# Why I want to be a Mathematician?

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A few weeks ago I revised my views about “Why I love Mathematics?“. It has been two years since I have been trying to get into mainstream mathematics research. It will take another four to five years for me to start contributing to mainstream mathematics research. In this post I will try to add a bit more to what I wrote an year ago.

Though mathematics is the main thing my life revolves around,  it’s not the only thing. I love doing few other non-mathematical things. Few months ago I watched the movie “Ship Of Theseus” by Anand Gandhi , and it is one of the few movies I have agreed to watch twice. In case you are curious to know about Theseus’ paradox, I will suggest this ted-ed video

As you may be aware of, there are a lot of people who are not mainstream mathematicians (i.e. working in a Research Organization in a specific research area) but still claim to love mathematics. They are called recreational-mathematicians (like Dattaraya R. Kaprekar, Tanya Khovanova,…), maths-popularizer (like Eric Temple Bell, Constance Reid,
Simon Singh,… ), maths-historians (like Bartel Leendert van der Waerden, Jacqueline Anne Stedall,… ) etc.  But I want to become a mainstream-mathematician (like full time professors in research organizations). Why?

I want to become immortal (i.e. to exist as long as humans exist).

You may be think that I have lost my mind, but please continue reading…

I hope we agree that our wish to live (as opposed to fear of death) motivates us to live. Paul Erdős used to tell following story about his second discovery as a child (first being that of negative numbers):

I knew I would die. From then on, I’ve always wanted to be younger. In 1970, I preached in Los Angeles on ‘my first two and a half billion years in mathematics.’ When I was a child, the Earth was said to be two billion years old. Now scientists say it’s four and a half billion. So that makes me two and a half billion….

I believe that Paul Erdős has indeed gained immortality, we just keep listing about his conjecture being proved now and then (recent one: Erdős-Rado sunflower problem).

From a biologist’s point of view (by the way, I also study a bit of Biology), our body along with our consciousness defines us as an individual. So, for a human to become  immortal his/her body as a whole must be preserved as it is. But, biologists have faced a dilemma of  conserving body versus consciousness. If you preserve body, by eliminating defects from our body at DNA level (since not every organ can be transplanted) , the you lose the distinctiveness in personalities (like clones) since all will be perfect and thus identical (causing threat to evolution). If you preserve consciousness, by transferring it to an artificial body (which will become reality with advent of quantum computing), then you lose your body (a major part of your personality).

Consciousness transferred to a robotic body in the sci-fi movie Chappie (© 2015, Sony Pictures Entertainment)

But, I believe that the only way to become immortal is by publishing (articles, books, movies, songs,…) and propagating (lectures, discussions,…) your ideas among others. As we know that our body is immortal in a sense that all its atoms remain as such (law of conservation of mass, energy…), and form various molecules like the molecules of life. For example, say an animal dies in a forest (without human intervention). After few days the microorganisms inside & outside the body (which are much more than the number of cells of that animal) will start decaying the body and release different chemicals. These chemicals will attract different insects which will start consuming the body and finally scavengers will completely clean the flesh part. The bones will take longer time depending on environmental conditions. Now these insects and scavengers will be consumed by bigger animals (and eventually, may be, by humans). In this way the atoms from the dead animal will disperse among various life-forms but will never cease existence. In case of humans, we make this process to take longer time by doing various rituals. So, if I am able to propagate all of my ideas (which will also evolve over time), then I am immortal.

Goddess Saraswati (symbol of knowledge in Hindu Mythology) used to popularize a mathematics conference in Belgium (url: http://www.mathconf.org/app-gvl-summer2016)

The  immortality “ideology” which I want to adopt is actually what various civilizations have done to make their gods/goddesses immortal! You make a story about a character in written form (which they called “sacred texts”) and propagate among others (which they called “religions”). After some time the stories become part of our life and characters of that story become immortal. I view the “library of Alexandria” as power house of  Egyptian civilization, since it was a major center of scholarship. Same is true for eminent people (the people about whom biographies are written and movies are made) in modern society.

In my opinion, only mainstream researchers like scientists, psychologists, economists, etc. have an opportunity to gain immortality. Whereas people like non-innovative-teachers, librarians, science-popularizers, non-research physicians, non-research engineers etc. ensure immortality of others, just like the craftsman reproducing work  of ancestors again and again thus helping to keep the work alive.  So, all professions are about “collecting knowledge” but what makes researchers stand apart from other professions is their ability to “create knowledge“. So all professions are important but in different prospective. For example, if you want to become powerful, become politician and so on….

I admit that my thoughts may be very childish and I in future I may change  my opinion…

# Beauty Beyond Language

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Mathematics is believed to be a language of symbols with  metamathematical meaning attached to them, for example:

$(\forall \varepsilon>0) (\exists N \in \mathbb{N}) \ni m,n \geq N \Rightarrow |a_m - a_n| < \varepsilon$

Can be translated in English as:

For every positive real number, $\varepsilon$, there exists a  natural number, $N$, such that, if  the natural numbers $m$ and $n$ are greater than or equal to $N$ then absolute value of the difference between $a_m$ and $a_n$ is less than $\varepsilon$

Many contemporary mathematicians (big-shots) like Jean-Pierre Serre , believe that instead of logographic language (symbols represent the words themselves), we should use alphabetic language (words are made up of various letters) . This also makes sense to me, because as seen in above example, symbols seem to hide beautiful simplicity of a mathematical statement. But, on the other hand, alphabetic language is too lengthy to write.

Because of above debates about language of Mathematics, many mathematicians love Proof without Words, consider an example by Mariano Suárez-Alvarez  (http://mathoverflow.net/q/8847):

$1+2+\ldots + (n-1) = \frac{n(n-1)}{2}=\binom{n}{2}$

But, there are some sub-domains in mathematics which doesn’t depend on language, for example Geometry. Let me illustrate this point with following Spanish video created by Cristóbal Vila (Instituto Universitario de Matemáticas y Aplicaciones of the Universidad de Zaragoza):

Irrespective of the language you speak, you can appreciate the relationship between different artistic works and mathematics (mainly, Geometry)

For full details of this project see:  http://www.etereaestudios.com/docs_html/arsqubica_htm/

# Metamathematics

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I like to predict things going to happen each day based upon some (il)logical reasoning. Also, earlier this year I wrote a blog post: “Inquisitive Mathematical Thinking“.

Today, inspired by various “wrong” interpretation of “Principle of Mathematical Induction” which leads to various absurd results, I came up with an idea of giving a “flawed” proof of (i.e. I will deliberately mimic what I call “rape of Mathematics”):

Every day is good day.

Let me start with following induction Hypothesis:
$P(1):$ Today is a good day.
This is trivially true (just like the statement “the sun rises in east”).

Now, let’s assume the truth of following statement:
$P(k):$ $k^{th}$ day is good day.

Now, what remains to prove is that $P(k) \Rightarrow P(k+1)$, where:
$P(k+1):$ $(k+1)^{th}$ day is good day.

Since, our past actions determine our future results (metaphysical truth), if today is good day then I will be able to prepare for tomorrow’s challenges and hence my tomorrow will be good. Thus proving the inductive step.

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The above proof has lot of logical flaws like: ” How do you define a day to be good?” and “Implication is based on a metaphysical truth”.

Bottom line: Life not as simple as Mathematics!

# Bitter Truth of Love

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I love mathematics (click here for WHY?), and many other creations of Nature. But every time you add one of the creations of nature to your “LOVE LIST” , some unwanted (bitter) things creep in. I will talk what so far I have experience in case of (pure) Mathematics by quoting some big shots who feel same as me.

Doing research in mathematics is frustrating and if being frustrated is something you cannot get used to, then mathematics may not be an ideal occupation for you. Most of the time one is stuck, and if this is not the case for you, then either you are exceptionally talented or you are tackling problems that you knew how to solve before you started. There is room for some work of the latter kind, and it can be of a high quality, but most of the big breakthroughs are earned the hard way, with many false steps and long periods of little progress, or even negative progress. There are ways to make this aspect of research less unpleasant. Many people these days work jointly, which, besides the obvious advantage of bringing different expertise to bear on a problem, allows one to share the frustration. For most people this is a big positive (and in mathematics the corresponding sharing of the joy and credit on making a breakthrough has not, so far at least, led to many big fights in the way that it has in some other areas of science). I often advise students to try to have a range of problems at hand at any given moment. The least challenging should still be difficult enough that solving it will give you satisfaction (for without that, what is the point?) and with luck it will be of interest to others. Then you should have a range of more challenging problems, with the most difficult ones being central unsolved problems. One should attack these on and off over time, looking at them from different points of view. It is important to keep exposing oneself to the possibility of solving very difficult problems and perhaps benefiting from a bit of luck.

Mathematicians usually have a hard time explaining to their partner that the times when they work with most intensity are when they are lying down in the dark on a sofa. Unfortunately, with e-mail and the invasion of computer screens in all mathematical institutions, the opportunity to isolate oneself and concentrate is becoming rarer, and all the more valuable

Second, the mathematician must risk frustration. Most of the time, in fact, he finds himself, after weeks or months of ceaseless searching, with exactly nothing: no results, no ideas, no energy. Since some of this time, at least, has been spent in total involvement, the resulting frustration is very nearly total. Certainly it seriously affects his attitude toward all other affairs. This factor is a more important hindrance than any other, I believe; to risk total frustration, and to be almost certain
to lose, is a psychological problem of the first rank.

We are mathematicians by choice. We chose the profession because we love the subject. Reading and assimilating deep results of masters and then solving some of our own small problems brings us pleasure to which nothing else compares much. Yet we live in a world populated mostly be non-mathematicians. We must survive and thrive in their midst. This brings
forth its own challenges and frustrations.

But what I & many other mathematicians feel as a compensation of this Bitterness of Loving Mathematics  is:

• Love Teaching (it has it’s own bitterness) : Share, propagate and preach the beauty that you can see by teaching others.  Enjoy teaching if it is a course of our choice and the class consists of a few eager, motivated, well-behaved students. That is only a dream. Often we must teach large classes of uninterested students who are there only for completing the requirements. But in spite of all this we must strive to teach, giving it our best and at the same time maintaining the standard of our subject. Compromises have no place here. We believe in teaching in a certain way and it can be fine-tuned depending upon the reactions of the students. But it should not prevent us from communicating the basic spirit of mathematics, especially the importance of logical enquiry. All aspects of mathematics, including history, biographies, motivation, definitions, lemmas, theorems, corollaries, proofs, examples, counterexamples, conjectures, construction, computation and applications can and should find a place in the classroom.
• Love Travelling: Attend as any conferences, workshops etc. and keep moving.  As Paul Erdős said :

Another roof, another proof