Highly Cited Researchers Spotlight Series: YeolJe Cho

Please introduce your research field briefly.

I specialize in the field of nonlinear functional analysis. More specifically, my main research topics are fixed point problems, equilibrium problems, variational inequality problems, complementarity problems, optimization problems and other nonlinear problems. These problems are applied to some kinds of spaces such as fuzzy metric spaces and probabilistic metric spaces to show the existence of solutions to these problems. Optimization problems, in particular, are largely applied to other disciplinary areas including sociology, engineering, medicine and natural sciences.

Could you explain what made you choose to study the field and what you have accomplished so far?

When I was an undergraduate student in mathematics at Pusan National University in Korea about 46 years ago, I was greatly influenced by Prof. Jae Keol Park. Since then, I have studied hard mathematics for all my life. After I received my Ph.D. degree at Pusan National University in August, 1984, I began my postdoctoral research on Banach’s fixed-point theorem and geometry of Banach spaces at Saint Louis University in the USA, which provided the starting point for my lifelong studies in nonlinear functional analysis. In fact, Banach’s fixed-point theorem is especially attractive in the sense that it makes use of various approaches for this theorem. What it means is that this theorem can be studied in many different ways, including generalizations of the theorem, involving many kinds of applications in applied sciences and other areas.

Please, tell us how you overcame challenges during your studies.

One of the challenges was to exchange research outcomes with other researchers all over the world. Before the era of the internet began, I relied on letters to communicate with many researchers in other countries. At times, such correspondence took up to one month or more. To overcome these difficulties, I tried hard to organize “International Conferences on Nonlinear Functional Analysis and Applications” and invited many renowned scholars to the conference sites. I was able to advance my studies through discussions with them and by conducting joint studies based on new ideas and solutions. I also worked hard as an editor for at least 20 local and international journals to keep abreast of trends in academe.

The efforts that I made for research conferences were motivated by my academic philosophy, “Bulgwangbulgeup(不狂不及),” which means “To be a master, be crazy about what you do.” Mathematics requires steady efforts; if you stop studying it for some time, you lose your scholastic sensitivity or have your study results downgraded. As a researcher, I have concentrated on mathematical problems for almost all of my life. Consistency is important in this subject to moving forward, as well as keeping track of past research results. This is why I think it is crucial to engage in conference meetings and to contribute to academic journals, establishing the living archives for references.

Please, tell us about how our academic environment could be improved to promote academic advances.

I find it lamentable that, these days, many universities are not treating mathematics with due gravity. Of course, it is important to invest in more pragmatic fields of study that provide economic benefit. Note, however, that basic science is as important as applied sciences. Applied sciences can thrive only if we have a solid basis in fundamental sciences. Mathematics provides an important academic base for scientific advances, even national progress. Many Nobel Prize winners in Economics, Physics, and even Literature have studied mathematics as their major subject in college. In other words, mathematics provides the base for many other fields of study.

Please tell us about the activities you are currently engaged in.

As a Mathematics Ambassador for the Korean Mathematical Society (KMS), I often give lectures at elementary, middle, high schools and universities. My lecture is based on the theme “View the World through Mathematics”; it also deals with what beauty is, how the human brain functions, what makes your studies more efficient, how to solve mathematical problems and how mathematics can apply to your real life. Finally, I tell the young ones to have dreams.

In my opinion, mathematics is based on philosophical thinking. Philosophy and mathematics both aim to dig into human thinking as deep as possible. The only difference between the two areas is the subjectivity and objectivity of thinking: that is, objective thinking is valued in mathematics, whereas subjective thinking is more valued in philosophy. Deep mathematical thinking is expressed and understood through logic, creativity, classification and system, and its benefits can reach to liberal arts and social sciences.

Could you give some tips to younger researchers and scientists who have just started their journey?

The current generation can now easily access abundant information and resources on any topic including mathematics. Many studies are being conducted worldwide and it is important for any researcher who wants to be successful to keep abreast of current trends in the field of interest. At the same time, it is also crucial to focus on a single aim over a period of time to produce excellent results. Even though I may be regarded as a well-advanced researcher at the age of 65, I still feel attracted to mathematics; just like my lifelong teacher, Prof. Jae Keol Park, who is still engrossed in research as if he is on active duty. I would like to ask young scientists to share their ideas with other researchers across countries, diligently seeking new ideas and solutions together. Fresh ideas and new stimulation from your peers can encourage you to continue studying. My exchange with excellent researchers overseas allowed me to acquire many assets, which I could not have achieved alone. This continues to the present day: my companions and co-awardees for HCR honors this year — Honorary Prof. Young Bae Jun, Prof. Shin Min Kang and Dr. Sun Young Cho — keep me encouraged and energized by valuable collaborations.

See the 2016 Highly Cited Researchers