Societal impact of research As someone who conducts research that is unlikely to be of any relevance to the common man, I would like a little perspective on the impact that pure research plays in society, and how I can, in some sense, feel better about my research contributions.
In a field such as pure mathematics, one can argue that most people are unlikely to understand, or even be interested in recent results. In my opinion, pure mathematicians are attracted to the unhindered joy of research and the challenges it brings, and this is a major factor in the field being active today. (For the record, I am not a pure mathematician.)
In contrast, research in fields such as medicine and environmental science seem to have a larger impact on the common man. A simple example would be the Covid-19 vaccines that will play a major role in bringing the world back to a semblance of normality. Even if it can be argued that today's mathematical results will shape the science and engineering of tomorrow, I continue to feel that these will not have as large an impact as medical research will continue to.
My question is simple: Though I am someone who conducts research motivated simply by the challenges it brings and the joy of achieving a solution, I do occasionally feel that I would like my research to have a larger impact on society (which it really does not). I would like to know if there are others that feel the same way, particularly from a field such as mathematics, and if so, how I can obtain a new perspective on this.
You need to think longer term. Decades, and perhaps centuries. Research done today may seem to have little immediate impact, and that is true. But over time, it contributes to the general knowledge that makes things possible. Think of any scientist from the past whose name is known today, even, say, Euclid. Some of what they did may have had some immediate effect, but much of it laid the groundwork for later advances.
In pure mathematics and theoretical physics, for example, an interesting question today may be vital in the future. Isaac Newton's calculus work was so unimportant that he put it in a drawer for years. Leibniz did &quot;interesting&quot; things in understanding real functions, but without their work, and what came after, much of engineering in the past 150 or so years would be impossible.
Think Mendel or Darwin. They studied and thought because certain questions were &quot;interesting&quot; to them. They laid the foundation of modern understanding and that led to &quot;useful&quot; things.
Note that Einstein's work took years to be accepted because the &quot;great minds&quot; of the day were focused on a different theory that turned out to have no basis - the aether.
Moreover, many of the advances of the &quot;great minds&quot; of science were only possible because of a general advancement in understanding, much of which was contributed by those whose names we no longer remember. The current state of understanding the world can be thought of as an advancing front with many contributors, some of whose contributions we remember specifically, but it is the front itself that makes them possible. All of us push against that frontier in our small, perhaps, ways.