Pure mathematics vs Mechanical engineering

[ode_to_joy]

This year, I will apply for University of Waterloo, and I am quite certain that I will attend this university. But I have been having trouble of deciding my major. Of course, I don't want you to determine my major on in stead of my self! I am asking for advice.

I really liked playing with legos since I was 5. I still do. This is the biggest appeal to mechanical engineering. I have always liked machines and chains and cams. Also, the job market is a lot better than pure math majors. But I feel like this is my alternative choice becase I am not smart enough to sustain a career in academia and stand the publish or perish pressure. (No offense to engineers but, statiscally or generally, pure math requires rigorus understanding of concept hence they need to be smarter)

I liked math too. Really. Especially numbers. And I feel like, I will certainly regret at the moment of my death not for dedicating my lifetime to pursue mathematics. The main reason I am pessimistic about math is I am not smart as Terence Tao, or even IMO medalists. They are too far ahead of me. I have seen tons of threads that say I don't need to be super smart to do mathe, but at least there is a minimum boundary. Apparently, you will discover your talent or elgibility in math after masters degree. I will not be unhappy with non-academic jobs.

I am really looking forward to some advice and thanks in advance.

 

[Kevin_Axion]

This year, I will apply for University of Waterloo, and I am quite certain that I will attend this university. But I have been having trouble of deciding my major. Of course, I don't want you to determine my major on in stead of my self! I am asking for advice.

I really liked playing with legos since I was 5. I still do. This is the biggest appeal to mechanical engineering. I have always liked machines and chains and cams. Also, the job market is a lot better than pure math majors. But I feel like this is my alternative choice becase I am not smart enough to sustain a career in academia and stand the publish or perish pressure. (No offense to engineers but, statiscally or generally, pure math requires rigorus understanding of concept hence they need to be smarter)

I liked math too. Really. Especially numbers. And I feel like, I will certainly regret at the moment of my death not for dedicating my lifetime to pursue mathematics. The main reason I am pessimistic about math is I am not smart as Terence Tao, or even IMO medalists. They are too far ahead of me. I have seen tons of threads that say I don't need to be super smart to do mathe, but at least there is a minimum boundary. Apparently, you will discover your talent or elgibility in math after masters degree. I will not be unhappy with non-academic jobs.

I am really looking forward to some advice and thanks in advance.

I'm in the exact same predicament as you, by exact I mean I'm looking at the same university.

 

[cmb]

Society values accountants/business types/lawyers, etc., more than engineers and mathematicians. Do engineering activities as hobbies and go think about what will earn you good money to pay for you to do all the lego, chains and cams you want.

 

[ode_to_joy]

Society values accountants/business types/lawyers, etc., more than engineers and mathematicians. Do engineering activities as hobbies and go think about what will earn you good money to pay for you to do all the lego, chains and cams you want.

well, if one is a full professor at a decent university, wouldn't people value him/her more than accountants? I do agree with the fact that lawyers are higly respected but not sure why accoutants deserve more respect than mathematicians or engineers (no offence)

 

[nlsherrill]

Society values accountants/business types/lawyers, etc., more than engineers and mathematicians. Do engineering activities as hobbies and go think about what will earn you good money to pay for you to do all the lego, chains and cams you want.

^Great advice. Not.


Since you(the OP) said "And I feel like, I will certainly regret at the moment of my death not for dedicating my lifetime to pursue mathematics.", then why would you consider anything else? I feel you have a misconception about mathematics. Yes it is a very tough subject, but why would you count yourself out like that? If you love it, then I am sure your determination can prevail.

Forget about what society values. 99 percent of the population doesn't know anything about how real mathematics is done. Do you really want to be sitting at your job in a few years wondering what an adventure studying something and possibly working in a field you love could have been like?

 

[chiro]

This year, I will apply for University of Waterloo, and I am quite certain that I will attend this university. But I have been having trouble of deciding my major. Of course, I don't want you to determine my major on in stead of my self! I am asking for advice.

I really liked playing with legos since I was 5. I still do. This is the biggest appeal to mechanical engineering. I have always liked machines and chains and cams. Also, the job market is a lot better than pure math majors. But I feel like this is my alternative choice becase I am not smart enough to sustain a career in academia and stand the publish or perish pressure. (No offense to engineers but, statiscally or generally, pure math requires rigorus understanding of concept hence they need to be smarter)

I liked math too. Really. Especially numbers. And I feel like, I will certainly regret at the moment of my death not for dedicating my lifetime to pursue mathematics. The main reason I am pessimistic about math is I am not smart as Terence Tao, or even IMO medalists. They are too far ahead of me. I have seen tons of threads that say I don't need to be super smart to do mathe, but at least there is a minimum boundary. Apparently, you will discover your talent or elgibility in math after masters degree. I will not be unhappy with non-academic jobs.

I am really looking forward to some advice and thanks in advance.

Hey ode_to_joy.

The first suggestion I wish to offer you is to not think about success on a purely social level. You do not owe the world ground-breaking discoveries and the world surely has no right to demand that in order to be a scientist, that you need to get a Nobel Prize.

If you want to maths because you like maths, or because you are enthusiastic and want to help others learn maths, or because you want to do maths as a means to doing something else (like an applied mathematician helping others make more informed decisions which happens everywhere, whether its health, government, pharmaceutical, finance, insurance, etc), then that is a good reason for doing maths. If you are doing maths for the reason of getting accolades, or because you think you need accolades for your work, then this is not a good reason, and it could cause you severe mental health problems.

Also remember that life can be a gamble, and sometimes things just don't work out. We all hear about the successes like the Nobel Prize winners, and Fields Medalists, the successful billionaire entrepreneurs and so on, and this has created a very dangerous psychological culture of success.

If you like maths and want to explore it, then with the right attitude and work, you should be able to learn math and apply it somewhere as a living.

However in saying the above, you should be researching any major life decision you make and use that knowledge to make a calculated risk. If your research shows that there are only 100 theoretical physicists in the country and there are 2000 people qualified for the job, then that should be a red flag. You should also, in your research, know your alternatives, and be open about the possibility that it may in fact not be an "alternative" any more.

There are many experienced members with a diverse range of careers that can give you their take and I recommend you get a diverse list of experiences to make a more unbiased informed decision. The fact is that most of us have very specific experiences, and even with the utmost honesty, anyone can not be aware of what else is out there: it may even be a stone's throw away from their/your backyard.

Your last line suggests however that you are not considering alternatives, and this might be a signal to you, that perhaps doing math may be something you should think twice about. I could be wrong though, you could put 110% focus into your work and get into the exact area that you planned on getting into, but many experienced people on here will tell you that this can be a very risky thing to do.

 

[ode_to_joy]

^Great advice. Not.


Since you(the OP) said "And I feel like, I will certainly regret at the moment of my death not for dedicating my lifetime to pursue mathematics.", then why would you consider anything else? I feel you have a misconception about mathematics. Yes it is a very tough subject, but why would you count yourself out like that? If you love it, then I am sure your determination can prevail.

Forget about what society values. 99 percent of the population doesn't know anything about how real mathematics is done. Do you really want to be sitting at your job in a few years wondering what an adventure studying something and possibly working in a field you love could have been like?

I tend to (or at least try to) not to care about what others think of me, unless my financial status is deplorable so that I am unable to maintain my life, family, hobbies, etc.

But the problem is, I don't know if I can survive among those so called geniuses. That;s the main reason I am considering engineering. In case of engineering, you don't have to be the top students (very few), as long as you belong top percentile (relatively larger group). Also, I don't know if I can stand the pressure.

 

[ode_to_joy]

Hey ode_to_joy.

The first suggestion I wish to offer you is to not think about success on a purely social level. You do not owe the world ground-breaking discoveries and the world surely has no right to demand that in order to be a scientist, that you need to get a Nobel Prize.

If you want to maths because you like maths, or because you are enthusiastic and want to help others learn maths, or because you want to do maths as a means to doing something else (like an applied mathematician helping others make more informed decisions which happens everywhere, whether its health, government, pharmaceutical, finance, insurance, etc), then that is a good reason for doing maths. If you are doing maths for the reason of getting accolades, or because you think you need accolades for your work, then this is not a good reason, and it could cause you severe mental health problems.

Also remember that life can be a gamble, and sometimes things just don't work out. We all hear about the successes like the Nobel Prize winners, and Fields Medalists, the successful billionaire entrepreneurs and so on, and this has created a very dangerous psychological culture of success.

If you like maths and want to explore it, then with the right attitude and work, you should be able to learn math and apply it somewhere as a living.

However in saying the above, you should be researching any major life decision you make and use that knowledge to make a calculated risk. If your research shows that there are only 100 theoretical physicists in the country and there are 2000 people qualified for the job, then that should be a red flag. You should also, in your research, know your alternatives, and be open about the possibility that it may in fact not be an "alternative" any more.

There are many experienced members with a diverse range of careers that can give you their take and I recommend you get a diverse list of experiences to make a more unbiased informed decision. The fact is that most of us have very specific experiences, and even with the utmost honesty, anyone can not be aware of what else is out there: it may even be a stone's throw away from their/your backyard.

Your last line suggests however that you are not considering alternatives, and this might be a signal to you, that perhaps doing math may be something you should think twice about. I could be wrong though, you could put 110% focus into your work and get into the exact area that you planned on getting into, but many experienced people on here will tell you that this can be a very risky thing to do.

Hi chiro,

Well, these are my aptitudes, I guess
1)I love math. I enjoy sitting on a comfortable chair, listening to classical musics, and try to explore the concept of mathematics theorem. (of course, when I do my coursework, I do not have these luxurious times) I get goosebumps when I understand concepts that I have heard of left by famous mathematicians.
2)But if I don't understand it, I get really stressed. Especially when people around me get in few seconds
3)I cannot deny the fact that I do desire glory. I will be really depressed if I eventually come up with a new theorem then realize that it's already been published.
4)Also, I really enjoy appling mathematics to other stuff, like physics or economics.

In the last line, I think I was bit unclear with my double negatives. I will be happy with non-academic jobs such as finance jobs or government jobs.

 

[cmb]

^Great advice. Not.

Please yourself. The thing is; do what you love for a job and it can go two ways - you are super-duper happy, or you end up hating the thing you once loved. I deduce it is usually the latter as I haven't met anyone truly in the former category.

Some do make jobs out of their hobbies, but that tends to imply they have had another job first so as to fund the hobby in the first place.

I would advise anyone against doing exactly what they enjoy the most as a job, because they may come to resent the thing they once loved. Do something close, if you will, but not exactly the thing.

Accountancy is close enough to maths in the real world. Savour the stellar evolution/rocketry/logic puzzles/whatever-maths-people-like-to-do in their own time, without a boss breathing down your neck for a result to the point that you think 'I HATE THIS!', because most do, and at some point you'll be groaning out of bed every morning thinking 'I hate my job' which, if it is also the thing you like the most, means you hate everything else even more. A recipe for misery.

 

[chiro]

In case of engineering, you don't have to be the top students (very few), as long as you belong top percentile (relatively larger group). Also, I don't know if I can stand the pressure.

You'll have pressure in engineering. It may not be the same pressure you have doing a full graduate load of pure maths, but it will be pressure none the less.

 

[chiro]

Hi chiro,
Well, these are my aptitudes, I guess
1)I love math. I enjoy sitting on a comfortable chair, listening to classical musics, and try to explore the concept of mathematics theorem. (of course, when I do my coursework, I do not have these luxurious times) I get goosebumps when I understand concepts that I have heard of left by famous mathematicians.

From personal experience, I have the same thing. When you finally understand something no matter how little, it can be very enlightening.

2)But if I don't understand it, I get really stressed. Especially when people around me get in few seconds

As you go higher up the food chain, this becomes the norm. Don't feel bad about this, we all face it sometime or another, and it is nothing to be ashamed about. Really high level mathematics is hard, confusing, and in some ways it's like these guys are on stage pulling rabbits out of hats when proving a theorem. Don't be discouraged, but know that everyone will at some point reach their limits if the pursuit of learning is genuine.

3)I cannot deny the fact that I do desire glory. I will be really depressed if I eventually come up with a new theorem then realize that it's already been published.

This is a big problem. If you want glory, there are other areas that are a lot easier than mathematics to attain this "glory" you speak of. Science and mathematics are two areas that require more "glory purchasing power" than other fields.

I guess at the end of the day you have to be honest about what you want to get out of anything in life, and that is a natural thing for all of us to face at least once.

4)Also, I really enjoy appling mathematics to other stuff, like physics or economics.

With that mindset, I don't think you'll have trouble finding something for a career if you play your hand right.

 

[ode_to_joy]

From personal experience, I have the same thing. When you finally understand something no matter how little, it can be very enlightening.



As you go higher up the food chain, this becomes the norm. Don't feel bad about this, we all face it sometime or another, and it is nothing to be ashamed about. Really high level mathematics is hard, confusing, and in some ways it's like these guys are on stage pulling rabbits out of hats when proving a theorem. Don't be discouraged, but know that everyone will at some point reach their limits if the pursuit of learning is genuine.



This is a big problem. If you want glory, there are other areas that are a lot easier than mathematics to attain this "glory" you speak of. Science and mathematics are two areas that require more "glory purchasing power" than other fields.

I guess at the end of the day you have to be honest about what you want to get out of anything in life, and that is a natural thing for all of us to face at least once.



With that mindset, I don't think you'll have trouble finding something for a career if you play your hand right.

I don't know if it is possible that a human being can be abstinent for desire for glory. I mean, winning glory is not the main reason that I want to pursue mathematics. But isn't it something that is always accompanied by?

 

[chiro]

I don't know if it is possible that a human being can be abstinent for desire for glory. I mean, winning glory is not the main reason that I want to pursue mathematics. But isn't it something that is always accompanied by?

We all need some kind of affirmation that what we are doing means something in some respect.

It might be the mother raising the child putting in all of their effort hoping that their child will one day grow up to someone who has good values and do something that will make them proud.

On the other hand it could be the sportsperson who trains day in day out hoping that they will play in and win the grand final.

As you can see these two examples do share some common threads, but in the first, the glory is a lot more private than the second one. The sportsperson will be in front of a large crowd and in the spotlight, while the mother will be at home out of the spotlight. Thousands of people will see the sportsperson play, but no-one will usually see or even know about the effort that the mother puts into raise their child.

So in this context, you have to ask yourself what glory you want to achieve and whether it is highly social or highly personal. Is the glory just the nature of finding something out, or does it have to do with having high acceptance from your peers?

This is what you will have to think about.

 

[micromass]

I don't know if it is possible that a human being can be abstinent for desire for glory. I mean, winning glory is not the main reason that I want to pursue mathematics. But isn't it something that is always accompanied by?

Human beings desire glory, that is true. And you can't put it aside completely. But you have to anyway. If you don't, then you will become very disappointed with your life. Basically: if you feel the need to please others, then you well never be satisfied. Other people are hell, you can't please them.

Would you be pleased if you won the Nobel?? Really?? No, you wouldn't be pleased. You would desire more and more. The clue is not to desire anything at all. Desiring something will get you nowhere.

A misconception that I would like to rectify: "mathematicians are smarter than engineers". I understand why you would think that, but it is totally false. Engineers have to know the theoretical knowledge (a bit) and apply it to the real world. This is much harder than just having theoretical knowledge. In fact, comparing people with "smarter" is useless. But I know that I'm a mathematician and that I could never succeed in engineering! (and undoubtly, there will be engineers that would never be able to do math).

You don't need to be Terrence Tao or an IMO medaillist to do math. Many math students are very normal people with average intelligence. The only things you need is an insatisfiable passion for math and persistence.

Lastly: math is not what you think it is. Math is not about playing with numbers at all. You will only understand what math is if you took some advanced course on the subject!
Mechanical engineering is also not what you think it is.

Do some courses from both majors and pick one then. But please, do not go into a field for the "glory" or the "prestige".

 

[ode_to_joy]

We all need some kind of affirmation that what we are doing means something in some respect.

It might be the mother raising the child putting in all of their effort hoping that their child will one day grow up to someone who has good values and do something that will make them proud.

On the other hand it could be the sportsperson who trains day in day out hoping that they will play in and win the grand final.

As you can see these two examples do share some common threads, but in the first, the glory is a lot more private than the second one. The sportsperson will be in front of a large crowd and in the spotlight, while the mother will be at home out of the spotlight. Thousands of people will see the sportsperson play, but no-one will usually see or even know about the effort that the mother puts into raise their child.

So in this context, you have to ask yourself what glory you want to achieve and whether it is highly social or highly personal. Is the glory just the nature of finding something out, or does it have to do with having high acceptance from your peers?

This is what you will have to think about.

I would say both. I want personal enjoyment by discovering something new and admiration from other people. However, these are not the original motivation. I want glory in return for my hard work, but I will not work for glory. I don't know if this makes sense but, what I am trying to say here is, glory is not the main reason, but I would never give my theorem to random bloke on the street and take my credit.

 

[ode_to_joy]

Human beings desire glory, that is true. And you can't put it aside completely. But you have to anyway. If you don't, then you will become very disappointed with your life. Basically: if you feel the need to please others, then you well never be satisfied. Other people are hell, you can't please them.

Would you be pleased if you won the Nobel?? Really?? No, you wouldn't be pleased. You would desire more and more. The clue is not to desire anything at all. Desiring something will get you nowhere.

A misconception that I would like to rectify: "mathematicians are smarter than engineers". I understand why you would think that, but it is totally false. Engineers have to know the theoretical knowledge (a bit) and apply it to the real world. This is much harder than just having theoretical knowledge. In fact, comparing people with "smarter" is useless. But I know that I'm a mathematician and that I could never succeed in engineering! (and undoubtly, there will be engineers that would never be able to do math).

You don't need to be Terrence Tao or an IMO medaillist to do math. Many math students are very normal people with average intelligence. The only things you need is an insatisfiable passion for math and persistence.

Lastly: math is not what you think it is. Math is not about playing with numbers at all. You will only understand what math is if you took some advanced course on the subject!
Mechanical engineering is also not what you think it is.

Do some courses from both majors and pick one then. But please, do not go into a field for the "glory" or the "prestige".

Hi Micromass,

I am sorry if you are an engineer and offended you, but my default assumption was, engineers usually get into industry with a Bachelors Degree while a PhD is required for (I would say all) mathematicians. Of course, engineers who have PhD and work in research are as smart as mathematicians. Or it is not even ethical to divide people into groups according to their intelligence, but I thought it;s the general consensus.

Hmm, I don't know what would I desire more if I win the Fields Medal or the Nobel Prize, but I guess it is true in the sense that human beings have a propensity not to satisfy with current status, maybe just like those capitalists that those communists criticize (in 20th century).

 

[micromass]

Hi Micromass,

I am sorry if you are an engineer and offended you, but my default assumption was, engineers usually get into industry with a Bachelors Degree while a PhD is required for (I would say all) mathematicians. Of course, engineers who have PhD and work in research are as smart as mathematicians. Or it is not even ethical to divide people into groups according to their intelligence, but I thought it;s the general consensus.

Hmm, I don't know what would I desire more if I win the Fields Medal or the Nobel Prize, but I guess it is true in the sense that human beings have a propensity not to satisfy with current status, maybe just like those capitalists that those communists criticize (in 20th century).

I'm a mathematician, so you didn't offend me. I just wanted to address the misconception that math people are very smart. They are not. They just enjoy what they do and they work hard. That's everything there is to it!

 

[chiro]

I would say both. I want personal enjoyment by discovering something new and admiration from other people. However, these are not the original motivation. I want glory in return for my hard work, but I will not work for glory. I don't know if this makes sense but, what I am trying to say here is, glory is not the main reason, but I would never give my theorem to random bloke on the street and take my credit.

No one would expect you to do that. You reap what you sow, and you should rightly the reap the rewards of your own work.

Having said, I would urge you to consider micromass's advice and not get into mathematics for the glory, because you will probably end up with depression or something akin to that just by probabilities alone.

 

[ode_to_joy]

Once I asked a question to my professor said, (well, actually not MY professor, I just went to a math camp at a nearby university), "Should I have to be born a genius to do math?", he said "No, you don't born a genius, you BECOME a genius as you study harder and explore the world". First I thought it was just a white lie not to disappoint me. But then I realized, if I have time to complain about my relative intellectual inferiority, I would go grab a math book and study.

But I still cannot deal with the accolade part. I mean, all human beings will be disappointed if somebody else publish a theorem that is exactly what they were working on. If they realized that the years that they have spend or their lifetime of effort (if you saw Fermat's Room) have been dissipated, they might have to go see a psycharist (or at least I will). My question is, how will I deal with this situation?

 

[ode_to_joy]

I don't think (or at least hope) the kind of person who is like "Oh Riemann's Hypothesis is one of the seven millenium problem. I have got to work on that problem and will earn an eternal glory!" but I am like "So apparently, I know I don't understand the hypothesis correctly, but how is it related to prime numbers?" And spend a decade on that problem, then someone else publishes it, then how would I feel?

 

[micromass]

I don't think (or at least hope) the kind of person who is like "Oh Riemann's Hypothesis is one of the seven millenium problem. I have got to work on that problem and will earn an eternal glory!" but I am like "So apparently, I know I don't understand the hypothesis correctly, but how is it related to prime numbers?" And spend a decade on that problem, then someone else publishes it, then how would I feel?

Yes, that would feel verrrrry painful, I understand. Being scooped is a horrible feeling (the most horrible feeling actually is in that somebody find a mistake in a proof you've made. I can't imagine how bad it must have felt for Wiles the first time they found a mistake in his proof. It is a HORRIBLE feeling!).

But even if somebody publishes it first, you still got to do what you loved for a couple of years. You understood the world a little bit better. You didn't get the glory, but you got to have the fun...

Whatever route you take, you will be disappointed sooner or later by something. It's best not to think about it much.

 

[chiro]

Once I asked a question to my professor said, (well, actually not MY professor, I just went to a math camp at a nearby university), "Should I have to be born a genius to do math?", he said "No, you don't born a genius, you BECOME a genius as you study harder and explore the world". First I thought it was just a white lie not to disappoint me. But then I realized, if I have time to complain about my relative intellectual inferiority, I would go grab a math book and study.

But I still cannot deal with the accolade part. I mean, all human beings will be disappointed if somebody else publish a theorem that is exactly what they were working on. If they realized that the years that they have spend or their lifetime of effort (if you saw Fermat's Room) have been dissipated, they might have to go see a psycharist (or at least I will). My question is, how will I deal with this situation?

You should know that this has happened quite a few times. One instance is the 1965 Nobel Prize in physics. These recipients came to the same conclusion as one another and published results at pretty much the same time.

Also you have to think that if two people do come up with the same result, they have different insights into the problem at hand. So just because someone published a main result before you, it would probably be beneficial to publish yours anyway if you had ideas and insights that differed from the other persons.

Your insights might even be considered more valuable because of the different perspective.

In terms of dealing with your situation, my advice is to speak to people in the profession that you wish to enter who have a lot of experience. This would probably be a senior professor who has done research (or is actively still doing research). Then when you have secured a bit of time via an appointment, just lay out your situation.

You might feel embarrassed to ask them this, but if you want to sort this issue out you need to ask someone in person, just like you have asked us here on this forum. If they are experienced and wise enough, they might even see themselves as they were when they were young when they were looking at you.

One person has already told you this kind of thing at the math camp, but if you need an alternative opinion, then I suggest you get it sooner rather than later.

 

[ode_to_joy]

So I have been thinking the whole problem as a race. Only the fastest shall win the glory, but not in academia.

I really appreciate your advices. You have been really helpful.

 

[ode_to_joy]

A scholar must discover a new thoerem periodically in order to stay in academia. I really want to hear about this publish or perish pressure from you.

 

[nlsherrill]

A scholar must discover a new thoerem periodically in order to stay in academia. I really want to hear about this publish or perish pressure from you.

Uhh really? Where did you hear this? I find that hard to believe.

I think you are simply scared of failure. And this isn't good, because if you are afraid, then your chances have already dropped.

 

[cmb]

... I asked a question ..."Should I have to be born a genius to do math?", he said "No, you don't born a genius, you BECOME a genius as you study harder and explore the world".

May I condition that statement to say 'you may become a genius as you study SMARTER and &c.'.

 

[ode_to_joy]

May I condition that statement to say 'you may become a genius as you study SMARTER and &c.'.

of course you may. he was playing with words

 

[ode_to_joy]

Uhh really? Where did you hear this? I find that hard to believe.

I think you are simply scared of failure. And this isn't good, because if you are afraid, then your chances have already dropped.

I am actually really scared of failure.

But isn't it ture? First during one's doctorate years and post-doc, one must publish substantional amount or high quality (I heard that quality is more preferred than quantity) of research papers. Then during the tenure track years, to receive a tenure, and so on..

 

[deRham]

I have seen tons of threads that say I don't need to be super smart to do mathe, but at least there is a minimum boundary.

Yes there is, but the key to wanting to succeed as a mathematician is doing what it takes. People underestimate this way, way, way too much. The truth is that the traits required to succeed as a mathematician (due to the small number of spots for tenure in a university) are probably a lot rarer than either intelligence or drive to work. You need to want to do mathematics, it's that simple. Not learn mathematics, not merely discover, but really do it. That means spending long periods of time fiddling with the moments that are much less enthralling than the 'aha!' moments. That means figuring out what the axioms should be.

One thing is that it takes a lot more time and energy to work something out in detail in mathematics than to just conceive of the idea, but in truth, you are only rewarded as a professional for doing both, or doing a lot of the former and part of the latter. Some great mathematicians have handed out very significant endeavors for their students to realize and complete, based on visions they had themselves.

At a certain point, a lot of people realize they don't care about doing all that, and doing it at the pace and volume required to succeed as a professional. And make no mistake, it is super competitive, so someone will be found to take your place in all likelihood.

Your insights might even be considered more valuable because of the different perspective.

This is very true. Mathematics is not merely about answers, it is certainly about filling in the road to the answers. Some mathematicians are very particular that their work is extremely far from ad hoc, and the steps required should be very crystal clear to them and their colleagues. So really, you could publish a paper on the same subject and even roughly the same results, and your way of doing it could have vastly more advantages.

In fact, you would be discovering new results because along the way, the things you proved to get to the same destinations would be important results themselves.

misconception that math people are very smart. They are not. They just enjoy what they do and they work hard.

I would say a lot of mathematicians are very smart, but so are a lot of engineers. But really it depends how meaningful one considers words like "smart" anyway.

 

[deRham]

And I feel like, I will certainly regret at the moment of my death not for dedicating my lifetime to pursue mathematics.

Some very deep stuff can go into mathematics used for mechanical engineering, I imagine. My advice is you should try to take some of these classes before you decide. You might decide a PhD in mechanical engineering let's you do all of what you want, because it is generally the case that a PhD in a somewhat mathematical field is much, much, much more mathematically based than its undergraduate counterpart.

Ultimately, a PhD is one way to train to be a professional researcher in that field. Hence, you ought to ask yourself throughout undergrad what questions interest you. Do you care about spending years answering questions about mathematical structures with only marginal interaction with other fields, or would you rather be somewhere in the intersection between certain areas?

 

[ode_to_joy]

Ultimately, a PhD is one way to train to be a professional researcher in that field. Hence, you ought to ask yourself throughout undergrad what questions interest you. Do you care about spending years answering questions about mathematical structures with only marginal interaction with other fields, or would you rather be somewhere in the intersection between certain areas?

I am interested algebra, number theory, and analysis

 

[jk]

I am interested algebra, number theory, and analysis

That is so broad it is almost meaningless.

 

[ode_to_joy]

That is so broad it is almost meaningless.

well, I am not in undergraduate yet but concepts like groups sounds facinating to me

 

[Functor97]

That is so broad it is almost meaningless.

I am interested in Geometry (Differential, Algebraic) , Topology, Analysis, Number theory (p-adic) mathematical physics and fundementals. The only area i dislike is combinatorics, and that is probably because i am so terrible at it. Its a shame we humans need to rest and eat :

 

[chiro]

Its a shame we humans need to rest and eat :

If you replaced "we" with "those", you'd sound almost like some kind of management consultant ;)