Comment by graycat

"Stupidity in math"??? Hmm ...!

The article for this thread has:

"First, I don't think students are made to understand how hard it is to do research."

Well, from my career and Ph.D., I found something different:

(1) In pure math, read some of the best materials, look for unanswered questions, and pick and try to answer one of those.

Took me 2 weeks. Paper got accepted in the best journal in the field.

(2) Applied Math. In practice, outside of math, see a need, problem, weaknesses in what is known/done, pick, and try to answer.

Another few weeks, then submitted to a journal and got published right away, no revisions.

(3) Engineering. In some real situation with some big, i.e., expensive, activity, see where a lot of money is being spent, pick, attack, maybe solve, and write it up.

Most of the work was done an airplane flight, and the results became dissertation in an engineering school.

One device: Pick some advanced topic in math, e.g., 'tightness' in probability theory, and use that as a tool to get some new results on the problem picked. There are problems where such a tool could be used but is poorly known by people concerned with the problem.

More difficult problems:

For the work in (1)-(3), still waiting for a check.

Problems:

(A) Getting hired for such work.

(B) When do get hired, get paid enough to buy a house and support a family.

Lessons:

(i) For academics, never saw where the professor got paid enough to buy a house and support a family.

(ii) For business, if do get hired and paid and are doing good work, then maybe, still, are not paid enough to buy a house and support a family. But the owners of the business are making more money from the good work than they are paying.

So, maybe start a business, do some good work key to the success of the business, and keep all the earnings for yourself.

Looking around, it appears that the people who make enough to buy a house and support a family own a successful business, although maybe just a successful LLC (limited liability corporation -- a relatively simple business type) as a physician, lawyer, tax expert, etc.

So, in simple terms, start a business, e.g., initially as just an LLC, and continue with hard work, good ideas, good insight, until have a successful business, and then sell it. Uh, if the money was from successful 'pesonal services', e.g., law, medicine, then may not have anything to "sell".

These days the Internet may provide some good opportunities.