Infinity, Mathematics and its Never Ending Study

Infinity is the concept that has puzzled mathematicians and thinkers alike for years. And this continues and will continue for the succeeding years. Too many questions out of curious minds that are needed to feed with answers, and eventually reveal the underlying truth regarding this ambiguity.

But really, what is infinity? In mathematics, infinity is simply defined as something not finite, hence it is endless. Mathematicians have defined “infinity” very closely but not exactingly. The notion for this can be considered as profoundly outside the human ability to understand. Even so, this has not stopped mathematicians from solving and finding certainty.  After all, the hunger to explore and delight in discovery is what makes us human- living and surviving.

The fourth episode of the Story of Maths entitled “To Infinity and Beyond” is an existing example of the saying “last but not least”. This final installment talks about the core study and highlights of 20^th century mathematics that has started with the assembly of International Congress of Mathematics in Sorbonne, Paris during 1900. One of the leading mathematicians of his generation, David Hilbert, has outlined a list of 23 unsolved problems (at that time in) which he called upon the attention of his colleagues. He revealed vital questions that opened areas of research that has spanned different branches of mathematics for the future generation.

Hilbert’s problems were highly influential  for the 20^th century study of mathematics. The problems overlapped several areas of mathematics; involving set theory, geometry, arithmetic, algebra, variable calculus and many more. Some of these were direct and thus immediately solved. Some problems, on the other hand, were vague and expansive that until now they still remain unresolved.

One of the theories (problems) needing for proof was proposed by Georg Cantor, a German mathematician, whom was the first to give mathematical accuracy and precision to the concept of infinity; and provided different types and sizes of infinities through his Continuum Theory. Another problem that had confused mathematicians during those times was regarding the orbits of planets in our solar system. This has led to the basis for Chaos Theory by Henri Poincaré, a French mathematician. Observing systems with a multiplicity of variables, this theory had been a great function in studying climatic conditions and applications in medicine. Further, showing any logical system that would result to true but cannot be proved statements, as done by an Austrian mathematician in the name of Kurt Gödel had revealed uncertainty through his Incompleteness Theorem. 

Undeniably, mathematics is not like a complete textbook as being taught and learned in schools. The subject that was once been defined had evolved through history became into the greatest abstract ideas that the human mind has encountered. Among all of these abstractions, uncertainties and infinities, the study of math will never be ended. Every proved theory would just lead into creation of other theories; unanswered questions into answers and answered ones to be questioned logically. Scholars and even ordinary people like math's challenges and at the same time its clarity- the point when you know when you are right! Finding a correct solution to a problem is not just satisfying, but at the same time exciting.

After watching and completing the documentary series "Story of Maths" here is my brief generalization:

The ability to count, compute, measure, study shapes and motions, and use numerical relationships by logical reasoning with a bit of abstraction, are the supremely significant among mankind’s achievements. Mathematics is not the creation of a single person but the product of gradual and social evolution. It all started as providing practical solutions for everyday problems for as far as written records exist. The Greeks then first used logic in making generalizations. On the other part of the world, most notably in China, India and other Muslim places, mathematics continued to develop. Until the 17^th to 19^th centuries mathematicians have started to take mathematics into a higher level. The 20^th century study of this field was even more advanced; giving rise to technologies and innovations that continues to the present day.

The study of mathematics is not just mystifying because some of us find it too complex to fathom. It is the basis of the universe, allowing us to fully understand the physical world.