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Still easier: (1) Pick a practical problem in physical science, engineering, medicine, some other field, e.g., ecology, or business, a problem not yet solved.

Still easier: (1) Pick a practical problem in physical science, engineering, medicine, some other field, e.g., ecology, or business, a problem not yet solved. (2) Get a good solution to this practical problem, mostly using math, hopefully at least a little new math. For publication, the math is supposed to be "new, correct, and significant" -- get the "significant" part from how much the math does for the practical problem. In medicine, your work might save thousands of lives. In business, your work might make/save millions of dollars. In ecology, you might help clean up a river. (3) Surprising blunt academic fact of life: Academics is very short on money and understands clearly that very little of their new theoretical work has any near term practical value. So, academics understands that they are short on money mostly because their work is short on valuable, current applications. Indeed, the words and applications are commonly in the titles of journals. So, publish in such a journal. Some high end universities say that the requirement for a Ph.D. dissertation is "an original contribution to knowledge worthy of publication" -- so, remove all doubt and publish your work. Advisor? Show them the letter that your paper was accepted. Done, fully, de facto, essentially, or nearly so. Where to get the practical problem? Typically outside of a math department and maybe off campus. For a job? Long the main source of good jobs for a Ph.D. in math was US national security, heavily near DC. That may still be the case. If you have any hope of a career that lets you be financially responsible, e.g., support a family and provide for retirement, stay away from academic careers. Academics just quietly assumes that any recent Ph.D. is just obsessed with research, even apparently useless research, and will pursue it neglecting nearly everything else in life including being financially responsible. Instead, go into business, e.g., start a business, own 100% of it, and make it successful. The business is likely a sole proprietorship and LLC (limited liability company). In that business, maybe some math, new, or new to the field of the business, will be an advantage. In particular, currently take advantage of the not fully exploited amazing technology of current computing and the Internet.

Test0129 4y ago
> Academics just quietly assumes that any recent Ph.D. is just obsessed with research, even apparently useless research, and will pursue it neglecting nearly everything else in life including being financially responsible. This isn't even an assumption. It's borderline enforced. I dropped from the program after paying my own way because my lack of interest in being financially irresponsible put me at the bottom of the bin for good research opportunities. Academics force you to take 9-10/hr. and work 60 hours a week (of course on a contract for only 30 hours), because if they don't have the constant meat-mill of H1Bs and young financially irresponsible people the entire industry would collapse into itself. It's not unlike tech itself which relies on exploiting the revolving door of new grads to get cheap labor. The only difference is the new grad working for BigCo for sub-par dollars can usually afford to eat. Where I went to school the MAJORITY (not an exaggeration) were on some kind of assistance. Either food or housing. Post-docs were barely able to afford rent.
goethes_kind 4y ago
In that case do not do a Ph.d in math at all. Do it within an engineering department instead, much more funding and you get paid accordingly. And then it is much easier to network your way into an industry job as well. Frankly, there is nothing in math research that is going to be directly applied to industry. Even applied math is entirely theoretical. To get to the level of your work actually being used, you need to wait for it to siphon through to the engineering department.
- graycat 4y ago
  > In that case do not do a Ph.d in math at all. Do it within an engineering department instead, much more funding and you get paid accordingly. The math I listed can be one heck of an advantage in doing research in engineering and other fields. First, get to apply math known poorly or not at all in the other fields. Second, get to do some research in math that in a math department does not look significant but still is regarded as significant for what it does for the problem selected from the other field.

Test0129 4y ago

> Academics just quietly assumes that any recent Ph.D. is just obsessed with research, even apparently useless research, and will pursue it neglecting nearly everything else in life including being financially responsible. This isn't even an assumption. It's borderline enforced. I dropped from the program after paying my own way because my lack of interest in being financially irresponsible put me at the bottom of the bin for good research opportunities. Academics force you to take 9-10/hr. and work 60 hours a week (of course on a contract for only 30 hours), because if they don't have the constant meat-mill of H1Bs and young financially irresponsible people the entire industry would collapse into itself. It's not unlike tech itself which relies on exploiting the revolving door of new grads to get cheap labor. The only difference is the new grad working for BigCo for sub-par dollars can usually afford to eat. Where I went to school the MAJORITY (not an exaggeration) were on some kind of assistance. Either food or housing. Post-docs were barely able to afford rent.

goethes_kind 4y ago

In that case do not do a Ph.d in math at all. Do it within an engineering department instead, much more funding and you get paid accordingly. And then it is much easier to network your way into an industry job as well. Frankly, there is nothing in math research that is going to be directly applied to industry. Even applied math is entirely theoretical. To get to the level of your work actually being used, you need to wait for it to siphon through to the engineering department.

graycat 4y ago
> In that case do not do a Ph.d in math at all. Do it within an engineering department instead, much more funding and you get paid accordingly. The math I listed can be one heck of an advantage in doing research in engineering and other fields. First, get to apply math known poorly or not at all in the other fields. Second, get to do some research in math that in a math department does not look significant but still is regarded as significant for what it does for the problem selected from the other field.