Can I solve research problems with only BS in Mathematics?

[Indiana]

Currently I'm undergrad in Mathematics and confused about getting a Phd. I'm not interested in academia. I'm more interested in startups or jobs in the industry.

The only thing that is making me to do PhD is solving research problems. Say I'm reading a machine learning book or QFT book or a random thought in my mind and I find something(a problem) that can solved in a different way(maybe a new discovery!) and more efficiently and it involves some research. Will I be able to do that research and solve that problem with only BS or do I need PhD?

 

[Ssnow]

There is no a special title that specify that you can solve research problem ...
A PhD or an academy member is supposed to be more suitable, but one thing does not exclude the other.

Ssnow

 

[Dr. Courtney]

Currently I'm undergrad in Mathematics and confused about getting a Phd. I'm not interested in academia. I'm more interested in startups or jobs in the industry.

The only thing that is making me to do PhD is solving research problems. Say I'm reading a machine learning book or QFT book or a random thought in my mind and I find something(a problem) that can solved in a different way(maybe a new discovery!) and more efficiently and it involves some research. Will I be able to do that research and solve that problem with only BS or do I need PhD?

Most scientists who can work as independently as you describe have earned PhDs. Lots of folks without PhDs solve real and interesting research problems, but in most cases they are working under the guidance or mentorship of someone with a PhD.

The process of earning a PhD not only gives one the depth of background and knowledge in the specific field, but it also gives one a lot of practical experience recognizing, defining, refining, lit searching, and estimating the time and effort needed to address a new problem in a tractable way.

I mentor a lot of high school and undergraduate research, as well as collaborations with colleagues with BS degrees. Most of my help is in matching a good problem with the skills and talents of non-PhDs. Without guidance, they tend to pick problems that are much too difficult for their skillset (or anyone's), already solved, or trivial and uninteresting.

Then there is the related problem of picking tractable and accessible problems that someone will pay you to solve. This is even a bigger challenge from someone with only a BS in Mathematics. There are a lot of math problems of corporate interest, including the emerging field of big data, that you can earn a decent living solving with a BS, but very few of these will be of sufficient interest to publish in the scholarly journals (even if your corporate employer would let you).