Welcome to my substack
by Eleftherios Gkioulekas, Ph.D.
This substack will host posts related to my research and teaching, as well as commentary. I will make the research and commentary posts freely available and limit some of the teaching-related posts to paid subscribers.
Short biographical note about me
I was raised in a small mining village, Stratonion, in Greece. My family then moved to Thessaloniki where I did my last six years of middle school and high school at the Anatolia College. I was inspired into a teaching career by the example of my high school Mathematics Teacher, Alexandros Pistofidis, and by independently studying all three volumes of "The Feynman Lectures on Physics" during the last four years of high school.
Mr. Pistofidis ignited my love for Mathematics by teaching algebra and geometry honestly at an advanced level, rather than infantilizing us with the pedagogical dumbed down gobbledygook peddled all around the world by American woke colleges of education. We learned Boolean logic and quantifiers as early as 10th grade, and got started with writing rigorous mathematical proofs in the context of Euclidean geometry as early as 9th grade. He wrote his own lecture notes and mathematics homework problems, and he taught us an interesting and innovative approach to the solution of radical equations that led me recently to publish two research papers in the area. Richard Feynman's lectures inspired my love for theoretical physics and my desire to pursue a university career doing research and teaching. Interestingly, one of my other inspirational teachers in High School, Aggelos Mastrogiannis, thought that I should become a biologist or a medical doctor. Mr. Mastrogiannis was also a carpenter, and one of the most memorable projects that we did in his extracurricular biology club was to build a big three-dimensional model of the double helix DNA molecule using pieces of wood and metal. I remember painting several of the pieces that represented the base pairs using different colors. It took us at least a year to put the whole thing together.
I started out my studies in the United States as an undergraduate student dreaming that I would become a theoretical physicist probing the mysteries of the universe. Then, I gravitated towards mathematics and scientific computing finishing with two senior projects in game theory and computational biology. In 1997, I earned my B.Sc. degree from the California Institute of Technology in Applied Mathematics.
During graduate school, I worked on theoretical fluid turbulence which involved applying mathematics that was originally created in the context of quantum field theory and particle physics into fluid dynamics. I ended up applying some of my results and insights in that area into a deeper understanding of questions that befuddled researchers working in atmospheric science concerning the energy spectrum of atmospheric turbulence. I worked under the advice and support of Dr. Ka Kit Tung, whose main area of research was atmospheric and climate science, but my true inspiration was the amazing work by two Israeli scientists from the Weizmann Institute of Science, Dr. Victor L'vov and Dr. Itamar Procaccia, who have done some groundbreaking but underappreciated theoretical work on the universal features of incompressible fluid turbulence. I completed my graduate studies in 2006 with a PhD in Applied Mathematics from the University of Washington.
As academic faculty, at the University of Central Florida, the University of Texas Pan American, and now at the University of Texas Rio Grande Valley, I published an actual theoretical physics paper [1] on a conjecture by Dr. Friedwardt Winterberg, one of the few Ph.D. students of Werner Heisenberg, on quantum entanglement, in addition to work on two-dimensional and three-dimensional incompressible fluid turbulence and atmospheric turbulence models. My most important work on fluid turbulence research to date, in my opinion, is my paper on the elimination of sweeping interactions from theories of hydrodynamic turbulence [2] and my paper on multilocality [3]. I also broadened my research interests to include curriculum innovations in mathematics education. My personal favorites are my two papers on radical equations [4,5], which as far as I know are also original mathematics research and not just mathematics education research.
With the onset of the COVID-19 pandemic I suddenly shifted my research attention towards statistics and epidemiology and published a fundamental breakthrough research paper [6] with Dr. Peter McCullough and the late Dr. Vladimir Zelenko on the early outpatient treatment of COVID-19. Zelenko's and McCullough's multidrug protocols were suppressed by some tyrannical, in my opinion, governments, but could have saved millions of lives, if they had been adopted as early as by the end of April 2020, which is when we had sufficient evidence to justify the emergency adoption of Zelenko's protocol. There is some additional work in that area currently ongoing.
It is interesting to look back now and realize that I have visited all the possible life histories that others and I envisioned for me, by doing work in all three areas of Physics, Mathematics, and now Medicine. From all the work that I have ever done academically, the most meaningful work so far has been my paper [6] with Dr. McCullough and Dr. Zelenko. The sudden shift into learning both medical and statistics research literature completely from scratch was like going through graduate school again, except this time with academic tenure. Normally this is not something that proper hyper-specialized academics are supposed to be doing, but I have learned that every time you look at a new research area from the outside, bringing in knowledge and experience from other disciplines, there is always something interesting that you are able to notice that many specialists in the area may be blind to.
Perhaps the purpose of my entire life’s journey was to prepare me for doing the work with Dr. McCullough and Dr. Zelenko, at the right moment and at the right time, and perhaps not. We will have to see what the future holds, and whether there are greater things ahead.
References
[1] E. Gkioulekas: "Winterberg's conjectured breaking of the superluminal quantum correlations over large distances", International Journal of Theoretical Physics 47 (2008), 1195-1205
[2] E. Gkioulekas: "On the elimination of the sweeping interactions from theories of hydrodynamic turbulence.", Physica D 226 (2007), 151-172
[3] E. Gkioulekas: "Multilocality and fusion rules on the generalized structure functions in two-dimensional and three-dimensional Navier-Stokes turbulence", Physical Review E 94 (2016), 033105, 25 pp.
[4] E. Gkioulekas: "Using restrictions to accept or reject solutions of radical equations", International Journal of Mathematical Education in Science and Technology 49 (2018), 1278-1292
[5] E. Gkioulekas: "Solving parametric radical equations with depth 2 rigorously using the restriction set method", International Journal of Mathematical Education in Science and Technology 51 (2020), 1255-1277
[6] E. Gkioulekas, P.A. McCullough, V. Zelenko: "Statistical analysis methods applied to early outpatient COVID-19 treatment case series data", COVID 2(8) (2022), 1139-1182