Pure mathematics vs Mechanical engineering

[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 ;)

 

[Mépris]

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.

I never thought I'd see the day...I thought kids would be wanting to be rebecca black or something these days.