About 2-4 times a month, I receive emails or Facebook messages from high school or early college students, usually in India, sharing their personal circumstances and asking me for help or advice. While I would like to respond to all requests carefully, I have many other demands on my time, so am not able to give personal attention to each query. I’m including below some of the common queries and the answers I usually give.

UPSHOT: If you send me an email with a query that’s among the ones below, or similar to some such query, I’ll either reply with something very similar to what I wrote below, or just link to this page or to one of the pages linked here. If you ask me a different question, I will again probably say I don’t know, plus give some links or suggestions for how you might explore the issue.

Please don’t take my lack of warmth or depth in response as a personal insult or a snub. It’s simply not scalable for me to respond in detail to individual questions. Often, the information that people seek is information that would take me a long time to collect, and that they could collect themselves in about the same amount of time (with some suggestions on where to look). If and when I do invest time in collecting the information, I’ll write up what I found and link to it, but until then, I can’t really be much help. It’s generally not possible for me to conjure up information beyond what I included below within a few days of receiving an email.

Query: I’m looking for advice on how to study mathematics or books related to mathematics or Olympiads.

Files describing my personal experience are available at my Olympiads page. As far as general resource lists go, see the contest mathematics learning recommendations I wrote for Cognito Mentoring, and also the answers to the Quora question What are the best resources for preparing for the IMO?.

The Cognito Mentoring wiki also has a lot of information, written up by me along with Jonah Sinick, on study habits and careers. Some of the college-related information is currently US-centric. We haven’t had time to expand on the wiki content after we moved Cognito Mentoring to maintenance mode.

If you have a very specific or narrow question, I might be able to answer it. For more general questions, if I haven’t had the time to write stuff up on the wiki, I probably won’t have time to write an elaborate response to your personal query.

What’s better, Chennai Mathematical Institute, Indian Statistical Institute, IIT, or some other institution? I didn’t get into [one or more of these], which one should I try?

The sad truth is that I haven’t been keeping track of the merits and demerits of individual institutions, that may have evolved considerably since my undergraduate days. I do describe my own undergraduate decision at my undergraduate institution selection page, and you should also read my undergraduate studies page and undergraduate experience page. But if you want more up-to-date information, you should look for more up-to-date suggestions. I have a few broad suggestions:

• Try Quora. For instance, you can get some idea about Chennai Mathematical Institute from the Quora topic on Chennai Mathematical Institute.
• Try one of the math problem-solving communities, such as the Art of Problem Solving or Brilliant. Brilliant in particular has a large number of participants from India, and you may be able to find people on the discussion boards who can give you an idea of the present state of various institutions.
• Some institutions might have (partial or complete) lists of their current students on their websites. For instance, Chennai Mathematical Institute lists its current students and alumni. Try contacting current students or recent alumni. But make sure you try the resources such as Quora and Brilliant first.

Somewhere on my list of things I’d like to do is “expand information on college possibilities for Indian students on the Cognito Mentoring wiki.” However, that is quite low on my priority list. If and when I do that, I’ll update this page to include relevant links.

What is the admission test for [insert institution here] like?

I did not have to take the Chennai Mathematical Institute admission test because I got direct admission due to my involvement with Olympiads. I did take the Indian Statistical Institute’s written admission test, but did not go for the interview. I also took the IIT-JEE. My vague memory of the ISI test, plus my impression of the CMI test, is that they were mostly like regional-level Olympiad questions, but perhaps also included some calculus. But you can probably get a better idea by looking at their sample tests. And for IIT-JEE, well, there’s a huge wealth of information on the Internet.

I want to eventually do a Ph.D. in the US. Is there any disadvantage of going to CMI/ISI relative to going to IIT?

My impression is that if you intend to do a Ph.D. in mathematics, CMI and ISI are comparable to, and arguably somewhat better than, IIT. For computer science, CMI is comparable to IIT. What matters more are your choices within college than your choice of college.

However, this is based on a very cursory impression. If I investigate the issue in more detail, I will put the details on the Cognito Mentoring wiki and link to it from here.

Anurag Bishnoi, a friend of mine currently pursuing a Ph.D. in mathematics, did his undergraduate studies at IIT Kharagpur. He opined that CMI would be better for people who intend to proceed to a mathematics Ph.D. He suggested looking at the following Quora answers of his related to coursework at the IITs: this, this, this, this. You might also want to check out other answers to the questions for which I linked to Anurag’s answers.

I want to take up a programming or finance or other kind of job. Does doing pure math preclude these possibilities?

Not really. Most of what you learn in college isn’t required for these jobs. I would recommend that if you want to make it easy to switch to programming jobs, join CMI rather than ISI. On the other hand, ISI is stronger on the statistics front.

It is the case that, if you join IIT, getting recruited immediately into a high-paying job in programming or finance is much easier. If you join CMI, you should not have trouble getting a programming job. But you may not immediately be able to land a high-status job. And unlike the case of IIT, you won’t have a huge number of recruiters reaching out to the college campus. You need to take more initiative.

Note that the above is based on general impressions that may be outdated. If I do a more thorough investigation, I’ll include the information on the Cognito Mentoring wiki and link to it from here.

I’d like you to become my mentor or coach or friend.

I do not have time to provide coaching or extensive guidance to individual students. But I do invite you to connect with me on Facebook, LinkedIn, Quora, LessWrong, and other places. If you just want to follow me or my thoughts, this would be an efficient way of doing so in a manner that is scalable for me. Friending me on Facebook can also help you find other people on my friend list who may have gone to the institutes you are interested in in the most recent past.

Many of the people who contact me are feeling frustrated at the lack of support or of like-minded people to talk to or seek guidance from given their interest in mathematics. If that describes you, I have a lot of empathy for you. However, it would not be feasible for me to provide personalized guidance to any of them. This isn’t scalable: my time and resources are better spent doing work that builds up the pool of general information and resources than coaching individual students.

The good news is that with the advent of the Internet, there are low-cost ways for you to connect to like-minded people and casually interact with them in ways that are more scalable and mutually beneficial. I recommend that you consider joining Art of Problem Solving, Brilliant, or finding like-minded people through Facebook, Quora, or other means.

How did you juggle preparing for the Olympiads with IIT preparation? How can I do so?

I describe my high school experience in detail here. Read through that. At the end of it I discuss some potential lessons for others and regrets I now have about how I did things. Take that and think about how to translate it to your own situation! Everybody’s situation is different. What worked for me may not work for you, but I hope it gives you food for thought.