This is an ongoing project, consisting of my views on research shaped through help of others. Some of the views may be problematic and even blatantly wrong. I am myself learning and open to views, will be figuring out and keep updating. 

Disclaimer

  • Also the first advice, an advice can be wrong for you and you can always choose to differ. There are best practices, but not universally good advice. Universal advice is too generic for you to not know it in advance. Good advice is the one which provides you with new information. Information is defined as \({\displaystyle I(X;Y)=H(X)-H(X|Y)\,}\). As you can see, the probability of the event (in our case the advice) should be low to provide you more information. A good practice is to negate the statement and then check if it is absurd, for example p = “We should focus”, ~p = “we should not focus”. ~p is too absurd hence it is generic and doesn’t provide us much value. On other hand, take q = “https://terrytao.wordpress.com/career-advice/make-your-work-available/”, ~q is not very absurd, it is tougher to argue but there is scope. Hence it is good advice.  1) should be less abundant  2) should be falsifiable 

Writing Matters

source: Writing Matters: Ravi Vakil, Professor of Mathematics at Stanford University

  • in mathematics, writing is more central because of the nature of the discipline which is centered around proof augmentation, and perspective, convincing people and making them understand
  • mathmatics not just about finding out WHAT is true and telling people what is true. We wanna know WHY it is true and we want to convince people that it is true. Also in retrospect it’s obviously true.
  • once you have an idea, you have to write it down. When you write it down clearly, concisely, and convincingly, that’s when you find out where the flaws in your thinking actually are. It is the revision, revision, revision process where you actually learn some of the most important mathematics. When you find gap in your argument, you realise that is where the heart really is, and that takes you back to days or weeks of further thinking. That’s where the real mathematics happens.
  • you should be able to convey the spirit of what you are doing with non-technical audience, and it is a difficult skill to learn.
  • the process of thinking is through doing what you are doing is very important.

Why Reviewing papers is important?

  • Reviewing papers is a great way to challenge yourself with a specific topic, and along the way, you will learn a lot of things related to it.
  • You will learn better ways to write, structure, and present your ideas.
  • Understand there is a human on the other side who will be reading your review. Hence, be careful about the language you use. Your task is not to judge them but to help them improve the paper to the best of your ability (do understand your limitations). Overall, it is in the spirit of science and scholarly communication.
  • Volunteering is very important for the community. It is a way to give back to the community and help others.

Talking about research is not the same as doing research

  • I am very gullible when it comes to believing in someone’s fancy words. Understand early, distinction between people who talk about research without actually understanding it and people who actually do research (or truly understand it). Do understand that you are not doing research just because you are talking about it. You are doing research when you are actually doing it. It is very easy to get on slippery slope of hype and lose sight of the actual research. As researcher we should be equipped to dismantle arguments, verify claims, and understand them.
  • It is very easy to lose confidence when someone throws a lot of fancy words at you.

I am here to learn

source: HERE TO LEARN (The Hard Way) | Tea Break

Find the simplest non-trivial example

source: My Advisor

Cognitive load

source: Veritasium: What Everyone Gets Wrong About AI and Learning – Derek Muller Explains

  • effortful thinking is required to activate the slow system.