actually the amazing thing is that mathematics can be useful. from its beginning, mathematics is not merely empirical study of everyday problems. number is bel

actually the amazing thing is that mathematics can be useful. from its beginning, mathematics is not merely empirical study of everyday problems. number is believed sacred and having divine implications and some special numbers worshiped across civilizations, Greeks included. In early days, some properties of number are not taken for granted as we do today. the duality of mathematics though, most mathematician don't have practical concerns in their minds. and this is reflected in the mathematics education. Arnold has advocated for long the intuitive teaching which basically is to introduce the ideas of mathematics using concrete tangible and often practical examples. However, in today's textbooks of all level, the Bourbaki style is still dominant.