We are living in an exciting era for highly interdisciplinary knowledge explosion. I would further state that this is a great time to be alive for all areas of discovery – physical, biological and social sciences; engineering, technology, humanities, arts and more. Mathematics, all its allied forms and, more importantly mathematical-thinking, are the center of it. The ongoing global pandemic COVID-19, with all the misery notwithstanding, offers a visceral example. So does the problem of climate change.
I want to posit three rules of our times not just in the engagement of pushing the boundaries of knowledge but also to function, thrive and enjoy all spheres of natural and anthropogenic world. Also, I use the COVID-19 as an example to highlight this.
• All exciting and interesting problems are at the intersection of traditional areas.
• Interdisciplinary thinking is imperative and not a luxury
• Mathematics and mathematical thinking is at the core of everything
Ancient world has seen numerous pandemics that has wiped large portions of human race.
Medical professionals were the first line of defense to take care of the afflicted, which
they still are now. But, they are also the talent pool to understand the pandemic and devise
cures. Several medical advances – understanding and cures, have followed such global
outbreaks (Penicillin, vaccines for TB, Measles, Small Pox etc.). This meant expertise in
core areas of biology and human physiology.
Let us look at this pandemic, COVID-19. In fact, we can look at SARS, H1N1, MERS more recently EBOLA, which are predecessors to this in the past two decades. The approach with these modern outbreaks is starkly different from those of the ancient world, illustrating the interdisciplinary research, described below.
• Genetic decoding of the virus, resulting in its unique biological signature. (Genome
discovery (DNA/RNA) has completely revolutionalized our approach) – Biology
• Then a massive search/comparison of the genome data base of existing viruses and their vulnerabilities. This helps to place the current virus in the context of our knowledge. This is how it was determined that COVID-19 is of the CORONA virus family which contains our seasonal flu viruses – hence, the flu-like symptoms. This requires knowledge of Computer and Mathematical Algorithms to do the searching efficiently and fast. Of course, overlaying this is the computer programming and data base skills to enable this.
• With the type and vulnerabilities identified (more are being identified) – mitigation
measures are devised quickly. Such as, use of soap to kill the virus, social distancing
(from the nature of virus) etc.
• Of course, clinical observations and data continue to come in – population that are impacted, how they are impacted (asymptomatic, mild, severe), medical needs (ventilators for severely impacted patients) etc. The data is analyzed using Mathematical Statistics and Probability Techniques to obtain risk estimates, based on which decision are made by policy makers.
• The above observational and analytical information is obtained in short order across the globe and shared instantly, so that societies can devise combating strategies which in turn can be shared and refined.
• Another important tool is contact tracking. Modern technology – cell phones and Machine Learning techniques. This involves collecting large quantities of data in real time for analysis using what are called machine learning techniques – which are nothing but mathematical statistics and probability ideas applied on large data sets.
• The mathematical and statistical concepts underpinning this have long been developed for decades. Since computational power was limited, most of these concepts and methods could not be translated into real-life applications. Bayesian analysis, Neural Networks, Trees, Multivariate analysis techniques – trees, clustering etc. – all have firm rooting in mathematical statistics.
• The ability to model and trace contacts requires knowledge of Algorithms, Data analysis, Visualization and programming.
Disease Modeling in Space and Time
• Policy makers have to make consequential decisions about locking down civic and economic
life to combat the spread of the virus. To enable such decisions efficiently, policy makers
need to know the extent and temporal evolution of the spread.
• Disease Models are the mainstay for this. These models use differential equations to model the space-time process. Which requires knowledge of Applied Mathematics, Numerical Methods and Computational Techniques
• The models have uncertainties in their parameters and projections, understanding of which require use of Probabilistic concepts and decision making under uncertainty.
Treatment / Vaccine
• With the genetic of sequence of the virus shared with researchers across the globe, a
modern approach is to search the historical data base of viruses and vaccinations to
identify potential vaccination strategies for this virus – a la finding optimal solution
from the multi-dimensional space to optimize on set of objective functions (multi objective
• The identified subset of ‘solutions’ as then explored biologically for their efficacy, manufacturing ability etc.
• The ability to zoom in on a promising set of alternatives for vaccines makes this process much faster, compared to earlier times when it would take years if not decades.
• Again, this uses ideas of Optimization and mathematical/statistical methods mentioned above.
• Similar strategies are employed in identifying promising treatment strategies
Lessons for Career Selection
• The running thread in an effective response to COVID-19 is a robust collaboration between –
Biologists, Mathematicians and Statisticians, Computer Scientists and of course,
• Mathematical and allied concepts – probability/statistics, applied mathematics, computer science (algorithms, programming) – are crucial for conceptualizing, understanding and advancing knowledge. More importantly, mathematical thinking enables to represent abstract ideas of the biological process in modeling framework, which helps bring to bear computational and mathematical power in solving.
• While domain expertise is still important, however, even to make fundamental advances in individual domains, knowledge of mathematics and allied topics are increasingly becoming critical.
• At the B.S. level get into a program that provides a good foundation in – Applied
Mathematics, Probability / Statistics, Physics, Biology and good programming skills (does
not matter what language, as long as you can developing the logical thinking skills that is
• In India a B.Sc. in a top college + M.Sc. (for you need 4 years of college to get these skills).
• Of course, it is hard to find top notch programs that offer this in India. The next best option is
to join in a good engineering program. My preference would be Mechanical Engg. and Civil Engineering (these two are highly flexible compared to others), combine these with good electives, this will give an good foundation in all of the above topics.
Electrical/Chemical/Computer Sc. Tends to be narrow and at this the B.S level I do not prefer specializing. My strong recommendation is be like a spunge and absorb everything.
It is much easier to move into any field later.
• Civil Engg. – exposes students to Environmental Engg. (along with the obvious – structural engineering, foundation, water etc.) – which these days covers microbiology, genetic engg. chemistry. It turns out all the methods used in human biology/medicine are also used in tracking pathogens in water – which are crucial for water quality and public health.
• Mech. Engg. – these days exposes students to biomechanics (using mech. Engg. to develop tools for medicine), bio medical, air pollution – along with all the traditional things (Internal Combustion Engine, Solid and fluid mechanics, Vibrations etc.).
• Either of these tracks – a solid B.Sc + M.Sc. or a robust broad based Engg. complimented with good elective courses, will set one up for an exciting and fulfilling career – industry, research or academia.