Every schoolchild learns that mathematics is a skill that can make life a lot easier. We understand physics, economics, and other subjects better with mathematics. However, we don't often consider its role in defining human characteristics. I didn't, until I came across a news article that proposed the formula:
real talent = ability × hard work + consistency.
The equation suggests that there could be really talented people who work less but are rewarded more, provided their ability is high and they maintain consistency. On the other hand, if you're less endowed with ability, then you need only maximize hard work to compensate for the lower ability factor. To succeed, you must practice regularly.
Let's revise the above equation slightly, to produce a relationship that seems more correct to me:
real talent = ability(hard work) + consistency.
You might have noticed that I bolded 'real talent,' 'hard work,' and 'consistency.' The idea is not to emphasize them more than the other factors, but to be mathematically correct. In my world of science (and mathematics), such quantities are vectors. They connote the idea that one needs to do hard work and be consistent in a profitable direction.

There is no guarantee that we will be rewarded for hard work. We may even have to pay a price if we consistently repeat mistakes. We must ensure that we are on the right track. In other words, talent doesn't matter a lot. Rather, what matters is that we use our talents in the right direction, lest they be wasted.
Now let's tinker with the above equation and extract more information by taking its time derivative, which gives:
d(real talent)/dt = ability × d(hard work)/dt,
assuming 'ability' and 'consistency' to be constants. The assumptions are valid: Consistency itself means constancy, and innate ability evolves slowly. Taking the time derivative implies that if we want to maximize talent, then we need to work not only hard but also relentlessly.
Let's take another mathematical aspect of this equation. If we want to find the solution of the differential equation, then we need to know the boundary conditions. Differentiation is easier than integration. Could that be the case in life, too?
Dividing (differentiating) the members of a group is a lot easier than unifying (integrating) them. Even so, wherever we work and live, we should keep in mind that collaborating in a group is of utmost importance in today's research environment. By doing so, we maximize the quality of research, and minimize risks, such as conflicting priorities.
You, too, may have experienced difficulty with integration. You might even have grappled with integrating complex functions, where you needed to find a singularity and integrate around it. I find that life is the same. Sometimes, when challenges arise in integrating a group, then unfortunately the solution is to find the problematic element (singularity) and throw it out. Though a potentially difficult or even controversial action, there is no point in keeping that element on at the cost of an integrated system.
Another important factor in research is time. If, for instance, someone else beats you to publication on the topic you've been working on, then your research will be perceived as less important throughout your career. In other words, we must understand the value of time. If time = life, which in one sense is literally true, then doesn't wasting your time mean wasting your life?
Arvind Singh conducts research in biogeochemistry at GEOMAR Helmholtz Centre for Ocean Research in Kiel, Germany.