Is it recommended to invest in stocks as a typical broke graduate students? I openly admit that I am financial illiterate and for most of my life neither know about nor cared about investing. I am currently doing research in a field that is tangentially, but not exactly related to financial mathematics (say physics: a lot of Brownian motions and what not going on). 

What has gotten me interested is over time is that I've met many people (who are much younger than me, like 19 years old right out of highschool) who are investing in stocks WHILE doing research. In fact, they appear to know a lot more than I do, which makes me feel a bit self-conscious and inadequate.

What has prevented me from doing the same:


Basically no family member or close connections who can guide me. Not born with a silver spoon. 
Research is a lot of work and requires dedicated focus. Can't imagine rushing a deadline while managing my assets. 
I literally have not taken a single course in finance, and assumed it would be easy given my extensive graduate school level math background. But I have no idea where to get started. 
No money. This is one of the key reason. I am your typical 20s something scholarship-living graduate student in North America. If I am investing anything it is my TA stipend or my scholarship itself (which I will need to pay back at the end of the semester). I literally do not have any other income source and cannot even take a hit of a few hundred dollars.  


1, 2, 3 I can fix, but I am worried about 4. 

Is there any advice on stock investments during your grad school for people who have tried their hands, especially if you were living as a low-paid graduate student like me?

Is it possible to achieve a balance between research, life and managing your finances?
Don't even think about investing until you've saved an emergency fund enough to cover at least 3 to 6 months (and perhaps a year) of living expenses.

Due to exponential growth, investing earlier does have huge advantages, but for PhDs in many fields you make more than enough after PhD that you will be able to invest enough to retire comfortably even if you save nothing before you get your PhD, so there's no reason to be stressed about this until you graduate.  And you may need your emergency fund for the time between graduation and your first job.  Once you have your first job out of graduate school and have saved an emergency fund then you can think about this.