I don't think I learned any mathematics as an undergrad

[TMO]

I got a B.S. in liberal arts and sciences from UIUC, with a concentration in general mathematics. My GPA, for a variety of reasons, is mediocre (2.5, roughly equal for math and non-math classes), but I nonetheless have an eye for graduate school. So I decided to look at the syllabus for the Harvard qualifying examination.

I realized that I don't know anything. Literally nothing. In fact, I think my knowledge is so bad that I might need to go through an undergraduate program for mathematics a second time. I want to go to graduate school because I would like to learn

(1) Why forms on differentiable manifolds generalizes vector calculus in such a way so that the methods and tools of vector calculus aren't arbitrary.

(2) How topological spaces can generalize much of real analysis without relying on an underlying metric.

So what should I do with my life?

 

[micromass]

I got a B.S. in liberal arts and sciences from UIUC, with a concentration in general mathematics. My GPA, for a variety of reasons, is mediocre (2.5, roughly equal for math and non-math classes), but I nonetheless have an eye for graduate school. So I decided to look at the syllabus for the Harvard qualifying examination.

I realized that I don't know anything. Literally nothing. In fact, I think my knowledge is so bad that I might need to go through an undergraduate program for mathematics a second time. I want to go to graduate school because I would like to learn

(1) Why forms on differentiable manifolds generalizes vector calculus in such a way so that the methods and tools of vector calculus aren't arbitrary.

(2) How topological spaces can generalize much of real analysis without relying on an underlying metric.

So what should I do with my life?

If your main goal is to get an answer to your two questions, then that' not really a good reason to go to graduate school. You can just think about it yourself or read a good book on the matter.

In fact, with a 2.5 GPA, your chances for grad school are practically zero. I'm sorry to say it, but it would be better to think of something else that you can do with your life.

 

[TMO]

I'm sorry to say it, but it would be better to think of something else that you can do with your life.

(1) Rot in cubical hell in some fortune 500 company.
(2) Manual labor.
(3) Army.
(4) Start my own company and pray to God that it doesn't go bankrupt.

Gee, look at all the possibilities I have with my life. </sarcasm>

 

[micromass]

Nobody said that you will necessarily enjoy grad school either.

Surely there must be something you enjoy doing aside from math? Teaching for example?
In the end of the day, a job is there to get you money to survive. It's fun if you enjoy it, but many people don't enjoy their job and their life is still fine. There are enough fulfilling things to do outside of your job.

 

[TMO]

In the end of the day, a job is there to get you money to survive. It's fun if you enjoy it, but many people don't enjoy their job and their life is still fine. There are enough fulfilling things to do outside of your job.

Most people spend their live raising their children (which is a recursive process with no terminating case), getting drunk and partying, and talking over sports with their friends. In comparison with the previous, mathematical research at least holds the promise of elevating life to something beyond a farce.

 

[Student100]

(1) Rot in cubical hell in some fortune 500 company.
(2) Manual labor.
(3) Army.
(4) Start my own company and pray to God that it doesn't go bankrupt.

Gee, look at all the possibilities I have with my life. </sarcasm>

What's wrong with the Army? In fact, it may be good for you.

You haven't addressed why you did so poorly to begin with. Why are you assuming that if you retook a second bachelors in the same field (easier said than done) that you'd do any better? America is the land of second chances, if you really wanted to go to Grad school there is probably way to do that; that said, you probably need to mature a bit first. You should seriously consider just trying to find employment, which is also easier said than done, before you start knocking it.

 

[micromass]

Most people spend their live raising their children (which is a recursive process with no terminating case), getting drunk and partying, and talking over sports with their friends. In comparison with the previous, mathematical research at least holds the promise of elevating life to something beyond a farce.

You shouldn't be so dismissive of people trying to have a simple life. As long as they're happy, I don't see the problem.
And mathematical research isn't really so glorious either. You spend all your time thinking on something and working on a paper to publish, and eventually only a very few people will ever read what you did. Mathematics research nowadays is completely useless except for doing mathematics itself. This is not only true for mathematics, most academic research is useless. Only very few researcher in mathematics or wherever get to do something useful to society.

 

[e.bar.goum]

Most people spend their live raising their children (which is a recursive process with no terminating case), getting drunk and partying, and talking over sports with their friends. In comparison with the previous, mathematical research at least holds the promise of elevating life to something beyond a farce.

I'm sure you didn't intend to insult the (roughly) 98.2 % of people in the US without a PhD. Or something like 99% of the world's population. Because nobody would be that much of an intellectual snob to think that having a PhD is the only way to live a fulfilled life, right?

It's not like people can possibly find fulfilment teaching, or gardening, working for startups, or for big companies, or acting, or raising children, or having a dog, or reading, or in politics, or sport, or enjoying hobbies like knitting (or ham radio, or windsurfing), or going camping, or exploring the world, or having close friendships, or helping out those who need it most in the community. Or any number of the different things that people do with their lives. Nah, that's impossible.

No, there's only one way for life not to be a farce. Mathematics research. Said nobody ever.

Look, perhaps for you the only way to be happy is mathematics research. Which, hey, is a little odd, but there are 7 billion people in the world and stranger things have happened. Probably. In which case, you'd better figure out how you got a 2.5 GPA and fix it.

 

[TMO]

I'm sure you didn't intend to insult the (roughly) 98.2 % of people in the US without a PhD. Or something like 99% of the world's population. Because nobody would be that much of an intellectual snob to think that having a PhD is the only way to live a fulfilled life, right?

It's not the PhD. That's just a piece of paper. It's coming up with an idea that changes the world. Am I a snob because I find the typical human's desire for food, shelter, clothing, and sex to be settling for far less than they should? It's like 98.2% are children making mudpies who are given a chance by their parents to go to the beach, but refuse to do so because they do not understand what it is meant by going to the beach.

 

[micromass]

It's coming up with an idea that changes the world.

You won't be able to do that if you pursue math. Do math because you enjoy it, not because you want to change the world or become famous.

 

[TMO]

You won't be able to do that if you pursue math. Do math because you enjoy it, not because you want to change the world or become famous.

You don't think Euclid or Pascal changed the world?

 

[micromass]

Am I a snob because I find the typical human's desire for food, shelter, clothing, and sex to be settling for far less than they should?

This at least indicates that you do have food everyday, that you do have shelter or clothers. If you didn't you would be talking very differently.

 

[micromass]

You don't think Euclid or Pascal changed the world?

They lived at least hundreds of years ago!
And not every mathematician will be able to be like Euclid or Pascal. The vast majority isn't.

 

[TMO]

This at least indicates that you do have food everyday, that you do have shelter or clothers. If you didn't you would be talking very differently.

All of those things are needs and very important, and I am certainly thankful for them, but life is so much more than food for the stomach and raiment for the skin. I am looking to do something with my life that at least strives for these higher, better things.

 

[Mirero]

All of those things are needs and very important, and I am certainly thankful for them, but life is so much more than food for the stomach and raiment for the skin. I am looking to do something with my life that at least strives for these higher, better things.

One doesn't have to become a world-famous mathematician to help the world become a better place.

 

[TMO]

One doesn't have to become a world-famous mathematician to help the world become a better place.

Yes, but keep in mind that a man who compares himself by himself is not wise. There were many people that sought to make the world a better place... in their own eyes. But the vast majority of those people (I can think of the two women who heckled Bernie Sanders recently) don't actually do good, even though they believe that they are doing good, simply because they are comparing themselves with themselves.

 

[e.bar.goum]

One doesn't have to become a world-famous mathematician to help the world become a better place.

In fact, I'd argue that a person who makes really nice icecream and sells it at a farmers market brings far more joy to the world than the average mathematician. The really excellent teacher changes far more lives than the average mathematician too.

 

[Student100]

All of those things are needs and very important, and I am certainly thankful for them, but life is so much more than food for the stomach and raiment for the skin. I am looking to do something with my life that at least strives for these higher, better things.

Your parent's/guardians lackluster life probably provided you this opportunity to study, why did you squander it? Figure out how to undo the mess you got yourself into. That starts with taking a good long look at yourself in the mirror, reflecting on everything that went wrong without shifting the blame to external circumstances.

Get a job, gain some life experiences and learn to have an appreciation for everything that's been provided to you. After that, attempt to find a school that will accept you for a second math bachelors. Hopefully the maturity you gain during the hiatus in school will propel you to do better. It will also show that went out into the world, and came back a more studious student to potential grad schools.

At some point you may have to accept you'll never get into grad school though, nothings guaranteed.

 

[TMO]

In fact, I'd argue that a person who makes really nice icecream and sells it at a farmers market brings far more joy to the world than the average mathematician. The really excellent teacher changes far more lives than the average mathematician too.

So am I a fool for wanting to do to mathematics what Pascal did, and lay a new foundation for viewing reality?

 

[micromass]

So am I a fool for wanting to do to mathematics what Pascal did, and lay a new foundation for viewing reality?

If that's your main goal for going into grad school: yes.

 

[TMO]

If that's your main goal for going into grad school: yes.

Then I don't what to go to grad school. I'll find another use for my time.

 

[Student100]

Then I don't what to go to grad school. I'll find another use for my time.

Get off your grandiose high horse, it obviously isn't doing you any good. I imagine that was one of your faults in school.

 

[micromass]

The thing is that science is so very specialized nowadays. It's not like hundred of years ago where one person could totally transform the way we see math and science. Math and science are still being transformed every day by researchers, but it takes a lot of people for a small change.

 

[e.bar.goum]

So am I a fool for wanting to do to mathematics what Pascal did, and lay a new foundation for viewing reality?

Yes and no. Mostly no, and for several reasons. Yes: it's nice to have noble goals. No: Most, perfectly successful, academics don't change the world. They learn small things, and add small things to the huge pile that is the sum total of all human knowledge. This is a perfectly good way to be fulfilled (I'm a PhD student, I've bought into this idea), but it's not the only way to be a fulfilled human being.

 

[Kilgour22]

So am I a fool for wanting to do to mathematics what Pascal did, and lay a new foundation for viewing reality?

While it's great to want to change the world, keep in mind that no one who's changed the world has set out on their journey with that specific goal.

Going to grad school isn't going to make you any more able to change the world than you are right now. Discoveries in mathematics aren't taught to students, they're DISCOVERED. It's not a good thing to want to be in grad school just to elevate yourself above the general populous in a superficial way. Strive for grad school only if you truly enjoy mathematics and can appreciate its intrinsic beauty. I bet if you were to ask mathematicians why they decided to get into mathematics, they would answer with something along the lines of "Mathematics is beautiful and it is a privilege to be able to explore and analyze it every single day", rather than "I wanted to become famous by discovering something that changes how the world functions". People get Ph.D's in a field because they love it and are truly interested in the subject, not out of selfishness.

Correct me if I'm wrong, but you also seem to be very ungrateful about having everything you need to survive. Not everyone is in such a privileged position to pick and choose based on their wants and not just their needs. I advise you to get out and travel and experience some culture shock; it'll change your perspective on how diverse the lives of humans are.

 

[radium]

If you have gone through undergrad without learning anything in your major, what makes you think you would like (or be good at) doing research in this field? You say your GPA is a 2.5 for a variety of reasons but then state you feel like you don't know the material. Don't you think that's the reason you have a 2.5? There's really no justifying that if this is the case.