What Constitutes Research in the Field of Computer Science?

Often, the notion of research in computer science is confined to the belief that it's all about improving the currently existing technology. However, the essence of research goes far beyond these boundaries. It involves the application of multiple disciplines such as mathematics, physics, philosophy, and even daily life to computer programming, with the ultimate goal of developing solutions that can benefit society. Essentially, it is an innovation, aiming to solve real-world problems.

Identifying Problems to Solve or Improving Existing Solutions

One of the key aspects of doctoral research in computer science is the identification of problems that are either not fully understood or have not been properly addressed. My own experience with my PhD research aligns with this. Under the guidance of my advisor, I focused on topics that were not well comprehended, even from his perspective. This involved a deep dive into pertinent papers and their references, deriving insights from the forest of academic literature available in our university's extensive academic paper databases.

Exploring the Unexplored

One of the fascinating discoveries in research is uncovering things that are known to work but for which the exact reasons remain a mystery. For instance, there are methods that work, but the underlying mechanisms are unclear. In the modern age, a vital aspect of research is recapitulation, a process where you follow a trail of papers backwards through their references to build up a historical context of a particular method. This allows you to see the choices made by earlier mathematicians and scientists based on what was feasible during their time, contrasted with what can be done with the computational power of modern desktop computers. This process can reveal new choices and pathways that were previously overlooked.

Leveraging Random Linear Algebra

A prime example of such an innovation is the field of Random Linear Algebra. This area focuses on using statistical methods to approximate solutions to complex problems, such as factoring matrices with billions of rows and columns. Such matrices are intractable when using traditional methods, but through randomization, we can approximate solutions with high certainty and useful results. This is a significant breakthrough because it addresses a problem that could not be effectively solved with previous computational methods due to the sheer scale of the matrices involved.

For my PhD, I identified and solved three previously unsolved problems, contributing to the growing body of knowledge in this field. My thesis included four papers, which addressed these problems, with two of them warranting their own detailed treatment. This led to significant advancements in the field, ultimately leading to the awarding of my PhD.

The journey to identifying and solving these problems began with extensive reading and understanding. It's crucial to find unsolved problems in the cutting-edge of science where countless new discoveries are waiting to be made. Focusing on well-established topics should be avoided unless you are prepared to commit a substantial amount of time (3 to 6 weeks) to understand why they haven't been solved yet.

In conclusion, computer science research is a vibrant area of exploration, constantly seeking to innovate and solve real-world problems. By leveraging diverse disciplines and historical insights, researchers can uncover new methods and solutions that push the boundaries of what is possible.