It’s a timeless language of truth and innovation
Mathematics, if approached in a very simple manner, means the science of truth. However, the decline in its respect among the evolving youngsters has many different causes. In earlier times, people who tended to study and continue with mathematics were regarded as individuals with high IQs, so only the fewest of the total population would choose to pursue this subject. In the meantime, with the advent of technology and Artificial Intelligence, this subject secures its rank in every manner, as Mathematics is considered the backbone of science. However, current times do not seem to comprehend the need to study Mathematics as a subject; rather, it has become a part of engineering courses.
Being a pure Mathematician, it becomes obligatory for me to contribute to the enhancement of Mathematics as a subject and the re-attainment of its position in the academic system. Let’s commence by recognizing the fields where Mathematics has played a crucial role. The ground for higher Mathematics is set by the concepts of Sets, Relations and Functions, Linear Algebra, and Modern Algebra. Nonetheless, everyday life demands the continuous use of basic Mathematics in terms of budgeting, driving, managing time, exercising, cooking, stitching, trading, etc. There is no such event that doesn’t require Mathematics in some way or the other.
Well, we can celebrate this National Mathematics Day by visualizing different shades of Mathematics beyond classrooms. Let’s first consider the concept of relations, which in Mathematics means how the elements of one set are related to the elements of another set. This concept enables us to understand how students are associated with their grades, how temperature varies at different times in a day, or even how a particular group of people relates to their ages, and so on. The next very immediate concept is a subset of a relation itself, called a function. A function is also a relation, but the only difference is that a function generates exactly one output for one input, whereas a relation can have multiple outputs for a single input. To see that in real life, we can consider human appearances—one person with exactly one unique appearance. Moreover, students in a particular classroom with exactly one identification number or Aadhaar number are also examples.
Next, we study the concept of differentiation, which in layman’s language means the rate of change. To further see that in real life, we can consider a moving car, where we can observe the change of distance with respect to time, the rate of change of speed with respect to time, or the change of velocity with respect to time, and whatnot. Similarly, we can see the rotation of the Earth with respect to the Sun and the rotation of other planets with respect to the Sun or the Earth and among themselves as well. Another important concept is that of matrices, which are used in geology for conducting seismic surveys and in computer sciences for programming 3D games, etc.
Another prominent application of Mathematics (in particular, Number Theory) lies in the field of Cryptography, which involves the encryption and decryption of data for security purposes. By using coding and decoding, one can secretly send a message from one place to another without anyone manipulating it. For example, if we divide the English alphabet into two sets, the first 13 and the latter 13, and then join them by a bijective function, we can write HELLO as URYYB. So the message becomes encrypted. This is a very basic way; we have advanced methods as well. This field itself has many efficient uses for national or international-level confidential communications or the transmission of sensitive information.
The Fibonacci series in Mathematics is a sequence of numbers in which each consecutive number is equal to the sum of the two numbers that come before it. For instance, if you start with the number zero, this is what a Fibonacci series would look like: 0, 1, 1, 2, 3, 5, 8, 13, and so on. The Fibonacci series is famously found in nature—trees, flowers, and other naturally occurring spiral structures grow leaves and petals that follow the sequence. It’s also particularly useful when it comes to cryptology, the study of codes and how to solve them. With modern technology, the Fibonacci series can be used to encrypt sensitive information over the internet for security purposes.
The toughest field of Mathematics so far known is Topology, which literally means the study of place or the study of surfaces. In this field of Mathematics, we study how we can transform one object into another without any cutting or pasting, yet one can mould, stretch, crumple, bend, or tear the object using proper transformation (preserving the features of the object, mathematically called a homeomorphism). Thus, for a topologist, a coffee mug and a donut (also known as a torus) are the same, as each of these two objects possesses a single hole, which is preserved during the transformation (homeomorphism). Such objects are mathematically termed as topologically equivalent. One more observation, as a topologist, is that we believe in two perspectives of looking at a particular object: one is local, and the other is global. Thus, for us, the Earth is flat (locally) but round (globally).
Another very eminent concept of Mathematics is that of metric spaces, which helps us understand the distance between any two points in a space or a set. This metric, being a distance-measuring function, has direct applications in the field of Biology. Since genotypes and phenotypes are of primary importance in Biology, we see how Topology is even useful in sequencing the right nucleotides in a DNA strand. Genotypes are the internally veiled and inheritable information of a living being, whereas phenotypes are the physical appearances of that information. Topology solves one of the most important problems in DNA research. As we know, DNA is composed of four nucleotides: Adenine, Cytosine, Guanine, and Thymine. These are arranged in a sequence, and the sequence of nucleotides on one chain of DNA determines the sequence on the other chain. The problem in DNA research is the comparison of distinct DNA sequences. Using the concept of metric spaces (a special type of topological space), we measure the distance between two sequences, where the distance function (metric) gives insight into the evolutionary history of species. Let’s consider 𝑥 and 𝑦 to be two sequences of letters 𝐴, 𝐶, 𝐺, and 𝑇. To calculate the distance between 𝑥 and 𝑦, we fix the number of operations on 𝑥 to turn it into 𝑦. We can apply three operations—insertion, deletion, and replacement—to transform 𝑥 into 𝑦.
In the current era, we owe Mathematics a standing ovation for preserving the logic behind theories. Let’s not underestimate the contributions of Mathematics in all fields of science and non-science.
The writer teaches Mathematics at the Government Degree College (GDC) Sopore
By Dr Mir Aaliya
mi**********@***il.com