Mathematics, Creativity, and Anxiety

[Dschumanji]

I am currently a university sophomore pursuing a degree in computer science. During the 2010 fall semester, my linear algebra professor approached me after class and suggested that I consider getting a concurrent degree in mathematics. I have always been very passionate about mathematics and have always thought I was decent at it due to excellent grades, so I am (or was) seriously considering getting that concurrent degree.

I have done some research on the upper division mathematics courses and found out most of it revolves around proofs rather than problem solving. I absolutely love proofs; I was never satisfied with theorems in my calculus courses unless a proof was provided. The proofs I had to present in my lower division linear algebra course were fairly easy and seemed pretty straight forward in my opinion. My professor commented that they were always "lucid." All of this increased my confidence in my mathematical ability. Recently, though, I have been questioning that ability.

I participated in all the AMC 10/12 competitions in high school and never did particularly well on them. Many of the problems seemed to require introducing some mathematical structure or an ingenious simplification that made solving the problem possible within the time limit. The competitions made me see and also appreciate how creativity manifests in mathematics. However, they also showed me that not only do I lack creativity in the arts, but also in the subject I am passionate about. Lately I have been looking up some interesting math problems to do for fun and each one seems to end up with me taking a really long time to solve or just plain failing. They all require that creative spark.

So what does this have to do with pursuing a concurrent degree in mathematics? I have noticed that many proofs involve quite a bit of creativity. If the upper division courses are all about proofs and I lack the creativity (well, I do have some strange "Eureka!" moments every now and then), how am I going to fare in such courses? This anxiety has spread to my thoughts about how I will fare in my upper division computer science courses. It is frustrating and depressing to feel that perhaps I am not cut out for these degrees and perhaps college in general.

Have any mathematicians or computer scientists on this board ever feel this way once or still sometimes feel this way? Am I correct in thinking I may not be cut out for mathematics and computer science due to a lack of creativity?

EDIT: This thread may actually be better suited for the academic guidance forum...

 

[micromass]

I am currently a university sophomore pursuing a degree in computer science. During the 2010 fall semester, my linear algebra professor approached me after class and suggested that I consider getting a concurrent degree in mathematics. I have always been very passionate about mathematics and have always thought I was decent at it due to excellent grades, so I am (or was) seriously considering getting that concurrent degree.

I have done some research on the upper division mathematics courses and found out most of it revolves around proofs rather than problem solving. I absolutely love proofs; I was never satisfied with theorems in my calculus courses unless a proof was provided. The proofs I had to present in my lower division linear algebra course were fairly easy and seemed pretty straight forward in my opinion. My professor commented that they were always "lucid." All of this increased my confidence in my mathematical ability. Recently, though, I have been questioning that ability.

I participated in all the AMC 10/12 competitions in high school and never did particularly well on them. Many of the problems seemed to require introducing some mathematical structure or an ingenious simplification that made solving the problem possible within the time limit. The competitions made me see and also appreciate how creativity manifests in mathematics. However, they also showed me that not only do I lack creativity in the arts, but also in the subject I am passionate about. Lately I have been looking up some interesting math problems to do for fun and each one seems to end up with me taking a really long time to solve or just plain failing. They all require that creative spark.

Somebody who does well at competitions will probably do well in math courses, but the converse is far from true. I had a professor once who was very, very bad at fast thinking and he was bad at such a competitions. Instead, he had to think the problem through and only then could he come up with a decent answer.

In my opinion, being able to think a problem through and becoming familiar with your material is essential. You'll need to know several techniques and several definitions very well before you can construct your own solutions. Creativity has not much to do with it (at least in undergraduate mathematics).

You said you sometimes think about problems for days. Well, join the club Really, all mathematicians tend to think for days about problems. That you're passionate enough to do that is a really good sign!

So what does this have to do with pursuing a concurrent degree in mathematics? I have noticed that many proofs involve quite a bit of creativity. If the upper division courses are all about proofs and I lack the creativity (well, I do have some strange "Eureka!" moments every now and then), how am I going to fare in such courses? This anxiety has spread to my thoughts about how I will fare in my upper division computer science courses. It is frustrating and depressing to feel that perhaps I am not cut out for these degrees and perhaps college in general.

Have any mathematicians or computer scientists on this board ever feel this way once or still sometimes feel this way? Am I correct in thinking I may not be cut out for mathematics and computer science due to a lack of creativity?

Yes, I have felt this way before too. It's not fun to think about something for days and still not finding the answer, but such a things are normal. It doesn't indicate a lack of creativity, it's normal. The only thing I can say is that if you keep persisting, then you will get there!

 

[dkotschessaa]

What I'm learning now (the hard way) is that if you love mathematics (and it seems you do) then the sooner you stop questioning your "inherent" ability to do math (on any level, in any capacity), the better.

- Dave K (who is still working on it)

 

[Dschumanji]

Thank you for the confidence boost and kind words, Micromass and Dkotschessaa!

 

[Karlx]

Hi, Dschumanji.
You have the passion for maths.
You have also the love for them.
Your professor is encouraging you to take a concurrent degree in maths.
Don't let you disturb yourself about AMC competitions.
Go on, take this degree.
You will enjoy maths (you have the ability for that) and you will gain self confidence when working more on them.
And with this self confidence, you will attain the "state of mind" that will bring to you those sparks of creativity.
Go on and enjoy one of the most beautiful creations of human mind: Mathematics.

 

[gsal]

I would like to offer a different choice of words...I mean, unless you are one of those few and far in between geniuses, you are not going to be "creating" anything...mathematically, anyway.

The way I see, it is just a matter of learning various mathematical tools (as many as you desired) and then just getting "tricky" when solving a specific problem and bringing into your solution mathematical artifices from other fields, etc...just by keeping and open mind and not letting the statement of the problem itself to narrow down your choices, etc...

 

[dkotschessaa]

I would like to offer a different choice of words...I mean, unless you are one of those few and far in between geniuses, you are not going to be "creating" anything...mathematically, anyway.

The way I see, it is just a matter of learning various mathematical tools (as many as you desired) and then just getting "tricky" when solving a specific problem and bringing into your solution mathematical artifices from other fields, etc...just by keeping and open mind and not letting the statement of the problem itself to narrow down your choices, etc...

Good points gsal. Music and art is actually the same way. What we call creativity even in those fields is kind of the same thing. You've just described it differently. It begins by learning basic mechanics (painting, playing an instrument), theory, etc. Then there is a process of imitation and absorption, then the mind and subconscious kind of do their thing. Then when we ask the mind for something (i.e. work on a really hard problem) it will at some point "cough" out something which we call an Original Idea. Going through this whole shebang is how you develop creativity. And that's the good news - that it's something that can be developed.

Case in point, I could sit down and write a composition for classical guitar right now without a problem. Not a great one perhaps, but I could do it. My creativity is developed in that direction, but with math it isn't there yet. Does that mean I'm suddenly not creative? I know it doesn't, so I'm excited to see what happens as I push forward.

Dschumanji, you are in a much better position than I as you already have some natural ability for math. I actually am not good at it unless I work extremely hard, but I love it. So you're in a great position, and you'll do wonderfully.

(Sorry that was a bit long winded. I think I let that french press coffee steep a bit too long).

-DaveK

 

[Shoku Z]

I am currently a university sophomore pursuing a degree in computer science. During the 2010 fall semester, my linear algebra professor approached me after class and suggested that I consider getting a concurrent degree in mathematics. I have always been very passionate about mathematics and have always thought I was decent at it due to excellent grades, so I am (or was) seriously considering getting that concurrent degree.

I have done some research on the upper division mathematics courses and found out most of it revolves around proofs rather than problem solving. I absolutely love proofs; I was never satisfied with theorems in my calculus courses unless a proof was provided. The proofs I had to present in my lower division linear algebra course were fairly easy and seemed pretty straight forward in my opinion. My professor commented that they were always "lucid." All of this increased my confidence in my mathematical ability. Recently, though, I have been questioning that ability.

I participated in all the AMC 10/12 competitions in high school and never did particularly well on them. Many of the problems seemed to require introducing some mathematical structure or an ingenious simplification that made solving the problem possible within the time limit. The competitions made me see and also appreciate how creativity manifests in mathematics. However, they also showed me that not only do I lack creativity in the arts, but also in the subject I am passionate about. Lately I have been looking up some interesting math problems to do for fun and each one seems to end up with me taking a really long time to solve or just plain failing. They all require that creative spark.

So what does this have to do with pursuing a concurrent degree in mathematics? I have noticed that many proofs involve quite a bit of creativity. If the upper division courses are all about proofs and I lack the creativity (well, I do have some strange "Eureka!" moments every now and then), how am I going to fare in such courses? This anxiety has spread to my thoughts about how I will fare in my upper division computer science courses. It is frustrating and depressing to feel that perhaps I am not cut out for these degrees and perhaps college in general.

Have any mathematicians or computer scientists on this board ever feel this way once or still sometimes feel this way? Am I correct in thinking I may not be cut out for mathematics and computer science due to a lack of creativity?

EDIT: This thread may actually be better suited for the academic guidance forum...

That's the problem I too have.It's frustrating at times.And like you,sometimes,it also takes me days to prove something.But,I am not going to give up.I,too,am not creative.Just don't give up,man.Dont give up.

 

[Shoku Z]

Creativity is just thinking differently or taking a different approach.And I believe that you CAN train your mind to think differently.

 

[Dschumanji]

Thank you all for the words of encouragement!