BIOMEDICAL ENGINEERs – Warriors of all time

In COVID-19 crisis, the real warriors were the Biomedical Engineers. They played an important role in medical technology in patient care. They involved themselves in making ventilators and PPE (personal protection equipment) kits to help the COVID patients. Biomedical engineers focus on inventing new devices and develop modern technologies which help in improving human health care system. With the help of the doctors and researchers, Biomedical Engineers are developing equipments to solve clinical problems. 

Electing biomedical engineering as métier is extremely rewarding. Biomedical Engineers has the ability to save lives through innovation and modern technology. That’s why experts from Human Resource Department’s planning team suggest that every doctor along with medical studies should be accustomed with biomedical engineering studies. 

Biomedical engineering, also known as medical engineering, is a form of engineering associated with the study in the fields of biology and health care system.  

The following qualities are required for Biomedical Engineers: 

  • Analytical skills 
  • Communication skills  
  • Listening skills 
  • Math skills 

Apart from these skills, they should have idea of all disciplines ranging from material science to electronics, life science to biomechanics and mathematics to computation. Because of these, Biomedical Engineering is completely interdisciplinary in nature and the Biomedical Engineers possess vast knowledge across of all domains.  

Create your future in Augmented Reality, Virtual reality and Mixed Reality

Augmented and virtual reality add a new dimension to technology-enabled teaching and learning. 

Through the use of augmented reality, we have the opportunity to see fragments of virtually inserted visuals, video, music, or GPS data and information superimposed over a view of the real environment. The GPS location on your smartphone is probably the most well-known example of augmented reality. In addition, you can have an experience of augmented reality by using other apps such as: 

  • Froggipedia
  • Augment
  • Jigspace
  • View
  • Quiver

A complete submersion into the world of computer-generated reality is what is meant by the term “virtual reality.” Although it is not always attainable at the moment, the ideal form of virtual reality will comprise the simultaneous stimulation of all five senses, namely sight, hearing, smell, taste, and touch. However, this is not always the case at the moment. The utilisation of virtual reality simulations can be beneficial to industries such as tourism, shopping, education, healthcare, and Industry 4.0. There are a plethora of virtual reality (VR) products currently available, including: 

  • Oculus Go
  • HTC Vive
  • Virtual Reality for the PlayStation®
  • The Hololens from Microsoft
  • Google Cardboard/daydream view

A combination of Augmented Reality and Virtual Reality is known as Mixed Reality (MR). Virtual reality (MR) is a technology that combines your vision of the real world with computer-generated or digitally-created images. In addition to this, it makes it easier to anchor and interact with things that have been virtually inserted into the area that you are in. Because MR and AR are now located in such close proximity to one another, this proximity may lead to some confusion. A form of augmented reality that is both more engaging and more interactive is called mixed reality (MR). The items found in Hybrid Reality are more accurate representations of their respective real-world applications. Take for example the Hololens app, which is considered a hybrid or mixed reality. 

Microsoft has designed the Hololens HMD (Head Mounted Display) with advanced sensors that detect your interaction within a mixed environment. It analyses how you interact with the digital data present in your actual view environment. The Hololens is an example of a holographic device used for mixed reality. Other Immersive devices include the Acer Windows Mixed Reality Headset and the HP Windows Mixed Reality Headset Developer Edition. 

Figure: AR image
Figure: AR image

The Hololens is also considered as holographic device. Other Immersive devices include the Acer Windows Mixed Reality Headset and the HP Windows Mixed Reality Headset Developer Edition. These HMDs are opaque and completely block out the outside world. In addition, they use a camera for tracking and surveillance purposes.

Hybrid Reality can be utilized for educational purposes, such as in the fields of mechanics, medicine, Biotechnology etc. It aids in worker assistance by providing clear instructions.

Figure: Mixed reality in Microsoft hololens
Figure: Mixed reality in Microsoft hololens

It interacts appropriately with the real-world scenario and generates superior solutions and practises.

AI and Metaverse: An Important Integration of Technology!

AI and Metaverse have the intention of driving and integrating various virtual transformation technologies. In addition, the future of the Metaverse is a hot issue of discussion among specialists in the field of technology. The Metaverse is a universe of virtual reality that enables user interactions by making use of a wide range of technologies, such as AI, augmented reality, virtual reality, and so on.

In addition, users are able to interact with three-dimensional digital items as well as virtual avatars by making use of a variety of technologies and solutions. AI and the Metaverse collaborate to bring out breakthroughs and advancements that herald the beginning of a new era of reality. Bloomberg predicts that the market for the Metaverse will reach $783.30 billion by the year 2030, with a compound annual growth rate (CAGR) of 13.10 percent. According to the findings obtained by McKinsey, fifty percent of respondents stated that their organisations had already incorporated AI in at least one aspect of company operations. According to a study conducted by Deloitte, forty percent of employees report that their companies have a comprehensive AI strategy. Artificial intelligence (AI), augmented reality (AR), virtual reality (VR), fifth-generation wireless (5G) networks, and blockchain are all expected to work together to create a virtual reality within the Metaverse, which is a primary component of Industry 5.0.

The term “Metaverse” is derived from the combination of two words: “Meta,” which refers to transcendence or virtuality, and “verse,” which is a contraction of the word “Universe.” To put it another way, the Metaverse is a digital reality that, by employing a wide range of technological methods, recreates the conditions of the physical world. In addition to this, it creates a virtual space for users by utilising various technologies such as virtual reality, augmented reality, artificial intelligence, and so on. In addition to this, it brings together the digital and real worlds in order to provide users with the ability to purchase and sell solutions, produce things, engage with people and locations, and so on. As a consequence, the following is a list of the primary Metaverse levels:

  • Infrastructure: The data centres, central processing units, graphics processing units, cloud computing, and other technologies are used to build the infrastructure and environment of the metaverse.
  • Human Interface: Human Interface also encourages people to interact with the virtual world by utilising cutting-edge technologies in their experience. The experience can be improved, for example, by using mobile phones, smartwatches, smart glasses, and other types of wearable technology.
  • Decentralization: In addition, the Metaverse manages massive data collections, which necessitates the use of a decentralised approach to problem solving. Edge computing, blockchain, microservices, and other similar technologies all offer options for the processing and examination of data.
  • Computing in Three Dimensions: Three-dimensional computing makes it easier to digitalize Metaverse products, services, and solutions. In addition to this, it makes Metaverse interactions and activities much simpler and more effective.
  • The Creator Economy: As the popularity of the Metaverse continues to rise, it drives creators, developers, and service providers to provide improved virtual solutions.
  • Experience: Artificial intelligence, virtual reality, augmented reality, and extended reality, as well as other technologies, are used to design the functionalities of the Metaverse in order to offer its users a one-of-a-kind experience.

What role does AI play in the Metaverse?

The purpose of artificial intelligence is to facilitate a wide range of Metaverse functions. In addition to this, it makes it easier for users to access a variety of virtual world environments. In addition to this, it helps users create content and promotes human engagement with other users while also providing support virtually.

Integrations of many types of reality, including augmented reality, virtual reality, and mixed reality, are what AI and the Metaverse are all about. AI also broadens the possibilities of the Metaverse by enabling users and businesses to produce, purchase, and sell a wide variety of products, services, and solutions. This, in turn, creates new opportunities. In addition to this, it would encourage users to work together with both other users and businesses in order to broaden their scope of available prospects.

AI not only enables the virtual world to deploy a variety of services but also enables the Metaverse to do so by combining the virtual world with NLP, computer vision, and neural interface. Because of this, artificial intelligence plays a significant part in the Metaverse, which provides dependability and enhances performance for a more satisfying experience.

In addition to this, the building of translation systems for new AI models and virtual assistants is a necessary step in the process of developing AI for the Metaverse. In order for the Metaverse to be realized, it is necessary for AI to reach its full potential and become reliable in people’s everyday lives. In addition to this, it claims to give pictures, sounds, and sensations that are extremely lifelike.

AI and ML for a better future

Have you ever considered about what motivates artificial intelligence programmes like Tony Stark’s JARVIS or the common man’s Alexa, Google Assistant, or Siri? These programmes can answer your calls and help you make decisions, but have you ever wondered what motivates them? In what ways does their brain operate? The application of Artificial Intelligence (AI) and Machine Learning is the straightforward response to each and every one of your questions (ML). The mechanical brains are controlled by artificial intelligence, which attempts to simulate human intellect so that they can perform like a human brain. With more and more research being done on AI and ML, there is the potential for AI and ML to assist in training computers to make decisions on their own, which will eventually make our lives easier by reducing the amount of work we have to perform. 

This article, which was meticulously researched and penned with the intention of depicting the future reach of AI and ML in India, was created with the goal of assisting students in understanding how this subject will be advantageous to them if they decide to pursue it. 

The potential applications of artificial intelligence in India are still in the process of being adopted, but the technology is gradually being put to use to find intelligent solutions to modern problems in almost all of the country’s most important industries, including agriculture, healthcare, education and infrastructure, transportation, cyber security, banking, manufacturing, business, hospitality, and entertainment. Readers who are interested in pursuing a course in artificial intelligence can find helpful information in this article. Candidates will gain some insight into the potential of artificial intelligence in India if they read this article and consider its contents. 

Scope of AI in India 

Both artificial intelligence and machine learning have a promising future in India and an immense potential to alter every area of the economy for the benefit of society. Artificial intelligence and machine learning have a bright future in India. AI is an umbrella term that incorporates a variety of helpful technologies, such as self-improving algorithms, machine learning, pattern recognition, and large amounts of data. Soon, there will not be a single business or market segment in India that is immune to the effects of this powerful instrument. This is one of the reasons why there is a growing demand for online courses in artificial intelligence in India. 

Scope of AI and ML in Education Sector 

By utilizing a variety of AI applications such as text translation systems, real-time message to speech, automating mundane and also repeated tasks such as taking presence, automating grading, and also customizing the learning journey based on ability, comprehension, and also experience, artificial intelligence can help our instructors be more effective. Within the purview of Artificial Intelligence education and learning is the consideration of the prospect of utilizing AI-powered rating machines that are able to evaluate solutions in an objective manner. This is being carried out in college and university settings in a step-by-step fashion. Real-time text-to-speech synthesis and text translation are two further AI-based applications in the educational sector. 

The Role of AI and ML in the Development of Chatbots 

The combination of chatbots in the digital framework or availability via the IVRS system education domain can be transformative in a country as diverse as India. They can be educated on the subject matter, and a large percentage of the students’ doubts can be answered quickly. This reduces the current workload of educators, allowing them to focus on more creative tasks. 

The Integration of AI and ML into the Automated Grading System 

On a more global scale, methods of machine learning such as Natural Language Processing could be used for automated grading of assessments on systems such as E-PATHSHALA, SWAYAM (Study Webs of Active Learning for Young Aspiring Minds), and DIKSHA. This would apply not only to inquiries that are subjective but also to those that are objective. This is because of the National Education Policy 2019, which places an emphasis on computer and internet literacy. 

The Role of AI and ML in the Healthcare Industry 

The healthcare industry in India is one of the most rapidly developing and competitive markets in the world. There is a dearth of doctors and services, including competent nurses and technicians, as well as infrastructure. This is one of the primary issues, but there are many others as well, including affordability and accessibility. As a result of the majority of high-quality medical facilities in India being situated in close proximity to tier 1 and tier 2 cities, access to healthcare in India is not uniformly distributed across the country physically. Aside from that, as Artificial Intelligence develops, there will be an increase in efficiency, which will lead to a reduction in the overall cost of medical treatment. 

Because AI is able to process vast volumes of data in a short amount of time, it can be of assistance in the creation of medical equipment, as well as in design and innovation. Having a system that is enabled with AI helps to eliminate medical errors and increases overall productivity. Artificial intelligence has the potential to both circumvent access barriers and provide a solution to the accessibility problem by applying early detection followed by suitable diagnostic conclusions. 

AI and ML in the Agriculture Sector 

In India, agriculture is a major source of income for many people. Traditional farming methods pose a slight challenge for Indian farmers. Thermal imaging cameras can be used to continuously monitor agricultural land to ensure that plants receive adequate water. When it comes to selecting the right crop and the optimum method of sowing, this tool can help you get the most out of your land and save money. 

As a result, improved insect control preparation can benefit from the application of artificial intelligence to predict behaviour and investigate parasites. Artificial intelligence-assisted anticipating modelling can be effective for delivering more detailed demand-supply details and for predicting the needs of farmers in terms of agricultural produce. 

Automated Vehicles Using AI and ML 

In the transportation industry, artificial intelligence offers a lot of potential. Artificial intelligence (AI) has the potential to be useful in a few specific contexts. Since its invention in 1922, autopilot has been used to keep ships, planes, and spacecraft on course. Self-driving cars are another field of research. Self-driving automobiles are being researched by companies around the world, including India. The use of artificial intelligence and machine learning has been prevalent in the design of these automobiles from the beginning. Self-driving cars, according to experts, will have various advantages, such as reducing pollution and eliminating human error from driving. 

Artificial Intelligence and Machine Learning for a Smart Home 

We are surrounded by artificial intelligence. Most of the time, we don’t even realize we’re interacting with devices powered by artificial intelligence. As an example, we routinely use OK GOOGLE, ALEXA, or CORTANA to execute a variety of chores by simply speaking to them. Artificial Intelligence and Machine Learning are used by these intelligent assistants for voice recognition. Learning from the user’s commands improves their productivity. You may ask a question, play a song, and buy anything online all with the help of this clever assistant. 

Applied Artificial Intelligence and Machine Learning in Cybersecurity 

Cybersecurity is another area where AI is being applied. Many companies have to deal with a lot of data. A security system is required, for example, in the banking industry or government entities that maintain vast databases containing the personal information of citizens. An good example of this topic is Cognitive Artificial Intelligence (CAI). Additionally, it helps analysts make better judgments by detecting, analysing, and reporting on hazards. 

Machine Learning formulae and Deep Learning networks are used to improve and strengthen the AI over time. As a framework and central point of control for safety and security responses, IBM Resilient is an open and agnostic platform. 

In the Manufacturing Industry, AI and ML 

The industrial sector is a popular target market for AI-based firms from India. In order to assist the manufacturing industry flourish, these companies are developing AI-based solutions. Various types of robots are controlled by artificial intelligence in the workplace. The ability to examine data and forecast the future is a unique AI technology. 

Using this AI capabilities, companies may estimate future supply and demand based on data from prior years’ sales or market surveys, allowing them to make faster decisions and better use of existing products. Artificial intelligence (AI) will be widely used in manufacturing in the future years. 

Are we having safe drinking water?

Water is one of the most precious, integral and important aspects of almost every living organism. About 3% of the water is fresh water. This fresh water does not contain significant levels of dissolved minerals or salt and two third of that is frozen in ice caps and glaciers and is unavailable for human consumption. In total only about 0.5% of the total water of the planet is accessible for consumption[1]. So, we have a very limited amount of usable fresh water. Now one of the basic human needs is clean drinking water. Unfortunately, more than one in six people still lack reliable access to this precious resource in this developing world[2].

India covers for 2.45% of land area and 4% of water resources of the world but represents 17.7% of the world population. If the population increases with the present population growth-rate of 1.9 % per year then the population is expected to cross the mark of 1.5 billion by 2050. According to the Planning Commission, Government of India water demand will increase from 710 BCM (Billion Cubic Meters) which was in 2010 to about 1180 BCM (Billion Cubic Meters) in 2050. Domestic and industrial water usage is expected to increase by 2.5 times. Increase in urbanization in India is putting a drastic stress on civic authorities to provide basic requirement such as safe drinking water, infrastructure and sanitation[2]. Overpopulation is putting a lot of pressure on available water resources, it is increasing the demand for the portable water, which in turn therefore requires exploration of raw water sources, developing treatment and distribution systems[3]. In this era of rapid growth of population, management, maintenance and monitoring of water and its quality becomes a problem. Therefore, it is important to ensure that the water quality should be maintained at its desired level and should be monitored on regular basis so as to provide safe and quality drinking water.

As our concern is to know the quality of water, so we have gathered some reports across India to understand the recent scenario. We found that many Institutions/Organizations such as Maharashtra Public Health Laboratory, PES university, BIS (Bureau of Indian Standards), Union Government, Jal Sansthan, Ministry of Jal Shakti etc. had worked on checking the quality of water. They checked the quality of water under 28 parameters[4].

Number of parameters in which samples are failing [4]

Water Treatment Process

Different communities have different procedures of treating the water. Treatment is on the basis of quality of the source water which enters the treatment plant. Now, the water which enters the treatment plant can be from two areas either surface water or ground water. Treatment and filtration are required more in surface water than ground water. This is because streams, rivers and lakes, contain more sediments like clay, sand, silt, soil particles,chemicals,toxins and germs than ground water[7].

The basic purposes of water treatment plant or water treatment process:

  1. Production of biologically and chemically safe water for human consumption
  2. Production of water should be appealing to the consumers meaning water should be clear, colourless, pleasant to the taste, odourless, cool, none staining, neither corrosive nor scale forming, and reasonably soft.
  3. Production of water should be accomplished using facilities with reasonable capital and operating costs[2].

Unit Operations and Unit Process of Water Treatment Units

Sl. No.

Unit Operations and Unit Process

Principle Applications



Before the treatment, water needs to be collected from various sources such as lakes, ponds, rivers, streams, etc[8].



Screening is the first step in the treatment process that is needed to remove larger items of suspended materials, such as plants, rubbish, large solid chunks of different materials, plastic packets, trees, animals and other debris[8].


Micro strainer

It is used to remove plankton &algae from water[2].



In this process water is supplied with air so as to take up oxygen form air. Aeration helps in making the water less corrosive. it helps in expelling soluble gases such as CO2, H2S and also expels volatile organic compounds. By aeration the taste and odour get improved[9].



This process provides rapid& uniform distribution of gases and chemicals into the water[2].



Ozone,potassium permanganate& chlorine, potassium permanganate acts as oxidizing agents in raw water. They retard the microbiological growth and oxidizes the taste, colour and odour causing compounds[2].



Coagulation is the removal of fine particles that are suspended in the water.  Rapid mixing of coagulant (positive charge) is done in this method resulting in neutralization with the negative charged particles. Lastly, fine particles come together to form flocs. Aluminium sulphate, ferric chloride, etc are the coagulants used in this process[9].



Flocculation isthe process where water is gently mixed in a flocculation tankto form larger and heavier flocs [7].



For sedimentation process a settling tank is used in which the large flocs that are formed in the previous process will fall because of gravity and settle on the floor of this tank[9].



Filtration removes dust, parasites, germs, dissolved particles, etc from the water. In this process the clear water that is above the settling tank is passed through filters with different pore sizes and are made up of different materials such as sand, gravel, charcoal, etc., [7]



This process is needed to destroy thedisease-causing organisms in water. Disinfection is done by oxidative chemicals such as bromine, chlorine, iodine, ozone &potassium permanganate, and also the ultraviolet radiation helps in disinfection[2].


How is Biotechnology impacting millions of lives?

Are you an avid lover of biology? Are you naturally inclined to apply the principles of biology to create an impact on people’s lives? Well, then the Biotechnology sector is where you may find your dream job.

With the world still reeking of over 520 million deaths due to the COVID-19 pandemic, it is undeniable that the figure could have been in billions or even more had it not been for the Biotechnology sector. Almost everything starting from the diagnosis and immediate treatment to the development of vaccines brought to light the promise that Biotechnology holds as a leading technology in the modern world. To know more about the potential of Biotechnology and the facets of human lives that it is able to impact upon, read further down.

What is Biotechnology?

Biotechnology is an industrial sector that deals with the manipulation of living organisms to create commercial products. For instance, the wealth of knowledge accumulated by cell biologists, botanists, zoologists, molecular biologists, and geneticists have been implemented by genetic engineers to manipulate information carried by the DNA in order to create transgenic animals and plants of commercial importance. Quite undoubtedly, the deepest penetrations of the biotechnology sector has been in the healthcare and agricultural markets. However, there are several other important areas where Biotechnology is making inroads with sustainable solutions. This blog highlights some fields wherein Biotechnological interventions are working wonders.

Vaccine development

Within a few months of the detection of coronavirus, scientists mapped the entire genome of the virus and it helped to understand how the virus operates. Genome mapping being an important technique in Biotechnology, the Biotechnology sector can boast of its towering presence in global markets across the map. Also, the highly effective mRNA-based vaccine for COVID-19 was first tested in cells inside the laboratory which entails practising some basic techniques of Biotechnology. Weighing the outcomes, government organizations and pharmaceutical giants have entered into strong public-private partnerships to pool resources and fund research in the domain of vaccine development.

Next-generation computing-aided drug discovery

Advanced computing technology such as artificial intelligence and machine learning have enabled Biotech companies to automate their processes and scale up operations. This handholding of technologies have enabled to reduce the cost and time required to take new drugs from bench to bedside. The ability to analyze large data sets helps medicine manufacturers to identify treatments based on the root cause of a disease. This holds immense potential to reduce the usual 90 percent failure rate for developing new drugs.  Data mining from current clinical trials can also help to predict the effectiveness of treatments down to a molecular level and even predict new or different uses for an existing drug thereby reducing cost and effort of establishing new drugs.

Genome editing

Techniques for manipulating the information present in the DNA, known as gene editing in technical jargon, has come a long way since they were first used to make edits such as addition, deletion, silencing, or replacement of a specific gene. Precise gene editing has been made possible by the advancement of technologies such as the revolutionary CRISPR-Cas9 systems. Engineered nucleases called CRISPRs acting as molecular scissors have unfurled a plethora of applications in gene therapy for the treatment of many conditions including rare genetic disorders and even fatal cancers. Furthermore, gene editing has also allowed the development of improved transgenic plants and animals capable of synthesizing a variety of medically important recombinant human proteins such as Insulin.

Precision medicine

Sequencing the entire human genome, an initiative known as the Human Genome Project, began in 1990 and was completed by 2003. This was another hallmarking achievement of Biotechnology that now allows extensive screening of patients and targeting of interventions. Improvisation of sequencing technologies have reduced the cost of genetic sequencing drastically ever since thereby making personalized gene sequencing affordable. This, in turn, has enabled the development of personalized treatment plans and targeted therapies, which are more effective than less-specific therapies because they focus on a patient’s genetic constitution. Furthermore, the falling cost of sequencing technologies has fostered the development of rapid and inexpensive methods to detect pathogens from clinical samples as well as soil samples.

Boosting agricultural yields

The global population is set to increase by 25% from 7.9 billion in 2022 to 9.7 billion in 2050. The basic need for a growing population is food, and hence its demand for feeding both people and livestock is about to increase proportionately. This automatically necessitates the use of increasing hectares of land for farming while practically cultivable land will keep on reducing as the expanding population of humans keep encroaching onto such lands. Biotechnology offers a solution to this alarming problem through the approach of gene editing. For example, crops such as wheat or corn may be engineered through the transgenic technology to grow in harsher conditions or produce more grain in a smaller area than other crop varieties while providing the same nutritional value. From another perspective, the development of biopesticides can enable protection of crops without the use of harmful chemicals thereby averting environmental damage. 

Bioprinting and tissue engineering

Another promising futuristic application of Biotechnology in the medical field is 3D bioprinting, wherein bioprinters are used to develop cell-based scaffolds using a ‘bio-ink’ comprising cells and biomaterials. This empowers one to develop skin, bone, and vascular grafts from the patient’s own cells for personalized medicine. The bioprinting technology has added a major thrust to the field of tissue engineering and regenerative medicine by enabling the creation of autologous tissue grafts for wound healing and organ transplantation.


These trends clearly show that the demand for biotechnology is on the rise. The fact that this particular sector is being able to solve real-life problems related to human health and nutrition has catapulted it to fame. It is also quite evident that biotechnologists need more than just a background in biology, chemistry, or pharmaceutical science to build their careers upon. With innovative solutions rooted to the genetic level, biotechnology is here to stay and offer myriad career opportunities to the brightest minds!

Dilemmas in Global Politics: India’s Foreign Policy Challenges in Afghanistan

The world woke up on the morning of 15 August 2021, to bear witness to one of the biggest turning points in the history of the post-Cold War world. The sudden withdrawal of U.S.-NATO forces coupled with the takeover of the administrative power by the Taliban since their rule from 1996 to 2001 in Afghanistan has led to a huge political and strategic uncertainty in the region.   Not long after the end of the World Wars does one find Afghanistan being sucked into the vortex of great power rivalry, the repercussions of which have come to be felt even in current times.   The land was ravaged by the violent repression of political power syndrome. The dramatic resurgence of the Taliban government led most of the regional powers to recalibrate their approaches and influences in protecting their national interests in the country.

Besides this, so far as regional interests are concerned, one has to take note of the strong and differentiated regional power interests of Russia, China, India, Pakistan, and Iran which trigger certain questions to shape the prospects of Afghanistan. They are – first, the withdrawal creates new opportunities for influence and control for Russia; secondly, the withdrawal is a net gain but not an unequivocal victory for China, which has new opportunities to extend its Belt and Road Initiative (BRI), address regional security threats, engage in significant economic activities, and challenge the ambitions of the United States and raised a big question about American dependability and assurance as an ally and security partner. Thirdly, the withdrawal represents the least optimal outcome for India and its troubled relationship with Pakistan, but there are opportunities to engage with AUKUS and the Quadrilateral Security Dialogue. Finally, despite the ongoing tensions with the Taliban, Iran may take advantage of the withdrawal in its international posturing toward the United States.

 This new environment led Indian policymakers to a serious quandary and raised a big question regarding India’s role and influence in Afghanistan under the new miliew. Although, ambiguity and flexibility are essential attributes of diplomatic life, however striking a balance between moralism and realism requires constant calibration. Although New Delhi has considered the Afghan Taliban as Pakistan’s proxy, engagement with them has been a regular feature of the Indian policymaker.

India can undertake four policy options in terms of its’ future with Afghanistan, firstly the Realist policy, where New Delhi need to shift theatre from Kashmir to Afghanistan and should work towards building a Delhi-Washington-Moscow Consensus to ensure peace and stability in Afghanistan. Secondly, the use of soft power as a major means to stay out of the Afghan quagmire, knowing fully well it can also endanger India’s investments in Afghanistan under the Taliban. Thirdly, smart power strategy, where India should come out of its Panipat Syndrome and pursue a proactive policy to safeguard India’s national interest and needs to engage with the new government in Afghanistan without damaging its carefully nurtured image of a trustworthy neighbour, which in other words means that it will neither confer legitimacy on the Taliban nor will it erode the legitimacy of India.

Fourthly, India should take on a mediating role among the different nations anxious to involve themselves in Afghanistan and produce a formula that would help maintain Afghanistan’s neutrality and ensure that it becomes a buffer zone to prevent further Chinese expansionism towards South Asia and by which it can preserve its national interests on its own without any butterfly effect.

Amidst the ambiguity over international recognition of the new Taliban government in Afghanistan, questions have arisen as to the fate of the South Asian Association for Regional Cooperation (SAARC). The largely dysfunctional South Asian organization’s future will largely depend on the road that Afghanistan takes.

নাথবতী অনাথবৎ- একটি বর্ণনাধর্মী নাট্য

শাঁওলি মিত্র বাংলা থিয়েটার ও সিনেমা জগতের এক প্রখ্যাত অভিনেত্রী। তিনি ঋত্বিক ঘটকের যুক্তি তক্কো আর গপ্পো চলচ্চিত্রে বঙ্গবালা চরিত্রে অভিনয় করেছিলেন। তাঁর পারিবারিক পরিচয় হল তিনি প্রখ্যাত নাট্যকার শম্ভু মিত্র ও তৃপ্তি মিত্রের কন্যা ,যাদের সুবাদে অনেক ছোটবেলা থেকেই থিয়েটারের সঙ্গে তার জীবনযাপন।

 নানান সাক্ষাতকার থেকে জানা যায় যে ছেলেবেলায় তিনি খুব ভুগতেন তাই পড়াশোনার বিশেষ চাপ তাকে দেওয়া হতনা। ২০১১ সালে তিনি রবীন্দ্র সার্ধশত জন্মবর্ষ উদ্‌যাপন সমিতির চেয়ারপার্সন হিসাবে তাকে নির্বাচন করা হয়। ছোটবেলা থেকেই নাট্যচর্চা করেছেন শাঁওলি মিত্র। বাড়িতেই থিয়েটারের মহড়া চলতো। কখনও কখনও বহুরূপী’র শোয়ের সময় উইংসের পাশ থেকে নাটক দেখতেন শাঁওলী।

কমলা গার্লস হাইস্কুলে তৃতীয় শ্রেণিতে পড়ার সময় বহুরূপী নাট্যদলের প্রযোজনায় ‘ছেঁড়া তার’ নাটকে অভিনয় করেন তিনি। তৃপ্তি মিত্রের পরিচালনায় ‘কিংবদন্তী’, হিমাংশু চট্টোপাধ্যায়ের পরিচালনায় বাদল সরকারের লেখা ‘ত্রিংশ শতাব্দী’ নাটকে মিসেস ইথার্নির চরিত্রে কিংবা পরে শম্ভু মিত্রের পরিচালনায় রবীন্দ্রনাথের ‘রাজা’ নাটকে সুরঙ্গমার চরিত্রেও অভিনয় করেছেন তিনি। ছোটবেলায় অভিনয় করেছিলেন রবীন্দ্রনাথ ঠাকুরের রচনা অবলম্বনে তৈরি ‘ডাকঘর’  নাটকে। অমলের চরিত্রে অভিনয় করে প্রশংসাও পান। পরবর্তীতে বাংলা নাট্য জগতের বিশিষ্ট নাম হয়ে ওঠেন তিনি, নিজের দলও গড়ে তোলেন।তাঁর তৈরি নাট্যদলের নাম ‘পঞ্চম বৈদিক’।

  • ১৯৮৩ সালের মাঝামাঝি সময়ে মঞ্চে এল নাথবতী অনাথবৎ। একক নাটক। মহাভারতের এক-একটি চরিত্র, এক-এক রকম স্বরক্ষেপণ, ভিন্ন ভিন্ন অঙ্গভঙ্গি , এক-এক রকম পদক্ষেপে মূর্ত হয়ে উঠতে লাগলেন শাঁওলী মিত্র। তাঁর মঞ্চে আয়ত্ত দক্ষতা সমগ্র দর্শক মহলকে বিমুগ্ধ করে দিয়েছিল, যেন সসাগরা পৃথিবীটাকে অযুত প্রশ্নেবিদ্ধ করছেন। এই নাটকে আমরা এক নতুন নাট্য গড়ন শুধু নয়,নাট্যভাবনার সম্ভাবনা চিহ্নিত করতে পারি। এক প্রতাবাদী নারীর সন্ধান পেলাম আমরা। তাই তিনি মঞ্চে কখনো যুধিষ্ঠির কখনো বা দ্রৌপদী হয়ে  স্বাভাবিক স্বতস্বূর্ততায় অভিনয় করে গেছেন। বিষয়ের সঙ্গে আঙ্গিকের এই পরীক্ষা সমগ্র বাংলা নাট্য দর্শককে চমকে দিয়েছে।  বাঁ হাতের তর্জনী ছুড়ে বলেন, ‘যুধিষ্ঠির’ বললেন এই কথা। ধম্মের  পুত্তুর যুধিষ্ঠির তখন আর কিছু বিচার করলেন না! গোটা সমাজের কাছে মহাভারতের এক নবরূপ অঙ্কন করেছেন। রাজসভায় যখন ভীষ্ম-দ্রোণ-কৃপ-বিদুররা চুপ করে বসে আছেন তখন কথক শাঁওলী যেন খেপে উঠলেন,
  • ‘ বাবুমশায়রা, এইরকম একটা কাল আসে পৃথিবীতে, যখন এইসব গুণীজনরা সব চুপ করে থাকে, আর যে অত্যাচারিত হয়, সে হয়েই যায়, হয়েই যায়, হয়েই যায়!’
  • সেই নির্মাণ দেখতে দেখতে পাঠক নিজের অজান্তেই পারি দেয় নাট্যকারের ভাবনার জগতে। এই নাট্যের মাধ্যমে শাঁওলী এক নতুন পথের সন্ধানে যাত্রা শুরু করলেন। এই অনুসন্ধান তার নিজেরি অন্তরে। দেশীয় যে নাট্য রীতির পুনরুদ্ধারের স্বপ্ন তার বাবা নাট্যকার শম্ভু মিত্র দেখেছিলেন,তার মূল সুরটি যেন স্পর্শ করেছিল তার কন্যার অন্তরে। তাই যে সন্ধান তার বাবা  , চাঁদ বণিক মাঝ রাস্তায় ছেড়ে দিয়ে পথের অনুসন্ধানে পথ হারিয়েছিলেন,তাকেই যেন পুনরুদ্ধরে  মগ্ন হয়ে উঠলেন নাট্যকার। যুগ যুগ ধরে চলে আসা পুরুষতান্ত্রিক নিপীড়নের বিরুদ্ধে এই পথ চলা। সেই জার্নিতে কখনও তাঁর সত্তার ভিতরে নৈঃশব্দ হাঁটু মুড়ে বসে থাকে,  কখনও এক অপার বিচ্ছিন্নতা। নিজেরই মুদ্রাদোষে কখনও হয়ে যান তিনি একা। তবু যাত্রা বন্ধ হয় নি।একার যে কী প্রচণ্ড বল হতে পারে, তা বোঝা যাচ্ছিল দিনে দিনে। নাটককে  আযূধ করে তিনি এগোতে থাকলেন। ১৯৯০ নিয়ে এলেন কথা অমৃতসমান। আধার সেই মহাভারত। তৈরি হচ্ছে প্রতিমহাভারত। একক অভিনয়।  
  • এই প্রবন্ধের মূল উদ্দেশ্য হল বিষয়ের চেয়েও নাট্য আঙ্গিক নিয়ে তিনি যে নতুন পথের সন্ধান দিলেন তার পুঙ্খানুপুঙ্খ আলোচনা। নাট্য সমালোচক সেলিম আল দীন এই নাট্য দেখে বর্ণনাত্মক অভিনয় রীতি বোঝাতে বলেছেন
  • “ বাংলা কথকতা ও পাঁচালি ধারায় সৃষ্ট অভিনয় রীতি। এতে অভিনেতা নাট্যস্থিত বর্ণনা সংলাপের রীতিতে উপস্থাপনা করে। এ সম্পর্কে প্রদত্ত যুক্তি এই যে, বিশেষ চরিত্রের মুখের কথাই যে সংলাপ তা নয় বরং মঞ্চে চরিত্র বা উপস্থাপনাকারী যা বলবে তাই সংলাপ। সংলাপ ও বর্ণনার দ্বৈত গড়ন অদ্বৈতরূপে মঞ্চে উপস্থাপিত হয় বলে বর্ণনাত্মক অভিনয় রীতি দ্বৈতাদ্বৈতাবাদী শিল্পতত্বের পরিপোষক নাট্যদর্শন রূপে বিবেচ্য।”
  • বিশ্বনাট্য ইতিহাসে বর্ণনাত্মক নাট্য ধারা আধুনিক কালের নাট্য নন্দন্তত্বের একটি পরিভাষা রূপে উদ্ভূত হয়েছে। ইংরাজী ন্যারেটিভ শব্দটির সঙ্গে একে অভিন্ন মনে করা যেতে পারে তবে গভীর পর্যবেক্ষণে এই দুইয়ের পার্থক্য অনুধাবন করা সম্ভব। ইংরাজী ন্যারেটিভ শব্দের অর্থ হল বর্ণনাত্মক, ঘটনার বিবরণ মূলক বা কোন ঘটনার ধারাবাহিক বিবরণ। অন্যদিকে বাংলা বর্ণনাত্মক শব্দটির অর্থ হল এমন একটি শিল্পবস্তুর অভিধা যা একি সঙ্গে শ্রবণ সুখকর শিল্পিত বিবরণ, নাট্যগুণ সম্পন্ন সংলাপ,বিচিত্র মুদ্রার নৃত্য এবং বিভিন্ন রাগ রাগিনীর আশ্রয়ে রচিত সঙ্গীত সম্পন্ন আদি-মধ্য অন্ত্য সমন্বিত একটি শিল্পরূপ।এদিক থেকে বিচার করলে বলা যায় যে বাংলা বর্ণনাত্মক রীতির নাট্যের সঙ্গে ইউরোপীয় ওড এবং ব্যালাডের সমগোত্রীয়।
  • নাট্যকার শাঁওলী মিত্র তার পারিবারিক শিক্ষা ও নাট্যচর্চার ফলে এই সমস্যাকে অনুধাবন করতে পেরেছিলেন। তাঁর আগেই তার বাবা শম্ভুমিত্র চাঁদ বণিকের পালা নাটকে এই ইউরোপীয় নাট্য ধারণা থেকে সরে এসে দেশীও নাট্যধারাকে প্রতিষ্ঠা করতে চেয়েছিলেন। বিদেশি শিল্প সাহিত্যের অনুসরণ থেকে সরে এসে দেশীয় চিন্তা চেতন নিয়ে নাট্যসম্ভাবনাকে আবিষ্কার করাই ছিল তখন নাট্যকারের প্রধান বিচার্য বিষয়। এই চেতনার স্বীকৃতি স্বরূপ আমরা নাথবতী অনাথবৎ  নাটকটিকে বিচার করতে পারি।
  • বাংলা নাটককে তিনি ঔপনিবেশিকতার কবল থেকে মুক্ত করতে চেয়েছিলেন । বাংলা নাট্যমঞ্চে অনুবাদনির্ভর পশ্চিম অনুকৃত নাট্যচর্চার যে রীতি গড়ে ওঠেছিল সেখানে তিনি প্রতিস্থাপন করেন বাংলা ভাষার মৌলিক নাটককে।প্রসেনিয়াম নাট্য মঞ্চ ধারণার বিপরীতে তিনি লৌকিক জীবনের সংগ্রামময় ইতিহাসকে তুলে ধরতে চেয়েছিলেন তার নাটকে। শুধুমাত্র বিষয়গত নতুনত্ব নয়, আঙ্গিকগত নতুনত্ব , তার নাটক  এক দেশিয় মঞ্চ ধারণাকে উপস্থাপন করে ।  তার নাটকের ভাষা বাংলা। বাঙালির আচার আচরণ, দৈনন্দিন জীবনযাত্রা তার ঐতিহাসিক সংগ্রাম-সিদ্ধি, অর্থনৈতিক অবস্থা, উৎপাদন ও বন্টন ব্যবস্থা, পুরান রূপকথা, সংস্কার বিশ্বাস, কৃত্যাদি, প্রথা-উৎসব,  খাদ্যাভ্যাস, সামাজিক রীতি, নৈতিকতা, উৎসব-ক্রীড়াদি ইত্যাদি বিষয়কেন্দ্রিক পরিবেশনযোগ্য রচনা বাংলা নাটক এবং একই সঙ্গে তা  বাঙালিরও নাটক। এই বিষয় বৈচিত্র্য ও মৌলিকতাই শাঁওলী মিত্রের স্বাতন্ত্র্য।  
  • তবলাতরঙ্গ বেজে উঠছে। বাজছে মন্দিরা, মৃদঙ্গ। মঞ্চে সার বেঁধে বসা জুড়ির দলের দিকে মুখটি ফিরে একটা কালো কাঠের জলচৌকির ওপরে দুলছে একটা লম্বা বেণী। একটি আলতারাঙা পায়ের নূপুর তাল রাখছে ছন্দে। জুড়ির দল গান ধরেছে, ‘‘কিছু কথা বলতে চায় ওরে মন…।’’
  • গানের শেষে কথক ঠাকরুণ পেন্নাম করে বলে উঠলেন ‘‘এক অভাগিনী মেয়ের কথা! রানি, কিন্তু রানি নয়!’’
  • ‘নাথবতী অনাথবৎ’- এই বঙ্গের ইতিহাসে পেশাদার রঙ্গালয়ের ইতিহাসে এই নাটক সম্পূর্ণ এক নবদিগন্তের সন্ধান দিয়েছিল যা ভবিষ্যৎ প্রজন্মের নাট্য কর্মীদের কাছে পথপ্রদর্শক রূপে চিহ্নিত করা যায়।
  • মঞ্চে সার বেঁধে বসা জুড়ির দলের দিকে মুখটি ফিরে একটা কালো কাঠের জলচৌকির ওপরে দুলছে একটা লম্বা বেণী। মঞ্চ সজ্জায় যেমন দেখা যায় প্রসেনিয়াম মঞ্চ ধারণা থেকে বেড়িয়ে আসার প্রচেষ্টা তেমনি রবীন্দ্রনাথের রঙ্গমঞ্চ প্রবন্ধটিরও গভীর প্রভাব লক্ষ্য করা যায়।
  • তাই তিনি প্রসেনিয়াম নাট্য মঞ্চের ধারণা থেকে সরে এসে নাটকটিকে প্রথমার্ধ ও দ্বিতীয়ার্ধে সাজিয়েছেন। প্রথমেই জানিয়ে দিয়েছেন যে নাটকটি ‘ কথকতার ভঙ্গিতে ’লেখা হয়েছে। জুড়ির গান দিয়ে আখ্যান বর্ণনা শুরু। ঠিক যেন চাঁদ বণিকের পালার অনুসরণে রচিত এই অংশটি।
  • এরপর শুরু হয় কাহিনি বর্ণনার পালা। কখনো দ্রৌপদী কখনো বা দুর্যোধন, যেমন স্বাভাবিক তার কন্ঠস্বর তেমনি দৃপ্ত তার প্রতিবাদ। প্রত্যেকটি অন্যায় ঘটনা বর্ণনার সময় তীক্ষ্ণ প্রতিবাদে ক্ষত বিক্ষত করে তুলেছেন আজন্ম লালিত চিন্তা ভাবনাকে। পুরাণে বর্ণিত যে কাহিনিকে আমরা স্বাভাবিক অভ্যাসে দীর্ঘ কাল ধরে মেনে নিয়েছি , তাকেই প্রশ্ন করেছেন নাট্যকার। যে ভাবনা নিয়ে তার নাটক লেখা সেই তীব্র প্রতিবাদই সোচ্চার হয়েছে তার অভিনয়ের মাধ্যমে।  
  • গঠন গত ভাবনায় প্রশ্ন করা যায় যে এই বিষয়টিকে উপস্থাপন করার জন্য এই বর্ণনামূলক নাট্যরীতিকে গ্রহণ করার সার্থকতা কোথায়? যেহেতু এই কাহিনি মধ্যযুগের ইতিহাসের অংশ তাই কি এই আঙ্গিক! গভীরভাবে অনুধাবন করলে বোঝা যায় যে শুধুমাত্র এইটুকু বাহ্যিক কারণে এই আঙ্গিককে তিনি বরণ করেন নি। একজন নারী, অর্থাৎ শুধু যদি তিনি দ্রোপদীর ভাষ্যে সমগ্র কাহিনিটি বর্ণনা করতেন তাহলে এটিকে এক নারীর প্রতিবাদ হিসাবে চিহ্নিত করা  হত।
  • সমগ্র পুরুষতান্ত্রিক সমাজের যে অন্যায় অত্যাচারের কাহিনি এখানে তিনি বর্ণনা করেছেন তা কোন একটি চরিত্রের দৃষ্টিতে সীমাবদ্ধ রাখলে এই নাট্যের সম্ভাবনা সমূলে নষ্ট হত। তাই নাট্যকার কোন একক চরিত্রকে বেছে নেন নি, একজন কথকের ভাষ্যে সমগ্র নাট্যটিকে উপস্থাপন করেছেন।
  • এরপর কথক দ্রৌপদীর ভাষ্যে সমগ্র মহাভারতের নবরূপায়ণ ঘটালেন। পঞ্চ পান্ডবের দুর্ভোগ ও দ্রোপদীর জীবন যন্ত্রণার কেন্দ্রে যে যুধিষ্ঠির ,যাকে সমগ্র মানব কূলের কাছে মহাপন্ডিত ও প্রাজ্ঞ হিসাবে ভূষিত করা হয় যুগ যুগ ধরে,একথা কথক স্পষ্ট ভাষায় জানিয়ে দেন। চিরাচরিত মহাভারতের কাহিনি ব্যাখ্যা নয়, মহাভারতের নতুন পাঠ তুলে ধরাই এই নাট্যের মুখ্য উদ্দেশ্য।
  • তাই প্রথাগত মঞ্চ ধারণা নয়,এই নতুন পাঠকে ধারণ করার জন্য প্রয়োজন দেশীয় মঞ্চ ধারণার কাছে ফিরে যাওয়া। তাই প্রসেনিয়াম মঞ্চ,চরিত্রের মুখে সংলাপ,দৃশ্যের আতিশয্যকে ত্যাগ করে নাট্যকার গঠন করলেন বর্ণনাধর্মী পালাগানের আসর। এখানে সামনে উপস্থিত দর্শকদের কথক শ্রোতা রূপে সম্বোধন করছেন এবং নিজস্ব পাঠকে দর্শকের মননের সঙ্গে মিলিয়ে নিয়েছেন।
  • দর্শকের মধ্যে জাগিয়ে তুলতে চাইছেন সেই সব আদি প্রশ্ন যা প্রাত্যহিকতার অভ্যাসে চাপা পরে গেছে। সমাজ পরিবর্তন তো শুধু মাত্র যুদ্ধ করে হয় না,মানুষ যখন নিজের চারপাশকে আরও ভালোভাবে তলিয়ে বুঝতে পারবে,প্রশ্ন করবে,অন্যায়ের বিরুদ্ধে সোচ্চার হবে তাদের চেতনা তখনি প্রকৃত রূপে মানব সভ্যতা অন্ধকারের থেকে আলোর পথের দিশা খুঁজে পাবে। এই কাজে নাট্যকার শাঁওলী মিত্র যে সম্পুর্ণ রূপে সফল তা এই নাটকটির সাফল্য ও দর্শকমহলে জনপ্রিয়তা থেকেই সুস্পষ্ট।

Search for Exact Rabbit Hole: What is the prospect for interdisciplinary

The challenge the current academic space faces are the fact that our post-millennials are virtually wanderers. The access to unlimited information, both visual and textual, has made this generation well equipped with knowledge. Because of the globalization, social media, and urbanization the exposure for a student has widened unimaginably. But studies show this also has created a very self-involved generation. In 2012 Wellesley High School Graduation speech “You are not Special” David McCullough said “Do not get the idea you are anything special because you are not…. even if you are one in a million on a planet of 6.8 billion that means there are seven thousand people just like you.”

How can a student inculcate this realization of one being part of a larger world, the need for empathy towards others and understanding other’s perspectives etc. How much our educational system can contribute to creating this awareness in a student. As Maya Angelou pointed out, “any individual is free only when one realizes that one “belongs to every place, not a place at all.” The education system has reached an exhausting level that the compartmentalization or the specializations have created this vacuum for being unaware of any other forms of knowledge. I guess this tendency also has contributed to the creation of a self-involved generation. In this context remembering C. P. Snow’s iconic lecture of 1959 “Two Cultures” would be helpful. He deliberated on the ‘dangerous cultural dichotomy;’ means the knowledge system’s divergence as science and humanities. He said,

A good many times I have been presented at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice, I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: ‘Have you ever read a work of Shakespeare’s?

But interestingly the Pandemic created space for thoughts like we might lose everything we have held on to. The emergency raised to create a capable society who has the energy to love and transform oneself and others without fear. The time asked for more socially committed scientists and doctors. The question on ethics, justice and democratic involvements became the point of discussions. The need to inculcate the courage to post-millennials to live with fundamental ideas like fear of loss became a challenge for even a primary teacher.

The urgency has arrived to channelize this endless information into a multitude of subject knowledge to a student. For this it is necessary to reimagine the stubborn walls of knowledge culture. The proposal for ‘fourth culture of knowledge’ as Jonah Lehrer puts it, can create more individuals who are comfortable in being part of social collective. The latter says “We now know enough to know that we will never know everything. Therefore, we need art: it teaches us how to live with mystery.” Unlike on the internet, the young generation should be able to freely embrace the ability to remain uncertain, doubtful, and put their actual experience in historical, political, and social context. These are the skills that can transcend the traditional outlook of a subject. Are we all equipped to adjust with this shape shifting? Shouldn’t we be trained to face contradictions and diverse individual and collective understandings?

This also brought a larger discussion on the need for bridging the sciences and humanities. I am reminded of the powerful passage in Frankenstein, where Victor meets Waldman the scientist. The latter advices “If your wish is to become really a man of science, and not merely a petty experimentalist, I should advice you to apply to every branch of natural sciences.” There is this need to become an interdisciplinarian and understand the extraordinary scope of this “cross-pollination” of the disciplines.

In a classroom when a student asks the question; ‘Is this text going to be important for the examination? Or regarding the texts we are reading now can you tell me a few areas from where the questions come? Or the ultimate question of why should we read if it is not covered in examination? The educators must not be afraid to reform these thought patterns. Both of us need to be comfortable being uncomfortable to reimagining the definition of skill to be acquired.

Debunking of scopes in Number Theory


Number theory has always occupied the significant historical importance from ancient times. It is an integral part of Mathematics not only from ancient times but also in modern times. It has a huge impact in human civilization for its various applicable contributions. It has its origin in ancient India. From ancient times to till the present modern days various mathematicians have given their contributions towards developing this subject for mankind. In this modern arena of scientific development we are in a new beginning after the pandemic caused by the deadly COVID-19. One can say what the helpful impact we can get from Number theory now a days. Rather we can say where and why we can apply Number theory for developing the new era. We have tried to expose some area which have the interest related to Number theory and its applications.

Brief History:  

Many great philosophers had contributed various aspects of number theory. Among those was Pythagoras (569 − 500 B.C). His famous Pythagorean theorem led many mathematicians to study squares and sum of squares. He has given us notable Pythagorean triplets. After 200 years, another Greek mathematician Euclid (350 B.C.) drew attention to the prime numbers. Few more studies on natural numbers had been done by Eratosthenes(276B.C.-196B.C.), Nicomachus(C.100) and Diophantus(C.250). Many more mathematicians has contributed in recent times also. But the most significant contributions comes in the field of Cryptography and prime numbers development.

Significant Applications:

There are significant applications of number theory in various fields which has an important impact in real world. Linear Diophantine equation is one of the important topic of number theory which has various applications in modern day life. This equation is of the form  where  ,   are positive integers. This equation has a solution if  divides. If we have n numbers of variables then we can solve the linear Diophantine equation by applying the process for two variables n times. If the Diophantine equation has n unknowns then it is of the form  where   are the variables.  This we can use in balancing chemical equations, determination of molecular formula and also for finding structure of viruses. In chemical equation if we consider an equation  then after balancing by Diophantine equation we can get . Here we can get two integers 2 and 1 for hydrogen and oxygen resulting 2 for water.

Another significant application in the field of number theory is encryption and decryption of messages. Here we use prime number concept and congruence relation together simultaneously.

The significance of coding and decoding increases time to time. In defence, the secret communication plays a key role. Now a days the privacy of data is needed for bank and any other financial transactions. In twenty first century, communications through social media creates a huge impact in our daily life. Essence of secured and encrypted medium is a vital issue for these types of communications. Hence there is a great deal of interest in the techniques of making messages unintelligible to everyone except the intended receiver. Many mathematicians and computer scientists have given their important contribution towards the growth of the discipline devoted to secrecy systems called cryptography. Cryptography is the part of cryptology that deals with design and application of secrecy system and cryptoanalysis is aimed at breaking these systems. Actually the word cryptography is thecombination of two Greek words ‘Krypto’means ‘hidden’and ‘Graphein’means ‘to write’.  In simple words, a message that is to be altered into a secret form is called plaintext while after transformation to a secret form, these messages is said to be ciphertext. The process of converting a plaintext to a ciphertext is called encrypting and the reverse process

of converting from ciphertext to plaintext is said to be decrypting or deciphering. A cipher is a method for altering a plaintext message to ciphertext by changing the letters of plaintext using a transformation. Various concepts of number theory are being applied in the process of encryption and decryption. The most widely used public key cipher known as RSA, is the. In the year 1978, RSA was proposed by Ronald Rivest, Adi Shamir and Leonard Adleman. This public key cipher is based on modular exponentiation.      

Impact after COVID-19:  

 We know that the deadly Covid-19 has affected our life in last two three years very badly. People are getting affected by this virus and the rate of mortality is persisting its significant figure in each wave after wave. Although the biologist, virologist, doctors and scientists are continuously giving their effort for inventing various medicines and vaccines all over the world but we are still very far from eradicating this virus from our society like before. In this process of inventing those vaccines they are using few mathematical calculation by means of number theory.

Again this critical scenario lead us to another difficult part of our society which is social distancing. This social distancing leads us to cashless and online transactions in various places. Now we can see many online payment platform in many shops and digital shopping is fully standing upon this online transactions. This type of transactions are touch free to others and it helps us to maintain social distancing up to some limit. But the main background of this type of transaction is security. The process of encryption and decryption assured us for this type of security. The process of encryption and decryption totally depends on cryptography which is another useful and impactful application of number theory.

Here we can transfer plain text to cipher text and vice versa. This aspect of number theory have huge impact in our society.

Although it is quit impossible to illustrate those aspects of number theory very briefly but from this above small discussion reader can understand the usefulness and significance of studying number theory in their course outline. It is also an interdisciplinary area of study which helps a mathematics student and computer science student. Now a days advance number theory and cryptography is in the course curriculum of various academic institutes. But to study those subjects a student should have a clear concept of some basic topics of mathematics like divisibility, greatest common divisor and prime number etc. Those concepts are very much clear for the students from very beginning of their study.


The most conclusive part of this blog for the reader is to understand the concept of number theory with their uses and to make themselves interested in studying number theory.

Mathematics in Operations Research and its Career Prospects

Operations research is an experimental and applied science devoted to observing, understanding, and predicting the behaviour of purposeful man-machine systems; and operations-research workers are actively engaged in applying this knowledge to practical problems in business, government, and society. – OR Society of America

Source of figure:

Most of the students in our education system might wonder whether they will ever use the mathematics which they learn from the studied courses. Students frequently asked a core question, such as, is any of the analysis, algebra, calculus, combinatorics, math programming, etc. really going to be of value in our daily life?

One exciting area of applied mathematics called Operations Research (OR) may give the answer of the above question. OR integrates the knowledge of numerous disciplines, like mathematics, statistics, computer science, engineering, economics, and social sciences to solve real-world problems. The notion of OR is applied from inventory to manufacturing; finance to marketing; routing to queuing; distribution to scheduling; data storage management to service measurement and reliability to artificial intelligence; agriculture to defence and among others using innovative and mathematical theories (analysis, algebra, calculus, probability, etc).

OR can be defined as the decision-making science. It is also known as Operational Research or Management Science or Industrial Engineering. There is no general process in OR to solve all the mathematical models related to real-world problems. One of the most prominent methods is linear programming which is useful to design a model with linear objective function and constraints. The techniques for solving linear programming problem (LPP) was developed by George Dantzig in the early 1950s and this is led to increasing interest of OR applications in business.

More than Mathematics:

Since the OR models are mathematical nature, people think that an OR study is always rooted in mathematical observations. But an OR technique should not be biased to start with a specific mathematical model before its proper justification of use (H.A.Taha, Operations research; an introduction, Pearson Education).  For an example, since linear programming is a successful process, people tend to use it as the tool of choice for modelling any kind of situations. Such an approach leads to mathematical model which may be take away from real situation. Thus, it is imperative that we first analyse the available data using simple processes whenever possible (e.g., aggregation, histograms, charts, etc.). Actually, most of the cases solutions are rooted in people but not in technology. Consequently, any solution that does not consider human behaviour may not be an appropriate solution.

OR with software library: There are numerous commercial software packages to solve the OR models. A few examples of such software are LINGO, AMPL, CPLEX Optimization Studio, MPL Modeling System, Gurobi. NEOS, COIN-OR, Matlab, R, Mathematica and Python, etc.

Scope of OR: OR has wide range applications in industry, government sectors, business hubs and many other organisations. Some important fields are:

  • In industry-manufacturing (production planning, assembly line, inventory control, quality control), production management (location and size of warehouse, retails outlet, logistics, transportation problem), airline industry, health-care systems, telecommunications, etc.
  • In Agriculture– Farm economics (optimal allocations of crop production, efficient production pattern), farm management (allocations of limited resources like as labour, water supply, working capital, seeds, etc).
  • In Defence-Selection of weapon system against enemy, ensuring minimum use of aviation gasoline, optimal strategy to win the battle.
  • In Marketing-Selection of product-mix, export planning, advertising and media selection, travelling salesman, sales effort allocation and assignment.
  • In Finance and accounting– Investment and portfolio management, public accounting, capital budgeting, financial planning
  • In personnel management– allocation of optimal manpower, determination of equitable salaries, skill development and retention.
  • In Government-Urban and housing problems, military, energy, economic planning, utilization of natural resources.

Job prospects: There are plenty of jobs after completion of specific programme with OR. Few of them are

  • Operations Research Analyst
  • Project Manager
  • Teaching Assistant
  • Research Assistant
  • Consultant
  • Software Engineer
  • Security Review Operations Analyst
  • Production manager
  • Optimal designer
  • Controller of network routing, transportation

Covid-19 impact:

 From the last two years, Covid-19 pandemic has disrupted all our lives, causing havoc to our health-care systems, education sectors, industries and especially economical systems. As with the early days of OR, presently multi-disciplinary and multi-locational teams of OR scientists have responded to the challenge, developing new models and methods for forecasting and tracing the spread of the epidemic, for vaccine allocation and distribution, etc. as part of the global effort to control the pandemic. (Janny Leung, IFORS News, Vol 17, No. 1, 2022).

      Recently, Bueno et al. (Luís Felipe Bueno, Antonio Augusto Chaves , Luiz Leduino Salles-Neto, Francisco Nogueira Calmon Sobral, Horacio Hideki Yanasse, IFORS News, Vol 17, No. 1, 2022) developed a web app for helping managements to plan classrooms considering social distancing by using  mixed-integer and nonlinear optimization approaches.

Why should be in course curriculum:

OR successfully provides a systematic and scientific approach to all kinds of service operations, defence, manufacturing, government. It is a splendid area for under graduate and post graduate students of mathematics to use their knowledge and skills to solve complex real-world problems in creative ways.  It has an impact on them to take critical decisions. Numerous companies in industry require OR analysts to apply mathematical techniques to a wide range of challenging questions in the said domain.

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