How much does reputation of the grad program matter

[I like math and CS a lot]

I go to a mid tier university. There is a prof I've worked with during my undergrad research and I liked working with the prof and the research was interesting. If it was a top school, I'd definitely apply to it for masters and phd and try to work with the same prof. But it is not. The prof is great but I dont wanna risk my career because I know that most phds never make it beyond grad school but I want to research all my life. Is it still possible to make a career in research even if you go to a mid university?,

[AverageEccentric]

There's no absolute answer to this, and roll your eyes at anyone who insists differently.  

It varies from field to field, but if you're seeking to become an expert in a specific niche, you have to study under someone(s) who can train you in that specific niche, and the top-tier schools do not have people in every single niche.  

It's also absolutely not true that "most PhDs never make it beyond grad school."  It sounds like you're thinking there's only one extremely narrow and specific way you can research your whole life (IE a tenure-track university position), which is **absolutely** not the case.  

It is true that there's a somewhat higher rate of folks getting a tenure-track position straight out of the "top tier" schools and those schools do have better funding.  They also have their own drawbacks (they're often more stubborn about only funding specific research that's trendy at the moment, beholden to specific giant donors, and sometimes outright horrible places to be).  And where did those top-tier programs get their professors?  From mid-tier or lower-tier institutions (after said prof somehow made it big).  

However, sometimes the top-tier schools don't have programs at all in something that suddenly will be in high demand, or the experts in your specific niche, or the department that's the right size for you.  Or the approach to research and methodologies that you know in your gut to be the right way to go.  

For instance in my field, the Ivies and other US News "top 25" programs don't love interdisciplinary work, often have small departments, and are mostly opposed to theory.  They're also freaked out by certain topics at the moment and defunding certain lines of thought to comply with political demands.  My work is considered by some to be "radical", it's multidisciplinary to the extreme, I use theory a lot and want to make theory, and it also has to do with topics taught most at "land-grant institutions" ... Furthermore, if I look at the job listings for professors in my field, I see a lot of requests for 5 specific "buzzwords" ... "if you can do 2 of these we'd especially want to hear from you" and HA I found a program where I can hit all 5.  2 specific subfields within my discipline aren't being taught much at all at the "Top tier" and are being taught *a lot* at the mid and lower tier.  

A lot of "top tier" are like the Titanic: they're so big and so entrenched they cannot turn in response to changing demands.  They can afford to stay "old school" because wealthy elites; meanwhile less-famous programs can take risks, change quickly, experiment, and maybe the prof you need is starting out their cool new thing there right now (before they get knicked by an Ivy after they've hit it big).  

Also keep in mind that the US News rankings are partly informative, partly total BS. They measure something very specific.  You're a researcher, go read their methodology statement.  There's a lot they don't say.  

The other side of that is that in order to get into a program, you as a candidate also have to stop thinking "how to be the best" but "how to be the most authentic version of an expert in this niche that fascinates me" and learn how to articulate not how good you are, but what problems you want to solve with your research. 

I did a PhD Pipeline program run by THE top tier (as in, ranked #1-#3 by US News) program in my field.  They advised a few things:  #1 don't go straight from undergrad into a PhD program.  #2 don't get into debt for a PhD unless you're *absolutely sure* (IE go for a funded program, any funded program, and some of those good funded programs are at institutions otherwise called "bottom tier").  #3 "Focus more on fit (find an advisor who is the expert in the thing you want to do) than on reputation" (specifically saying US News, even their own ranking, was mostly baloney), and #4 Don't go straight from undergrad to a PhD.  Take a year, get some work experience.  Maybe do an MA, not necessarily in exactly the same field maybe a complementary one.  

If that's not convincing I'll also note:  My "best fit" came from a "mid tier" program.  The people at that #1 institution said "Yes, that's a better fit for you than us, because we don't teach ___ unfortunately ... even though it's become crucial, our program hasn't changed course as quickly as others."  I also found out that the prof I wanted to work underneath at #1, because of her cutting-edge work, had herself turned down an opportunity to get her PhD at #1 and selected the "mid tier" program which is so far my own best fit (and then she went straight to the tenure track at #1, though apparently the cutting edge thing I wanted to learn from her isn't something she gets to teach a lot yet).  

Maybe go talk to the career center at your university.  There are TONS of ways to do research forever.  

Edited March 9 by AverageEccentric

[Laboni765]

Yes, it is absolutely possible to build a research career from a mid-tier university. The university’s reputation can influence opportunities, especially for highly competitive academic positions, but it is not the only factor that matters.

For a research-focused career, I would pay particular attention to the advisor and research environment. Working with a professor you already know, whose research genuinely interests you, can be a significant advantage if they are actively publishing and have strong collaborations.

During a PhD, things such as quality of publications, research experience, conference participation, collaborations, and recommendation letters can become much more important than the name of the institution alone.

I would not choose a program solely because it has a higher ranking if the research fit and mentorship are substantially worse. If your goal is to stay in research, having an advisor who can help you develop a strong research profile may be more valuable than choosing a more prestigious school with a poor fit.