After that, will it be a difficult, but possible, problem?
Do the math yourself to calculate your odds. Only one of the 7 Millennium Prize Problems have been solved so far, and that by a person widely considered a math genius since his high-school days at one of the best math-oriented schools in Russia and possibly the world at the time. And he was lucky that most of the scaffolding for the Poincaré conjecture happened to be in place already.
So, your odds are pretty bad, and if you don’t set a smaller sub-goal, you will likely end up burned out and disappointed. Or worse, come up with a broken proof and bitterly defend it against others “who don’t understand the math as well as you do” till your dying days. It’s been known to happen.
My sense is that you are underestimating the number of extremely smart mathematicians who have been attacking N ? NP. And further, you are not yet in a position to accurately estimate your chances.
For example, PhDs in math OR comp. sci. != PhDs in math AND comp. sci. The later is more impressive because it is much, much harder.
If you find theoretical math interesting, by all means pursue it as far as you can—but I wouldn’t advise a person to attend law school unless they wanted to be a lawyer. And I wouldn’t advise you to enroll in a graduate mathematics program if you wouldn’t be happy in that career unless you worked on P ? NP
You are underestimating the number of extremely smart mathematicians who have been attacking the problem. And further, you are not yet in a position to accurately estimate your chances.
If your father has a PhD in Comp.Sci., he’s more likely to know than a lawyer like myself.
That said, the Wikipedia article has 38 footnotes (~3/4 appear to be research papers) and 7 further readings. I estimate that at least 10x as many papers could have been cited. Conservatively, that’s 300 papers. With multiple authors, that’s at least 500 mathematicians who have written something relevant to P ? NP.
Adjust downward because relevant != proof, adjust upward because the estimate was deliberately conservative—but how much to move in each direction is not clear.
The Millenium Prize would be a nice way to simultaneously fund my cryopreservation and increase my prestige. I clearly need a backup plan, though, and I don’t have one. Will someone with a BS in mathematics and computer science be able to find a good job? Where should I look?
Sorry to put it bluntly, but this sounds incredibly naive. One cannot plan on winning the Millenium Prize any more than one can plan on winning a lottery. So, it’s not an instrumentally useful approach to funding your cryo. The latter only requires a modest monthly income, something that you will in all likelihood have regardless of your job description.
As for the jobs for CS graduates, there are tons and tons of those in the industry. For example, the computer security job market is very hot and requires the best and the brightest (on both sides of the fence).
In addition to what shimnux said (and which I fully endorse), I think you sell your father short. He doesn’t just teach, he does research. Even if he’s stopped doing that because he has tenure, he still helps peer-review papers. Even if he’s at a community college and does no research or peer-review, he still probably knows what was cutting edge 10 to 15 years ago (which is much more than you or I).
Regarding actual career advice, I think there are three relevant skills:
Math skill
Writing skill
Social skill
Having all three at good levels is much better than having only one at excellent levels. Developing them requires lots of practice—but that’s true of all skills.
At college, I recommend taking as much statistics as you can tolerate. Also, take enough history so that you identify something specific taught to you as fact in high school was false/insufficiently nuanced—but not something that you currently think is false.
In terms of picking majors, its probably to early to tell—if you pick a school with a strong science program, you’ll figure out the rest later. Pick courses by balancing your interest with your perception of how useful the course will be (keeping in mind that most courses are useless in real life). Topic is much less important than quality of the professor. In fact, forming good relationships with specific professors is more valuable than just about any “facts” you get from particular classes—you’ll have to figure out who is a good potential mentor, but a good mentor can answer the very important questions you are asking much more effectively than a bunch of random strangers on the Internet.
Yes, I do.
Do the math yourself to calculate your odds. Only one of the 7 Millennium Prize Problems have been solved so far, and that by a person widely considered a math genius since his high-school days at one of the best math-oriented schools in Russia and possibly the world at the time. And he was lucky that most of the scaffolding for the Poincaré conjecture happened to be in place already.
So, your odds are pretty bad, and if you don’t set a smaller sub-goal, you will likely end up burned out and disappointed. Or worse, come up with a broken proof and bitterly defend it against others “who don’t understand the math as well as you do” till your dying days. It’s been known to happen.
Sorry to rain on your parade.
My sense is that you are underestimating the number of extremely smart mathematicians who have been attacking N ? NP. And further, you are not yet in a position to accurately estimate your chances.
For example, PhDs in math OR comp. sci. != PhDs in math AND comp. sci. The later is more impressive because it is much, much harder.
If you find theoretical math interesting, by all means pursue it as far as you can—but I wouldn’t advise a person to attend law school unless they wanted to be a lawyer. And I wouldn’t advise you to enroll in a graduate mathematics program if you wouldn’t be happy in that career unless you worked on P ? NP
I was definitely engaging in motivated cognition.
If your father has a PhD in Comp.Sci., he’s more likely to know than a lawyer like myself.
That said, the Wikipedia article has 38 footnotes (~3/4 appear to be research papers) and 7 further readings. I estimate that at least 10x as many papers could have been cited. Conservatively, that’s 300 papers. With multiple authors, that’s at least 500 mathematicians who have written something relevant to P ? NP.
Adjust downward because relevant != proof, adjust upward because the estimate was deliberately conservative—but how much to move in each direction is not clear.
The Millenium Prize would be a nice way to simultaneously fund my cryopreservation and increase my prestige. Will I get it? No.
Sorry to put it bluntly, but this sounds incredibly naive. One cannot plan on winning the Millenium Prize any more than one can plan on winning a lottery. So, it’s not an instrumentally useful approach to funding your cryo. The latter only requires a modest monthly income, something that you will in all likelihood have regardless of your job description.
As for the jobs for CS graduates, there are tons and tons of those in the industry. For example, the computer security job market is very hot and requires the best and the brightest (on both sides of the fence).
In addition to what shimnux said (and which I fully endorse), I think you sell your father short. He doesn’t just teach, he does research. Even if he’s stopped doing that because he has tenure, he still helps peer-review papers. Even if he’s at a community college and does no research or peer-review, he still probably knows what was cutting edge 10 to 15 years ago (which is much more than you or I).
Regarding actual career advice, I think there are three relevant skills:
Math skill
Writing skill
Social skill
Having all three at good levels is much better than having only one at excellent levels. Developing them requires lots of practice—but that’s true of all skills.
At college, I recommend taking as much statistics as you can tolerate. Also, take enough history so that you identify something specific taught to you as fact in high school was false/insufficiently nuanced—but not something that you currently think is false.
In terms of picking majors, its probably to early to tell—if you pick a school with a strong science program, you’ll figure out the rest later. Pick courses by balancing your interest with your perception of how useful the course will be (keeping in mind that most courses are useless in real life). Topic is much less important than quality of the professor. In fact, forming good relationships with specific professors is more valuable than just about any “facts” you get from particular classes—you’ll have to figure out who is a good potential mentor, but a good mentor can answer the very important questions you are asking much more effectively than a bunch of random strangers on the Internet.
Good luck.