Should I Pursue Math After BSc in Physics?

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yoyo100
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I just wanted some advice about my situation:

I will soon graduate with a BSc. in physics after 4 years of undergraduate eduacation. However, for the past few years I have increasingly been losing interest in the subject. There is no topic that really excites me. Nonetheless, I have continued on with my undergraduate studies since I have been doing very well grade wise.

Recently, I have been enjoying solving math problems and proving things. I have perused more advanced (than what I am used to) topics such as advanced algebra and analysis which both seem very interesting. In fact, after some reflection, I have started to realize that what drew me to physics in the first place was the use of equations and numbers as well as proof. The more I think about it, the more interested I get in math. I have obviously taken math classes for my physics degree, but they were mostly exercise rather than proof based (Stewart for calculus, etc.) I am now starting to think about taking action and taking some advanced math classes for math majors after I finish my degree.

My concern is that if I continue with undergraduate studies (beyond the usual 4 years), then I will be wasting valuable time which could be spent getting job experience, etc. Furthermore, I feel that if I change directions now then it will be kind of like admitting that the past four years have been a big waste of time and money. Should someone in my situation pursue his interest in studying math or is the whole idea simply just a silly diversion.

Sorry for the long post. Any advice or comments from people (particularly someone who was in a similar situation realizing a passion for mathematics late in his/her education and took action on it) would be greatly appreciated.
 
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I think the only reason you should switch is if you're looking to go onto graduate studies in maths. However, from the sounds of your post, you are looking to get a job, and so it won't matter whether you have a maths or physics degree.