There is barely any person in the world who has never been in touch with mathematical knowledge. Most of the children become aware of the term “mathematics” itself in the nursery or at the elementary school, where a subject called Mathematics is introduced. Actually Mathematics is a compulsory subject at elementary school as well as at secondary school and is considered to be one of the most essential fields of study. Some of the knowledge obtained during the Math’s course is directly related to reality and can be practically applied, but the rest remains an abstract knowledge, with actually no functional use, thus the meaningfulness of the mathematical knowledge can be argued.
First of all, in reality people have to study in order to reach goals set by themselves or some other authorities and in discovering areas of knowledge other than mathematics, mathematical knowledge serves as a tool, which relieves the process. Examples of such areas of knowledge, which are actually based on mathematics, are natural sciences – chemistry, physics. Even though, laws and formulas involve problem of knowledge, as they are drawn from a particular amount of observations, and it is not possible to know that this is the way it will always be, they do provide the opportunity to make calculations necessary for our daily life.
For example, in construction process of some technical items it may be important to determine the centripetal acceleration. In the physics there is a formula that can be used for calculating it: ac = v2 / r 1. It can be seen that this formula involves two significant mathematical operations – division and raising to the power of two. Without the mathematical knowledge of how to do it, the formula in such a form could not be applied. Probably another way how to estimate the acceleration would be found, however, usage of the formula relieves the process. Another field of knowledge where mathematical knowledge serves as an important background is architecture. In fact historically, architecture was part of mathematics, and for a long time these two fields were indistinguishable2. In Classical Greece and ancient Rome, architects were required to also be mathematicians.
Architecture requires a strong grasp of geometry and this enables planning and constructing buildings according to mathematical principles. The presence of the Golden Mean (? = 1.618), the ratios 5:3, 8:5, and square root of two proportion are found throughout all of architecture, and without knowledge in mathematics they could hardly be applied. Also in social sciences, such as economics and sociology, at least basic mathematical knowledge is necessary. For example, the economics’ program of International Baccalaureate includes also calculations of elasticity of supply and demand. When acquiring the topic, we were required to calculate percentages and use also others skills obtained during the course of Algebra, like adding, dividing, subtracting, as elasticity can be calculated dividing the percentage change in quantity to the percentage change in price3.
We become acquainted to graphs and curves also in the course of mathematics, but we use them for example in economics as well. Even though in the areas of knowledge which are more based on the emotions rather than reasoning and numerical data, mathematics play smaller role and can be practically applied in rarer cases, music which is actually based on the way of knowing through perception – hearing, also has links with mathematics., such as mathematical patterns in musical compositions (for example, Golden proportions and ratios, symmetry, tact measure expressed in mathematical means).
Mathematical knowledge can be practically useful not only when researching other fields of knowledge, but also in our everyday actions. Most of the time people are not even aware that they are applying mathematical knowledge, they do not identify the methods used at a particular cases. However, an example of probably inadvertent practice of mathematical means could be situation when street sweeper scatters salt or send on icy and slippery pavements. Of course, not the highest mathematics are used, and the calculations are probably not even put down on a paper, but still when calculating how much salt or sand will be necessary for scattering a particular area, the street sweeper is responsible for, mathematical knowledge is applied.
For example a proportion may be put up – if one bag of salt is enough for scattering 10 square meters, then unknown amount of bags will be needed for scattering 55 square meters. These calculations the street sweeper may bring out in his mind and maybe even unconsciously. In this and many other cases similar to this, knowledge of mathematics serves as a tool actually relieving life. Take again the street sweeper as an example. If he was not able to bring out such calculations, he would either have to carry much more salt with him or he would take too little of it, which would mean that his work would be of a low quality or he would have to return for some more salt.
However, not all the mathematical knowledge and not in all cases can be practically applied, there is actually a lot of mathematical skills that most people will not be able to put into operation. At the moment in the course of mathematical analysis we are going through the derivations. Even though, it maybe develops our thinking and will be necessary for acquiring further mathematical skills, great majority of us will not be able to utilize practically the knowledge of derivations in our daily lives. Mathematics is a very broad science, and only a small part is taught in the mathematics’ course at schools and also in universities, except of course the faculty of Mathematics, and only a part of what is taught is actually going to be practically applied. This means that the rest of the mathematical knowledge can be considered to be a toy, as people can live without it very well.
Toy in a sense that it can only be used as a pastime. You may spend time deriving or analyzing complex functions, but there is no use of this knowledge. Actually, it is extremely hard to evaluate at the moment, of which mathematical knowledge I will be able to make use in future and also probably I must admit that the mathematical knowledge that is taught up to the secondary school is only the very bases of all the science, thus it should be acquired, but, however, it seems to me unnecessary to learn logarithms, if in the real life there is no way to see them and actually it is hard to imagine where the knowledge of them could be applied. Some of the mathematical knowledge can be assumed to be a toy also in the hands of the mathematicians, who puts themselves a challenge, to find out something new, to widen the are of mathematical knowledge, without actually any purpose.
To conclude, I would like to say that mathematics can actually be divided into two parts. One of which is the knowledge that can be applied, thus can be considered to be a tool, and the other part consists of the mathematical knowledge that could be called a toy, because of inability to be practically utilized. Of course it is not possible to draw a strict line between the two groups, because the division differs from each individual, as every person in his life can apply various amount of the mathematical knowledge, however, it can be assumed that such division might exist. Therefore, the question whether mathematics is a tool or a toy cannot be answered firmly.