Would you mind telling more about your general experiences of grad school and afterwards?
Aside from the issues that I had with my adviser, graduate school was a really great place. When I first started out, however, I was overwhelmed, because I was placed on a very, very large grant project and given a very complex, open-ended mathematical task to complete with little direction. To make matters worse, no one on the project told me what they expected of me, where I should pick up relevant information, what journals I should be reading, who I could possibly collaborate with, how long I had to complete certain objectives, and so on. As well, they assumed I joined the project with a deep knowledge of probability and statistics, which I didn't have (and they should have known, considering that I mentioned it to them several times during the interview process), since all of my undergraduate coursework was on the hardware side of electrical and computer engineering.
In any event after a few months of floundering, banging my head against the wall, bringing myself up to speed, slogging through classes, and just trying to find the time to go out and meet people, I heard that I was accepted into medical school and also was set to receive a fellowship. As if by magic, all of my worries melted away with that news, since I wouldn't have to rely on my position on the grant to pay for tuition or my shoebox-sized apartment, I could afford to go out to eat, and would ultimately have much more freedom with regards to how many classes I took or how much free time I could allot myself. In fact, looking back, I really made the most of those 5 years of funding, as I had enough time off to meet a lot of new friends (something I didn't do when I was an undergraduate, since I spent all of 2 years, after high school, on my S.B. EE), was able to travel the world, see new places, experience new foods and cultures, could afford to take whatever classes I wanted without question (I loaded up on math, biology, neuroscience, and statistics courses during my off-years of medical school), could work on any research projects, and, overall, just enjoy life.
While I did relish all of that freedom, one of the biggest hurdles I ran into was publishing on my own, as I had no collaborators and was fairly isolated due to my fellowship. Instead of sticking it out and spending 2-4 months per journal paper, I decided that it would nice if I could offload some of the work, give up some credit, and churn out journal papers every 3-4 weeks (under a light class load). Initially, I tried doing this with one of my publishing-inclined peers, but I ended up having a huge argument with him, as he tried to usurp ownership of an idea (despite contributing only a small proof that turned out to be wrong and unmendable) and publish it on his own at some conference. Eventually, I thought that it would be good try collaborating on a grant project again, as there would be a bit more oversight and I could avoid having someone trying to claim ownership of my work. Unfortunately, I made a big mistake when I mentioned this desire to my adviser (who had the authority to cut the strings on my fellowship after 4 years) and he effectively strong-armed me into working on his grants if I wanted to keep my fellowship. (The only upshot to that arrangement with him was that he had to pay me by the hour, to get around the fellowship restrictions, so I ended up making almost as much as the assistant professors in the electrical engineering department my final year there.)
In any event, after my entire ordeal with him and the justice system, I had the option of going back, getting another adviser, and paying to finish a Ph.D./M.D. Instead, I opted to head back to my alma mater for a bit, to build up my network of contacts and find people to write letters of recommendation, before transferring to a better school. Fortunately, with my body of coursework and publications, I was able to test out of the classes that were similar to ones I had taken before or was able to write a journal paper with the professor to "demonstrate" my knowledge of the subject matter. As well, I was able to find a younger, MUCH better adviser that time around, who recognized that I was a paper-writing fiend (which helped with building up his case for tenure) and just threw a bunch of money and support at me so that I would keep publishing.
Since graduating, I've had a fair number of opportunities ranging from becoming a tenure-track professor or a research professor to taking a job out in industry doing biostatistics work or designing hardware. However, despite all of my problems I had with academia, I truly enjoy the environment, let alone publishing, researching, and sometimes teaching.
What kind of mathematical work do you do?
A good majority of the mathematical work that I do is relatively simple compared to the stuff you'd find in some of the higher-end SIAM journals, Journal of Differential Geometry, Geometry and Topology, Journal of Algebraic Geometry, etc. For instance, in a typical paper that I send to engineering journals, e.g., various IEEE/ACM Transactions, the most I'll end up doing is: (i) constructing a Gibbs, reversible-jump Markov chain Monte Carlo, or variational Bayes sampler for a generative model (the latter of which just involves taking some derivatives), (ii) proving some simple properties about a statistical model (such as its mean and variance, that one can obtain a predictive formula through marginalization, or that it behaves a certain way, which basically amount to taking some anti-derivatives and recalling basic probability assumptions), or (iii) possibly giving a convergence proof of a method to show that the iterates tend to a local optimum (which relies on modifications of standard nonlinear programming results like from Zangwill, transforming the method into a contractive fixed-point algorithm, etc.). All-in-all, the amount of work usually takes a day or two to complete on my own.
Now, there will be times where I break out of this mold and actually flex my mathematical muscles. A recent example of this is a paper that I just submitted that provided a means of simplifying the algorithmic complexity of a method by casting the underlying computational problem on a very special kind of manifold (which, unfortunately, resisted simple analysis). In order to finish the paper (which was a relatively short 30 pages) I ended up having to translate and rework the concepts in several differential geometry books and papers (which made for a 150 page appendix) to ensure that all of the derivations my work relied on were correct. While I can't remember exactly when I began on the project, I believe it took approximately a year to complete, along with the input and help of a few mathematicians.
You have explained some of why your advisor behaved the way he did. Sadly, he has lots of company. What about the larger environment? What is it about the way we run schools that drive people to such desperation? Too competitive perhaps? Science is so highly regarded that some people will stoop to anything to obtain recognition. Or, not selective enough? Maybe the tenure system is a big part of the problem? I have this uncomfortable feeling that too often we hand out PhDs to cheaters, who go on to be the monsters who give academia and science a bad name as they continue the dishonesty that they used to obtain the degree. They won't settle for a lesser role, so they have no choice but to continue to cheat, because they aren't capable of honest science. One PhD I was stuck working with for a year was so bad he never even tried honest work. Never should have been given a PhD, as he himself admitted in one of his rare honest moments. He felt that what was wanted was impossibly hard. He pushed everyone very hard to come up with stuff he could use to snow the customer, and of course blamed everyone else when that didn't work. Even worse, despite the desperate need, if anyone looked like they were on to something good, he'd sabotage them out of fear it might show him up and cost him his job. In the end, we all lost.
I also happened to omit lots of details about my adviser and painted a rather one-sided story above.
Touching on what you said, though, my adviser got to where he was at through hard work and perseverance during the first 25 years of his career. In fact, he was one of the top five researchers in a rather large field, which is why I went to work with him in the first place.
In any event, the problem wasn't that he was desperate, that the environment was too competitive, that he was a cheater, or that the school wasn't selective enough in choosing him so many years ago for a faculty position. The problem was that once he became famous, and hence was tenured with a named professorship, had offers to transfer to places like Dartmouth, etc., there was no need for him to produce anything of substance. That is, he was finally able, after 25 years, to finally sit back and let his well-oiled machine run its course without much hands-on involvement. For example, he had his pick of the top students and didn't need to spend much time grooming them and could instead turn them loose on problems and expect to them to write up and publish their papers in his pet conferences and journals. He also was able to join some of the upper level scientific committees that would spend an inordinate amount of money to fly him, and other members out, to various high-profile spots so they could recount stories, get free food, and do only the minimal amount of work necessary at the meetings to justify the need for a face-to-face trip. As well, he had joint departmental appointments out the wazoo, had tons of perks through the university, was insulated from politics, and really had nothing to worry about once he became an emeritus professor and eventually retired, as he would be making around $110k/yr at that point just for showing up every so often and wandering the halls.
Of course, with all of this, my adviser slowly started to distance himself from doing actual research, i.e., proving theorems, writing papers, and possibly designing and running experiments. From what I can tell, I think he actually forgot how to do any of it and pushed himself back into the fray when I showed up and started publishing like crazy. Further, I'm sure it was incredibly disconcerting, from his point of view, to have some young 20 outdoing him, ignoring his input (since he was incredibly out of touch with the state of the art), and so forth. (Had there had been safeguards in place to ensure that he was forced to do a certain amount of original, top-quality work on his own, though, I'm certain that our contention could have been avoided.)
That was very helpful. The only thing I can add is a reiteration of your last point. It sounds like your situation was worse, [...]
It was rather bad.
To preface everything, my adviser was around 65 years old and nearing retirement, whereas I came into the Ph.D. program way too early (at 19) and was treated very differently from the rest of his students (who were 29-35 years old) almost at the get-go, but definitely after being there for four years. For instance, he would talk down to me, saying that I was a kid and wouldn't be able to understand something, or would belittle my work, despite not having authored a paper on his own or done anything but managerial tasks in over 10 years. Heaven forbid if I made a mistake when proving a theorem or in not exhaustively completing a task: he would never let me forget about it and would bring it up at any moment it suited him, especially to call into question the validity of heavy mathematical work that I was going to publish on my own or to question why I had time for pursuing other endeavors beyond those he paid me to do for 20 hours per week. The only reason I put up with his bullshit for so long was that he was paying me incredibly well for a research assistant ($35000/yr) and basically gave me a fellowship that waived both my grad. tuition and my M.D. tuition (which would have saved me something like $400k overall).
Ultimately, from what I've corroborated from other sources, this guy was rather jealous of my ability to work, without supervision, on whatever suited my interests, have my papers accepted in better venues (not because I was smarter, just that I knew the value of presentation, getting 3d artists to make my graphics and figures, etc.), live in a relatively care-free environment, be able to travel on a whim to conferences, regard him as a manager/peer and not as someone who was a "better" researcher, and so forth. Since he was nearing retirement age, these issues were even more poignant, and he took on more responsibilities to prove to himself that he still "had it." Unfortunately for him, the more duties he picked up, the less time he had for actually doing anything remotely research-oriented and the more he became jealous of my infinite free time and the 50 hours per week that I'd spend on my research.
Eventually, due to all of these bottled-up feelings, he exploded into a profanity-laden tirade and lashed out at me during one seemingly routine one-on-one sit down where I was presenting my work for one of his grant projects. Needless to say, I wasn't keen to stick around after all of that and sought to move up to a much better school. However, I was fairly distraught to find that I was rejected from all of the schools I had applied to, despite being sole or lead author on every paper and only publishing in top-tier journals and having a better overall profile than students already in the Ph.D. programs at those schools; later, I found out that he had a hand in unduly blocking my admission, as he basically wrote the letter of recommendation, if you could even call it that, for a junior professor I had tapped, which precipitated my legal action against him.
[...] but I got screwed by my graduate adviser and two years after leaving the school I haven't been able to find a job or another graduate program.
With regards to your situation, if you want to go back to graduate school, I would recommend taking some time out to publish on your own, depending upon your field, even if you can't target the top-tier journals. For example, if you're in computer science or engineering, there are plenty of topics that you can work on that only require access to literature (which you can often get through friends at a university or by signing up for a 0 credit hour class for a semester), a decent computer, MATLAB/C/C++ programming knowledge, and some creativity.
To render in real-time for a video game (say 60 FPS), you would need a processor that was around 1 million times faster than what we have today.
What is needed is an architectural paradigm shift, not necessarily a more beefy, faster (single-instruction, multiple-threaded-based) GPU.
To elaborate, with a naive implementation where independent kernels are run in parallel, one of the major bottlenecks for ray/path tracing via GPGPU processing is that every warp, a set of 32 threads, essentially executes the same instruction, with branching realizing by transparently masking out threads; as such, if branching often leads to divergent threads, then there will be low hardware utilization and performance will degrade. With a more robust implementation, you can improve hardware utilization by appropriately partitioning sub-kernels, but you'll run into issues when you start handling secondary rays.
For ray/path tracing to be carried out in an expeditious manner, it would be prudent to move to a programmable multiple-instruction, multiple-threaded (MIMT) architecture with many small cores that can handle many threads. In fact, researchers have been moving in this direction for quite some time now and the results are rather promising: while an NVIDIA GTX 285, which has a die area of around 300mm^2, can handle around 100M primary rays/sec and 60M diffuse rays/sec, with a thread issue rate of ~70% and ~50%, respectively, a custom MIMT ASIC solution, with an area of 200mm^2 at the same fabrication level, can reach around 400M primary and diffuse rays/sec, with a thread issue rate of ~70-80% for both. (As an aside, I have a paper, that's being submitted to either the ACM Trans. Graphics or IEEE Trans. Comp. Graphics and Vis., on an FPGA and theorized ASIC solution that blows these numbers away.)
Umm, if you're so rich traveling the world on interest payments and patent royalties why are you wasting time making a hackintosh and not just buying a mac pro? Haha.
On top of everything else you have reading comprehension issues. To help make things clear for you, I never said that I owned a hackintosh.
However, I will mention that I assembled my workstation, if you can even classify it as such, and it is far more powerful than a Mac Pro: it has 8 Xeon E7-8870s, for a total of 80 cores and 160 threads @ 2.4/2.8 GHz, a Supermicro X8OBN-F motherboard, 512 GB (16x 32 GB DIMMs) DDR3 RAM, and 4 NVIDIA M2070s. (As an aside, a single Xeon E7-8870 costs more than the entry-level, dual-socket Mac Pro and the entire computer is a few thousand dollars short of the price of a new Porsche 911 Carrera.) Oh, and yes, I routinely develop software or run simulations that actually require that much, or far more, computing power: try running lattice-Boltzmann/finite element or Stokesian particulate flows, for modeling thousands to hundreds of million red blood cells, on a Mac Pro.
Oh, you meant you're an unemployed old baby boomer who lives off his retirement account from Honeywell and has a very fixed income. Haha.
Continuing the above remark, it's laughable that you take what I've written and automatically default to assuming that I'm "unemployed," let alone a baby boomer. Just so you know, I'm not even 30.
Real Users never use the Help key.