Georg Cantor’s Journey and Discoveries in Mathematics

Do you love being organized that you keep everything well arranged? For example in your kitchen, your mom makes sure that plates are kept separate from mugs and spoons. Like on how you arrange your playlist of songs from classical to any other different genre. Well, this idea is an example of sets. Set refers to the collection of objects which is the main focus of set theory. Set theory on the other hand is a mathematical theory of well-determined collections of objects. Basically, set theory is about sets analyzing sets and their behavior. In fact, set theory has become the standard foundation for mathematics. Each mathematical object can be seen as a set and as it provides the axioms from which the rest of mathematics is built up. This shows that set theory is really an important field for mathematics. Perhaps, it is the right time to note who discovered it. George Cantor founded set theory. But before that, let's have a little glance to the life of George Cantor. Do you know who's George Cantor is? Or even his life before being the founder of set theory? Well, on March 3, 1845, at St. Petersburg, Russia, a genius mathematician named George Ferdinand Ludwig Philip Cantor was born. His father named George Voldemort Cantor whose interest is inclined in culture and arts. He was a wool-selling agent in Petersburg which later on became a broker. While her mother named Maria Annabelle who loves music, the talent of George Cantor matters explains his musical and artistic talent. In fact, he was described as an outstanding violinist. Due to his father's poor health, they moved to Germany to find a warmer climate. George Cantor completed his education for different degrees in different schools including Darmstadt, Zurich, Berlin, and Göttingen. On his 15th birthday, George Cantor starts to emerge his mathematical skills. However, his father wanted him to be an engineer, but Cantor was very dedicated to pursue mathematics. In 1863, he specialized physics, mathematics, and philosophy at the University of Berlin. In 1872, Cantor at the age of 34 was promoted as a professor at Yale wherein he met Richard Dedekind. Their connection lead to the birth of set theory. In 1884, he was diagnosed with depression. Cantor suffered from mental illness which was directly linked to his studies and criticism of his works. In 1913, he retired and admitted at Yale sanatorium hoping to recover from depression. He regularly write to his wife begging to be allowed to go home. Sadly, on January 6, 1918, George Cantor died due to heart attack. However, behind his tragic life, a genius mathematician who offers his works which contributes in the development of mathematics which we have today. It was mentioned that Cantor's met Richard Dedekind. Their exchange of letters commenced the generation of Cantor's idea about set theory. During 1973, Cantor demonstrated that even if the rational number are infinite, it can be counted because this number can be placed in one-to-one correspondence. He also illustrated that the set of rational and irrational number was infinite and cannot be counted. This study that Cantor had made was ready to publish, but Leopold Kroniker who was an editor's staff opposed Cantor's idea about infinite sets and views it as meaningless. Luckily, with the help of Dedekind, Cantor paper was published in 1974. On the other hand, have you ever watched a debate or even know what debate is? Well, Cantor's studies of continuum hypothesis is one of the most debated and open problem in set theory. Many mathematician tried to prove this hypothesis to be true or false, but guess what? None of them succeeded. The word continuum means a set of real numbers. Cantor's believed that set of real numbers is uncountable and are large infinity compared to natural numbers. Cantor's developed a way of identifying the size of infinity according to their cardinality using the formula given. In 1895, Cantor's theorem was established that indicates that the cardinality of a set is strictly less than the cardinality of its power set. When Cantor's theorem was applied to an infinity set, the outcome is an infinity hierarchy of infinite cardinals. This also implies that there is no maximum cardinals or no biggest infinite. Well, in 1872, Cantor's discovered the transfinite number which means beyond limit. These are one of the important steps in developing set theory. In 1915, Cantor's published his best-known work entitled Contribution to the Funding of the Theory of Transfinite Numbers. It is about the transfinite numbers where he introduced continuity and infinite. He showed that infinity sets can be put in one-to-one correspondence. For us aspirants, George Cantor is truly a math hero. He received many objections from his colleagues and suffered from mental illness. Still, those did not stop him from working and doing things that he was passionate about. We matrix are truly inspired by his braveness and great contribution in the field of mathematics. We are hoping that sharing this interesting life story will inspire and motivate more people. We have learned that sometimes, your hardest times often leads to the greatest moment of your life. Keep the faith and it will be worth it at the end.