Curvy Mathematics

Curvy Mathematics


Interviews with Giants

21 Sep 2018

Karl Schmedders

Chocolate, cheese, neutrality and financial institutions is what Switzerland is known for to most people. Located in the middle of the european continent, the country provides 1/3 of housing to the CERN Collider and 3/3 of housing to the University of Zurich, which had been the alma mater of Albert Einstein and Karl Young. These days, another "Karl" is teaching at the Department of Business Administration. Karl Schmedders gladly shares his passion for probability theory and he is definitely going to inspire you to dig deeper into this section of mathematics whether you are fond of mathematics or not.

Mathematics captured his attention during school years and a lifetime relationship has been developed since then. Being afraid to dive into pure mathematics, he has thankfully turned himself to the applied side of mathematics by studying business engineering at the University of Karlsruhe. It was during his studies that he discovered his true love, operations research and he has been occupying himself with it ever since.

Insisting and persisting has always been his best shot against difficulties. On the one hand, there was his unfinished task writing his PhD thesis, on the other hand, there was the lack of social life. On the verge of abandoning his duty, he continued with his work, even if this was "an incredibly lonely, frustrating and often “depressing experience". Although publishing some work alone would produce greater acknowledgement from his colleagues, he clearly states that assistance is helpful, even if this would cause to be looked down by his colleagues.

Even though he is not fond of networking in order to promote one's work, he accepts the valid fact that it is inevitable. Marketing and promoting oneself, both unfortunately exist in the world of natural science too. There are many scientists researching the unknown, an activity which can easily be overlooked. This could dishearten the scientist and would definitely result in a drawback for humanity.

Regarding compensation and recognition, academic (aka useless) research is not a good option if one is pursuing wealth and fame whereas applied scientific research provides higher odds to acquire the above. Still there are scientists who dare to follow the path of knowledge in order to comprehend the way our world is turning even the compensation for their time spent studying is not proper.

He believes that daily lives take so much time and energy out of peoples' lives that they have neither the time nor the energy to learn new things "just for fun" after having entered their adulthood. Our chance to turn people's attention to mathematics is to "convince" somehow the children to become engineers or scientists. Humanity has always needed them.

If only he could turn back time, he would not have chosen the same path of studies. It is way "too applied" for his standards, he would prefer something more abstract with a background enriched with mathematics and statistics. Young students would probably find it beneficial to study mathematics, statistics and computer science since it is very interesting to explore our universe by processing our given data. This could result in financial benefits too apart from already being extremely intriguing.

25 Jan 2018

Gregory Chaitin

Greek alphabet can be found all over the mathematical universe, circle’s π, Fibonacci’s Φ, etc. Among them resides a not very common one too, the “big O” or as it is called, Omega number (Ω). Turing’s halting problem and Gödel’s incompleteness theorem are just two igniting inspirations for the discovery of Omega number by a modern iconoclast, Gregory Chaitin.

During his childhood, his mind was excited by general relativity and quantum mechanics, so his path was foreshadowed/predetermined. Then Gödel’s beliefs had a severe impact on him resulting in abandoning his spyglass watching the skies for the peculiar and obscure path leading to the abyss of theoretical mathematics. It is a periculous path contrary to what most people may think about it but the discovery of fundamental facts is an extremely attractive idea. Despite the danger that lurks at these distant regions of the human mind, where the borders of sanity can sometimes easily crossed, very few, brave mathematicians and scientists dare to walk over there and get lavishly repaid! “Sometimes, in mathematics one thinks like God”.

He was no exception in facing difficulties obstructing his way. The toughest part is to realize that one is standing in front of a treasure, not to discover the treasure. Since his twenties, he had already developed the proper toolkit to mathematically study life and evolution but it took him almost a lifetime to completely conceive the potential of his development. Just like everyone, young minds can easily get distracted and attention gets diverted to different objectives. Thankfully, mathematics are indifferent of age.

It seems that being a good rhetor can be beneficial in all occupations, in all eras throughout human history. Although the ideal scientist should behave as a hero or as an immortal, mortal needs tend to alter human characters even if they are trained to be scientists. “Fields of science are power structures and do not welcome new ideas especially from outsiders.” Like the guilds a few centuries ago, nowadays a scientist has to get adopted by a modern scientific team, if one would like some recognition for one’s scientific work. In the past, there was only a bunch of scientists and good science was a relatively easy thing to do.

Mr Chaitin is clear that things have changed - big time: “Science is a big business with a giant administrative bureaucracy” he states. Scientists get paid which means that they have to be productive. “That explains why there have been no fundamental advances in physics since the 1920s. The shut up and calculate dogma has killed physics”.

The current tendency in the modern societies is to spend money that one does not possess to buy things which one does not need. Very few are left wondering very basic questions like “Why are we here?”, or very few seem to be interested in trying to find an answer to the primordial questions that almost all humans have when they gaze at the night sky during their childhood.

He considers himself as a very fortunate person as he had the chance to work on many fundamental, philosophical questions which many mathematicians have no interest anymore. If he could have chosen a different road in life, then becoming a mountain climber or a martian colonist would probably be some of his options. Definitely, he honours creativity of human mind, he admires people who use their mental resources in order to advance the understanding of how our universe works instead of spending their time and resources in doing politics and contracting or improving scientific, public relations.

Just like his hero, Leibniz who created new, mathematical fields in order to give an answer to questions which have remained unanswered for countless centuries. Most of Leibniz’s precious ideas were discovered after his death among his writings.

Unfortunately, many scientific advances have been attributed to the wrong people. Dead cannot speak and the truth is extremely difficult to be unveiled. Additionally, too much attention on one’s work draws the admiration of non-specialists as well as the envy and hate of one’s colleagues. In the end though, science should be above all these mortal and pathetic matters. “Real science is a lonely, solitary pursuit between you and God”.

29 Nov 2017

Andrew Siemion

A few decades ago, human kind managed to launch their first manned rocket in orbit. A few decades later, human kind realised that other beings may exist out there, maybe we are not alone. Some people believe we have been created as the only intelligent life form across the universe while some others tend to find this opinion quite arrogant. My belief is that questions concerning valid facts can only be answered experimentally; it is not a matter of belief but a matter of what really happens. This is what Andrew Siemion does via the SETI programme.

Motivated by a deep sense of awe and wonder about how the universe we live at works, he is now processing signals and all kinds of information that our telescopes and antennae provide in pursuit of conscious life. Many of us have been wondering whether there is life on another planet or whether there is intelligent life when gazing at the bright, celestial bodies. Thankfully, some people managed to work on seeking answers to such questions.

It is not an easy task. Obstacles have been surpassed, difficulties still exist, adversities will never cease appearing. One factor cannot be yet evaded or overpassed and that is the human factor. One has to understand that we are all only humans and we tend to think like that, unpredictably. This can result in a major problem when a task is not properly accomplished or at least not in the way it was initially supposed to be accomplished. On the other hand, a different opinion may result in a solution against a problem which seemed to have no solution. “Coming to understand that even the profoundest missions are ultimately carried out by human beings and face universal human challenges”.

Astronomy and marketing cannot coexist. Time, apart from having become relative, is precious and in astronomy “it is important to spend time doing careful and rigorous science than promotion”. Natural science should be like this at all subjects, not only astronomy, but it seems that the flow of money alters humans and human scientists tend sometimes to try to promote their work in order not to lose funding or gain some for their research. Personally, I would like to see researchers not having to worry about survival as their social work is extremely valuable but not always appreciated on time.

People’s attitude towards science is usually indifferent. This happens probably due to the fact that we faced difficulties in mathematics during school years. Even Einstein’s statement regarding the relation between imagination and knowledge has not been enough to inspire most of us to admire a scientific breakthrough, not until this finds an application to everyday life and can become commercial. An interesting point of view is that although there are museums all over the globe trying to promote natural science, still many people do not have the opportunity to visit them.

Natural beauty is here, is there, is everywhere around us and natural scientists put all their effort to comprehend the way nature works and creates such spectacular wonders. Unfortunately, there are people struggling to survive and not only can they not have access to such places but they are not at all interested in science as they have a more important issue to worry about, to live another day. Maybe natural science could achieve greater accomplishments if social inequalities did not exist or were reduced.

Astrophysics or astronomy (never before have I wondered about their difference but judging from the words’  etymology and scientific history, astronomy has too much of geometry and mathematics generally whereas astrophysics studies interactions between celestial bodies) seem to be able to capture and stimulate human mind and imagination. In some occasions the heart is devoted to these subjects of science. The best way to approach these subjects is an endless study of physics and mathematics. Even if the results seem pointless, most probably they are of vital importance but we have to discover their avail. Never give up in studying physics and mathematics: “I would always like to have taken more!”

28 Sep 2017

Jeff Chasnov

Hidden treasures can be found all across our planet. Real educators live their lives all around the world too but they are rarer than treasures. One of them lives in Hong Kong. He can initiate you into mathematics just by watching one of his online courses.

Jeff Chasnov is neither from Hong Kong nor he studied to be a mathematician. He started his career as a physics student. It seems that his research area in fluid turbulence had a turbulent effect on his life and career too. Jumping from physics, he ended up in a Math department (thankfully, for the rest of us). It is obvious that interaction between natural sciences occurs as it happens between molecules.

Just like everyone, he faced difficulties during his scientific career, although he might have been more familiar with chaotic life events due to his research in the fluid turbulence field. A low quota in his initial choice of scientific departments forced him to stay outside and almost to abandon all efforts. Despite the fact that a mountain of difficulties and disappointment obstructed his initial path, he persisted on pursuing his goal to study thoroughly natural science and “managed to find a supervisor at NASA” who took him as student. An obstacle can be overpassed or bypassed, the idea is not to forget the target and not to abandon efforts; persist and there are chances to succeed, withdraw from trying and there are no chances at all to succeed.

Either if money is the scientist’s motive, although “most of us scientists did not go into our careers looking to make a lot of money”, or if the mainspring is fame as “certainly, we would like our work to be known”, the art of marketing of one’s work may be of great importance. Unfortunately, scientists have been relegated to common professionals and since they already come in vast numbers, their work must be categorised and maybe differentiated from one another. Since the procedure is not done by a strict and unconscientious computer but human thoughts and emotions intervene in judging, then it is inevitable that good marketing of a scientist’s job and good public relations can cause a severe impact in one’s career, good or bad. Nevertheless, both marketing and public relations are considered to be sciences anymore and they are taught at universities evenly like natural sciences.

Some people have an innate tendency towards mathematics and science. These people would be attracted to natural science sooner or later. The rest would keep a passive stance towards mathematical thought. For those interested, there are plenty of videos online which “can serve to inspire more young people to go into math and science”. Many of these videos are extremely interesting but people seem to ignore their existence. It is of vital importance to make people turn their attention there and discover the greatness of mathematics.

Has he regretted for any of his decisions concerning his studies? "I am sure my study path would be somewhat different concerning what I know now”. Decisions usually oblige people not to choose what they want but what they are going to leave behind. The initial decision is the little start, the big bang of all the consequent events. And luck, just like turbulence, “has a lot to do with the trajectory of one’s life”. Still, we have not managed to fully comprehend luck and turbulence although we try. Some of us feel unlucky while some others feel as they have been favoured by luck. “And I feel like I have been lucky”. Perhaps it is just a matter of one’s point of view.

14 Jul 2017


It is doubtful that there are chemists in the western world who have never heard of the name P.W. Atkins. He is famous mostly as the author of a spectacular volume of university books about chemistry. In my opinion, he should be honoured for 'The Periodic Kingdom' as it is an outstanding book capable of attracting newbies into the art of manipulating matter: chemistry.

He chose chemistry back at the age of 15 for several reasons, the most important of which was "the urge to share my joy of understanding from science". For many of us, the joy of understanding an obscure concept or meaning, the pleasure of comprehending a difficult problem or overpassing a mental obstacle is probably the greatest feeling. All students face difficulties, they get disappointed but those who insist, they manage to feel this overwhelming joy of understanding, the quintessence of learning. Science is plenty of such opportunities.

Difficulties arose during his scientific career too. His real problem was time devotion. Research is extremely demanding, "to do research requires total, obsessional commitment". But "to write books on a large scale requires the same". So how can one organise one's time? Human beings require some dead time to sleep, eat, drink, enjoy... No human mind can always be stretched and under tension, eventually it will crack like a bow. The decision though to abandon original research because "I was neglecting the young minds of my research group" reflects the altruism which, thankfully, exists into some scientists. There are many university professors and researchers who become pure and strict professionals, they just care about their work and neglect the painful job and stressful role of young assistants and students who sacrifice a lot of their time in order to demonstrate devotion and goodwill to their scientific supervisors.

It seems that science has not avoided the shroud of marketing. Fame, acknowledgement, money, vanity, still exist among human scientists too. So, this means that apart from being a good scientist, does one have to be a good marketeer too? Unfortunately, science has a gap that allows marketing and public relations to play an important role in one's career. Even today, physicists use the phrase "we believe that...", as in religion or other scientific fields different than natural science which are not based on mathematics. We should not "believe", we should accept facts as valid only when they are proven experimentally and they are consequently backed by mathematics.

Regarding ordinary people's attitude towards science, we all know that it is of vital importance to alter it. Science needs to become more attractive, more intriguing. Once upon a time, "I would have said 'television'", since television could be described as the fourth authority to create and alter consciences, "but these days people are spending more time away from broadcast TV and more on the Internet, where central authority has no influence. Perhaps some really good scientific version of 'Downton Abbey' would inspire interest". Many people avoid scientific thinking, mostly due to their bad experience with mathematics during school years. If mathematics could become more approachable with a less repulsive appearance, then more people would be attracted to science and spend at least a few Saturday nights occupying their minds with scientific matters. Definitely, mathematics are already simple, pure, universal and democratic as there are no discriminations but a lot of effort is demanded in order to think simply and discover their divine beauty.

When asked if he would choose the same field of study, if he had the chance to turn back time, the answer is clear: "Yes, it is the central science and enables you to embrace all others". It seems that this answer depends on the point of view of each scientist and the educational system at one's country. In any case, a scientist ought to do everything about science at one's maximum effort and capability. Choose properly, present properly and write about it properly.