Can I Make a Contribution to Mathematics Without a PhD?

[Icebreaker]

I'm currently studying physics in an undegraduate program. It's fascinating and all, but my real interest lies in mathematics. My goal is to get a master's and eventually a PhD in math, but, in the words of my professor, "you will need to go pretty far before you can make a contribution to math."

My question is, "how far?" I don't want to spend 10 years getting my PhD. Maybe I should stick with physics or switch to something more applied, like computer science, as a master's?

 

[Gonzolo]

The most important thing is to pick something you enjoy doing. Start with a master's doing something you like. Go to conferences, talk to professors, and read about various fields to see what turns you on the most. Think of a Ph.D. only when you have a good grasp of what research actually is.

 

[JasonRox]

Same here.

I was going for Physics and Mathematics, but I believe I will be doing just a Pure Math degree.

I don't care about making contributions. I do what I want.

 

[Parth Dave]

I Agree with Gonzolo and JasonRox. If you like math more, than do math. If you like physics more, than do physics. For me, I hate physics, but I'm good at it. I love math, but i suck at it. So in the end, I'm choosing biology.

 

[NeutronStar]

..., in the words of my professor, "you will need to go pretty far before you can make a contribution to math."...

What's that supposed to mean?

Does that mean that you don't need to go very far before you can make a contribution to physics? :rofl:

 

[cepheid]

^^You know, it certainly seems that way to me.

 

[Icebreaker]

Well, we didn't get physics involved in that conversation, heh heh.

 

[NeutronStar]

Icebreaker,

I don't know what you mean by "contribution". If you're looking to contribute to society or technology you can do that by simply getting involved at any level. There are always people starting out that need low-level instruction so you can contribute to society in almost any field at any stage if you want to.

On the other hand, if you are looking to contribute to science or mathematics by advancing human knowledge in that area, then I propose that you are going about it all wrong. Instead of picking a subject where you are most likely to make a breakthrough, you should follow you passion and just study whatever interests you. Most major discoveries are made, either because the discoverer had a passion for the subject approaching obsession, or via pure dumb luck like the discovery of the CMBR. Not to imply that Penzias and Wilson where dumb, but they were lucky!

Where's your passion? Are there any unsolved mysteries that send synaptic lightning bolts flashing through your brain cells whilst you're trying to slumber in the darkness of night? If so, perhaps you may want to consider methodically constructing a lightning rod to see if you can capture the essence of these untamed concepts. A careful analysis of these feral ideas should help guide you in your academic preferences.

On the other hand, if you sleep well at night you might want to consider applying for something akin to a job at Bell Labs and just hope for the best.