cradle of the natural sciences and the starting point of geometrical theories.
Astronomy was the cradle of the natural sciences and the starting point of geometrical theories.