How to become a mathematician ?

I don’t know from where to start to tell you about my story because i have’t become a mathematician until now, but on the track in the race of becoming a mathematician. So, whatever i will tell you that will be the my thoughts during learning and understanding in the journey of continuum hard work how i am actually transforming myself from a first class passed out master student that have a litle exposure to the research due to my masters thesis on topics of discrete differential geometry and its applications to become a researcher in mathematics after publishing papers.

There are some question you have in you mind, why i did’t joined the PhD program to some institute? The same question first time asked by my master thesis superviser Prof. Bankteshwer Tiwari(Research Interest - Differential Geometry and Applications). I have answered him with following sentences but with a sequence of questions again thrown at me.

What does it take to publish in Mathematics ?

Question

1. Who can publish paper in mathematics ?
   • No pre-requisites to reach certain level to publish research paper.
2. What we wanted to achieve or do ?
   • To publish a paper in mathematics
   • May be go distracted and avoid for now to do
3. What we wish to achieve or do ?
   • To publish a paper in mathematics ?
   • Uninterupted and best utilization of your free time to think about the problem that you have.
4. How to balance between research study and publish ?
   • Any area of mathematics infinite for research study but to publish a paper in that area we have to do some research study about that area. How much i should to research study and then think about the problem or idea or notion that are’t been developed or invented ? and working on that idea. There must be a balance between them ok! Ex-1 Lecture Notes from start to finish Book from start to end of chapter After reading most of Research paper in that are after that then i will think about doing research

Its not the great idea and does’t work in practice but there must be a balance between the idea i got from the area of mathematics and doing research study into that area.

There is no ending to the learning process because each time we do research study leads to some questions and solving them again we do study find some more question onto our ideal again and again…

I got an idea from an area of mathematics

1. I only understand the bigger picture not the technical details on it
2. There are cetain question that i should ask
   • What this area/topics wanted to talk about ?
   • What are the major idea/structures/questions actually have been discussed in highlights of topics ?
   • Then we able to see what kind of results already been done and what are’t. Ex-1 : $X \implies Y$ Done but what about inverse $Y \implies X$ ?. Investigate is there any condition.
   • another way is to thinking of new problems.
3. As our knowledge of study grows in that area then we can handle many cercumstances.
4. Qsking these above questions can leads to answer the questions of How to think like a mathematician for publishing a paper.
5. Most of the time what stop us from publishing paper is the our unknown fear.
   • may be what i am thinking be good enough.
   • It may be too trivial
   • What people think, i don’t know about enough things
   • Asking such kind of questions and bothering about other people.
   • What if i send it to a journal and they says its too trivial.
6. These unknown fears stops us from asking more questions and also stop from writing paper.
7. Means i am not getting in a position of publishing paper out of this.
8. Unknown fear needed to be overcome Ex-1 We are working on Algebraic Structure
   • What structure we love to work with ? : Ring
   • Some well known mathematician actually worked on this structure able to publish the paper in high ranking journals.
   • Thus, let me work on the same structure. Most of the time it may not work but some time it works. Also not sure wheather we like X structure/topics/area or not. But Love or pretending to love.
   • Its another dilema that stop from publish. - Where should i starts ? : Communtative Ring/ Non-Commutative Ring -> Read a paper in that area. - After conformation that i will work on this topics then - Decide do we wanted to work on structure or substructure of the commutative ring ? or Applications of Commutative ring ? -> what kind of substructures we have : Subring/Ideal which one should i look for it. Ex- Ideals : Prime, Maximal, Reducible, Irreducible etc. - Extend certain properties of the ideals - Create a new kind of ideal. - Came up with at least some trivial ideals. - Then come up some non-trivial examples. - Then will be confident that our idea may be working but not generalized to work always - Get the both types of counter examples then both claim : it may exists in general - Study properties of ideal -
9. If we love then any way we will do mathematics and leads to publish.

Lectures

1. What does it take to publish in Mathematics ?

References

1. How to Write Mathematics by Paul R. Halmos
2. The Princeton Companion to Applied Mathematics : Mathematical Writing by Timothy Gowers
3. How to Read and Understand a Paper by Nicholas J. Higham
4. How to Write a General Interest Mathematics Book by Ian Stewart
5. Workflow of Mathematical Paper Publication by Nicholas J. Higham
6. Reproducible Research in the Mathematical Sciences by David L. Donoho and Victoria Stodden
7. Experimental Applied Mathematics by David H. Bailey and Jonathan M. Borwein
8. Teaching Applied Mathematics by David Acheson, Peter R. Turner, Gilbert Strang and Rachel Levy
   • What’s the Big Picture ?
   • Computation, Modeling, and Projects
   • What to Teach and How?
   • Industrial Mathematics Inspires Mathematical Modeling Tasks
9. Mediated Mathematics: Representations of Mathematics in Popular Culture and Why These Matter by Heather Mendick
10. Mathematics and Policy
    • Ya-xiang Yuan: How Chinese Mathematicians Influence Government
    • Maria Esteban: A Personal Experience in France and Europe of How to Influence Government as a Mathematician.
    • James M. Crowley: SIAM and Science Policy in the United States
    • Alistair D. Fitt: Making the Case for U.K. Mathematics Research in a Rapidly Changing Environment