8 ms·

Was a PhD necessary to solve outstanding math problems?

57 points by reedwolf 6y ago

DanBC 6y ago
The article is missing mathematicians who do not publicize their results. These would mainly be mathematicians working for agencies like GCHQ, NSA, etc. If you want to work on certain math problems, don't mind working for the government, and don't care about being published you can get good jobs with these kinds of agencies.
- black_puppydog 6y ago
  * and don't care about why these results will go unpublished
  - unishark 6y ago
    meaning that everyone who works for the government would agree they are only enabling bad things?
  - beefhash 6y ago
    * and don't have anything on your track record making it impossible to land this kind of job due to the security clearance required
  - i_am_proteus 6y ago
    Or you are comfortable with why they will go unpublished.
    - black_puppydog 6y ago
      of course, or that
- mcguire 6y ago
  Of course, in science, if it isn't published, it doesn't exist.
- carlosf 6y ago
  Financial markets as well.
  - fractionalhare 6y ago
    I know of a boutique proprietary trading firm wherein a researcher solved an open problem in probability but won't publish the results because it's integral to a trading strategy. That always gives me a chuckle :)
bo1024 6y ago
The article seems to treat a PhD merely as a credential - maybe assuming that a person would be equally capable with or without it. Why? The whole point of a PhD in math is to learn to do effective research in math and there are almost no substitutes. This seems like being surprised that so many professional violinists took violin lessons. (I admit my bias here but still.)
- hn_throwaway_99 6y ago
  The same mindset occurs a lot in the software engineering world, and I think it's somewhat baffling and potentially dangerous. I find software engineering quite difficult, and I am relatively intelligent, studied computer science at top universities, and have decades of experience where I learned a ton. So I'm all for coding bootcamps, but we wouldn't expect someone who went to a violin bootcamp for 3 or 4 months to be able to play in an orchestra, but I don't think that's the standard message coming from these coding bootcamps (understandable, they have a biased motivation) or from higher ups in the tech industry at large (more problematic IMO).
  - ludamad 6y ago
    "scratch the surface of programming, which nonetheless equips you for real world jobs" could possibly be fair to say about a bootcamp. It certainly filled a certain demand, although one has to wonder if better software won't just eat 4 month configuration++ bootcamps
    - seibelj 6y ago
      I think a better use of coding boot camps would be to go deep in a very specific DSL. Like learn how to do Salesforce or Excel programming deeply. A lot of companies actually need this to improve processes, and restricted environments reduce the cognitive load a novice needs to become productive.
- AnHonestComment 6y ago
  Many SDEs I know spend years working on mathematics (eg, implementing economic models) — and the job of being an SDE is being an applied type theorist. To me, your comment is the classic classism that engineers have nothing to contribute to science.
jitendrac 6y ago
From what I believe, many of the old days Mathematicians were given PhD by various institutes after they got famous. Not all had PhD, but most of good one got it after being recognized. Also don't forget many people of that time did not publicize their work.
graycat 6y ago
Hint, quiet, don't let this out, a Ph.D. is not really a knowledge degree but a research degree. From that degree on, in blunt terms, everyone knows that no one can carry the whole library around between their ears and so no longer much cares what you know but cares what you can create! There can be and are some exceptions, but overwhelmingly successful research in math requires the background of a Ph.D. for (1) finding a suitable problem and (2) having the knowledge to attack it. And it helps to be in a relatively good school so that will get relatively good versions of (1) and (2). But with everything in good shape, apparently there is one more challenge -- being successful in the actual research. For a hint at this challenge, buried in D. Knuth's The TeXBook is: > The traditional way is to put off all creative aspects until the last part of graduate school. For seventeen or more years, a student is taught examsmanship, then suddenly after passing enough exams in graduate school he's told to do something original. That is, the research is work that is suddenly different, maybe for some people quite different and challenging, than all the academic work before. E.g., there are cases where a student made A's and was the darling of all the teachers from kindergarten through college but in all that time never encountered anything like having new ideas. Bad such cases can lead to stress, loss of self-esteem, crippled ability to work, more stress, burn out, clinical depression, and ... suicide. No joke. For me, part of what helps in research is some qualified respect for some of the existing material. So, I look at what is there as needing improvement and try to do that. If look at the existing material as some nearly perfect construction, then maybe won't feel confident should or could improve on it! One thing rarely taught in math is the importance of intuition: It is needed to do well at guessing, guess a suitable problem, broad outlines of a solution, attack, tools, etc. Good guessing is important since that's most of what there is to do, and good intuition helps with good guessing. Sure, when the results are obtained and in clean form with polished proofs, there can be little or no view of the sources, the intuition. There can be some question about how good some Ph.D. research is: The professors don't want to grant Ph.D. degrees for poor research but don't really know how to ensure good work, indeed, for either the students or sometimes themselves. So one standard that can remove some possibly painful ambiguity is that the Ph.D. research should be "an original contribution to knowledge worthy of publication" with the usual standards for publication being "new, correct, and significant". If a student does some research and the professors question if it is publishable, then the student can settle the issue in an objective way -- try to publish the work. E.g., computer science is concerned with computational time complexity, i.e., good algorithms where good means running time that grows no faster than some polynomial in the size of input data for the problem (rough statement -- more details in the famous Michael R. Garey and David S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, ISBN 0-7167-1045-5, W. H. Freeman, San Francisco, 1979. and more recent sources). IIRC that polynomial criterion came from J. Edmonds. More IIRC, he left his Ph.D. program early and did and published some of his work on networks. Eventually a committee of his former professors came to him and said that should he stack his publications and put a staple in one corner, that stack would be accepted as his Ph.D. dissertation and he would get his Ph.D.
mcguire 6y ago
"A PhD is less important for doing groundbreaking applied engineering and entrepreneurial work, especially in tech." I'm just going to sit here and ponder "groundbreaking entrepreneurial work" for a while. Is it like "financial innovation?" Anyway, I'll also point to Matt Might's illustrated guide: http://matt.might.net/articles/phd-school-in-pictures/ http://matt.might.net/articles/phd-school-in-pictures/
- AnHonestComment 6y ago
  I don’t read that quote as “groundbreaking” applies to both terms, but rather “groundbreaking applied engineering” and “entrepreneurial” as two kinds of applied domains where the knowledge gained in a PhD is perhaps less useful than 4-6 years of work experience. I’m not sure why you’re mocking “financial innovation” — do you think there aren’t new ways to do commerce or finance than what we have now? Also, that post is dumb: the topology of knowledge isn’t nearly so simple — and that’s worth remembering because the places where you can create new knowledge aren’t all at some boundary which only can be reached by a vaunted PhD. The oversimplification isn’t enlightening — it’s a self-serving justification for classism.
jokoon 6y ago
There's a difference between a degree and an education. The problem is how we consider the destination (the degree), to be a proof of competence and knowledge, while it's really the journey (the education) which actually matters. That's why degrees should be abolished, and a certificate of education be given to the student as long as he/she is present. School should not act as a social filter. As long as you go to school and go to classes, and shows motivation to learn, it's enough. There are no proper ways to evaluate how a student really learned and absorbed the knowledge that was given. There are many students who love the knowledge, but cannot accept scholasticism, the competition, the selection and the filtering. It often ends up being about "belonging to a group", and honestly it was never the goal of education. It's up to companies to really check if someone if competent and has the knowledge, it's not the job of universities. Higher education is an enormous source of inequality, and an immense social barrier. It's really easy for people with degrees to disagree with this, I can only answer with survival bias.
- quickthrower2 6y ago
  I have a degree, and I agree with you. At least for software engineering. What there could be is a standardised test, that is a national or international standard, not linked to a uni. Learn to program and do the test and that is your credential. Maybe it costs $200 or something. That way you can skip uni, self teach but be able to show you can code without employers needing to find novel ways to evaluate. Just spitballing!
  - injb 6y ago
    Ultimately if you standardize something, people will gamify it. The point of employers finding novel ways to evaluate candidates is to win that game and beat the average. Good for them! It can't/shouldn't be otherwise (imo).
    - tprice7 6y ago
      They aren't mutually exclusive approaches, e.g. the standardized test could be used just to get past the initial resume filter.
LudwigNagasena 6y ago
This doesn’t prove that PhD is needed. This just proves that people prefer to get paid.
- black_puppydog 6y ago
  The author clearly articulated that it is needed in practical terms. That is, empirically (according to their small sample) people who don't do a PhD don't feature in the list of notable maths achievements.
  - LudwigNagasena 6y ago
    Why then did he only mention money once in passing? Sounds like a very practical concern to me.
fizixer 6y ago
PhD is not strictly necessary, but the process and training that results in a PhD degree is. Case in point, Freeman Dyson, brilliant mathematician/math-physicist, never got a PhD degree, but did research work all his life. Note, he was deeply embedded in the research community, and pretty much everyone he collaborated with, was a PhD or eventually got a PhD (meaning he went through the motions just like other researchers). Final note, the process and training required to be able to conduct research is massively undernurtured, i.e., in my opinion, most PhD graduates are barely an iota better-trained than MS graduates these days. This is getting increasingly true as world population grows, and PhD diplomas get handed out willy nilly (a topic I could go on at for hours). In short, Sturgeon's law is in full swing.
- leereeves 6y ago
  > PhD is not strictly necessary, but the process and training that results in a PhD degree is. I was just about to post the same. I just finished a master's in math (in fact, with additional coursework in physics and statistics I've almost completed two master's) and I don't feel ready to tackle outstanding math problems. And the PhD students I knew were receiving a lot of help from their mentors as they learned how to tackle outstanding problems. There's just so much to learn to contribute to research math these days, it's hard to imagine anyone learning it all on their own.
- mudita 6y ago
  Freeman Dyson studied in very unusual circumstances and got more support than most PhD students. He was regularly playing billiard and discussing math with famous professors at age 17. From his collection of letters "Maker of Patterns": >I arrived as a seventeen-year-old undergraduate at Trinity College, Cambridge, in September 1941. It was a great time to get an education, in the middle of World War II. The famous old professors were all there, but there were hardly any students. >I have fixed up all my lectures now, they are: Hardy on Fourier series, Besicovitch on integration, Dirac on quantum mechanics, Pars on dynamics. The lectures are very select; Hardy has an audience of four, Besicovitch three, Pars four, and Dirac about twenty Here's a video of him speaking about the PhD system, part of a great interview series: https://youtu.be/DzC1IRYN_Ps?t=98 https://youtu.be/DzC1IRYN_Ps?t=98 (“It is an evil system and it has ruined many lives”)
deleted 6y ago
[deleted]
strikelaserclaw 6y ago
If u were gifted at math and wanted to do it all the time, would you a) get paid for doing it with peers while getting a PhD or b) work a job as a janitor to support yourself while doing math. With the amount of depth modern math has, i think to achieve results you need to be able to do it full time, so getting a PhD seems to be the most logical route for aspiring mathematicians. Not to mention that most pure math don't have much practical application at the moment, you certainly would not convince your manager in industry to let you solve random problems just for the sake of solving it.
- formercoder 6y ago
  There’s probably a middle ground given how little phds are paid. Consult as a software engineer for 1/3 time, make double janitor comp, 2/3 time on research.
  - varjag 6y ago
    It never ends at 1/3 time.
    - andrewstuart2 6y ago
      I feel like at 1/3 time you'd spend most or all of it catching up on what happened in the 2/3 of the week you missed. Unless you're not on a team.
  - quickthrower2 6y ago
    I think you would miss out on having a supervisor and peers to learn from. You’d need to replace that. Might be possible with IRC etc. but I don’t know.
    - sushshshsh 6y ago
      Imagine learning from a supervisor, yikes. It is almost always the individual contributors who have to explain things to the supervisor, who might as well be a child at that point.
adamsea 6y ago
It also depends on the person, no?
prionassembly 6y ago
I dropped from grad school with a Master's degree in applied math, and vowed to keep studying for the rest of my life. It's really hard to study "real maths" on your own. It's harder to understand materials without the aid of someone who has already deep-dove and built some intuitions, metaphors and visual schemas. More critically, it's very hard to know if you're doing proofs correctly without feedback.
nottorp 6y ago
If you're interested enough to do math research, you're likely to get a PhD in mathematics because it's, well, full time math research?
YeGoblynQueenne 6y ago
>> How many mathematical, biological, and physical discoveries would never have been made, if it weren’t for robotics (invented by someone with no higher education) and cheap compute (provided by the business sector)? Who does the article mean, by "robotics (invented by someone with no higher education)"? Wikipedia tells me that [in] 1948, Norbert Wiener formulated the principles of cybernetics, the basis of practical robotics [1], but Wiener had a PhD from Harvard [2] and certainly much education, at all levels. The wikipedia article on robotics has a number of other names of people who contributed in various ways to robotics from ancient to modern times, but I'm not sure who fits the article's description. Did Heron of Alexandria have a "higher education", sensu stricto? ____________ [1] https://en.wikipedia.org/wiki/Robotics https://en.wikipedia.org/wiki/Robotics [2] https://en.wikipedia.org/wiki/Norbert_Wiener https://en.wikipedia.org/wiki/Norbert_Wiener
- eindiran 6y ago
  It's really unclear who they could mean. A few of the people in the History of Robotics Wikipedia article[0] didn't have PhDs[1], but seemingly all of them had some higher education. Maybe they are referring to someone who wrote fiction about the idea of robots before robotics really existed: Karel Čapek (who came up with the word "robot") had a PhD though[2]. Perhaps it refers to L. Frank Baum, as he appears to have had no higher education[3]. [0] https://en.wikipedia.org/wiki/History_of_robots https://en.wikipedia.org/wiki/History_of_robots [1] See William Grey Walter for example: https://en.wikipedia.org/wiki/William_Grey_Walter https://en.wikipedia.org/wiki/William_Grey_Walter [2] https://en.wikipedia.org/wiki/Karel_%C4%8Capek https://en.wikipedia.org/wiki/Karel_%C4%8Capek [3] https://en.wikipedia.org/wiki/L._Frank_Baum#Childhood_and_early_life https://en.wikipedia.org/wiki/L._Frank_Baum#Childhood_and_ea...
Joof 6y ago
I'd agree with the hypothesis that a PhD let's you hang out and get paid to do a lot of math. My brain is pretty spent from writing code -- I don't have time to spend doing more math.

57 points by reedwolf 6y ago

The article is missing mathematicians who do not publicize their results. These would mainly be mathematicians working for agencies like GCHQ, NSA, etc. If you want to work on certain math problems, don't mind working for the government, and don't care about being published you can get good jobs with these kinds of agencies.

black_puppydog 6y ago
* and don't care about why these results will go unpublished
- unishark 6y ago
  meaning that everyone who works for the government would agree they are only enabling bad things?
- beefhash 6y ago
  * and don't have anything on your track record making it impossible to land this kind of job due to the security clearance required
- i_am_proteus 6y ago
  Or you are comfortable with why they will go unpublished.
  - black_puppydog 6y ago
    of course, or that
mcguire 6y ago
Of course, in science, if it isn't published, it doesn't exist.
carlosf 6y ago
Financial markets as well.
- fractionalhare 6y ago
  I know of a boutique proprietary trading firm wherein a researcher solved an open problem in probability but won't publish the results because it's integral to a trading strategy. That always gives me a chuckle :)

bo1024 6y ago

The article seems to treat a PhD merely as a credential - maybe assuming that a person would be equally capable with or without it. Why? The whole point of a PhD in math is to learn to do effective research in math and there are almost no substitutes. This seems like being surprised that so many professional violinists took violin lessons. (I admit my bias here but still.)

hn_throwaway_99 6y ago
The same mindset occurs a lot in the software engineering world, and I think it's somewhat baffling and potentially dangerous. I find software engineering quite difficult, and I am relatively intelligent, studied computer science at top universities, and have decades of experience where I learned a ton. So I'm all for coding bootcamps, but we wouldn't expect someone who went to a violin bootcamp for 3 or 4 months to be able to play in an orchestra, but I don't think that's the standard message coming from these coding bootcamps (understandable, they have a biased motivation) or from higher ups in the tech industry at large (more problematic IMO).
- ludamad 6y ago
  "scratch the surface of programming, which nonetheless equips you for real world jobs" could possibly be fair to say about a bootcamp. It certainly filled a certain demand, although one has to wonder if better software won't just eat 4 month configuration++ bootcamps
  - seibelj 6y ago
    I think a better use of coding boot camps would be to go deep in a very specific DSL. Like learn how to do Salesforce or Excel programming deeply. A lot of companies actually need this to improve processes, and restricted environments reduce the cognitive load a novice needs to become productive.
AnHonestComment 6y ago
Many SDEs I know spend years working on mathematics (eg, implementing economic models) — and the job of being an SDE is being an applied type theorist. To me, your comment is the classic classism that engineers have nothing to contribute to science.

jitendrac 6y ago

From what I believe, many of the old days Mathematicians were given PhD by various institutes after they got famous. Not all had PhD, but most of good one got it after being recognized. Also don't forget many people of that time did not publicize their work.

graycat 6y ago

Hint, quiet, don't let this out, a Ph.D. is not really a knowledge degree but a research degree. From that degree on, in blunt terms, everyone knows that no one can carry the whole library around between their ears and so no longer much cares what you know but cares what you can create! There can be and are some exceptions, but overwhelmingly successful research in math requires the background of a Ph.D. for (1) finding a suitable problem and (2) having the knowledge to attack it. And it helps to be in a relatively good school so that will get relatively good versions of (1) and (2). But with everything in good shape, apparently there is one more challenge -- being successful in the actual research. For a hint at this challenge, buried in D. Knuth's The TeXBook is: > The traditional way is to put off all creative aspects until the last part of graduate school. For seventeen or more years, a student is taught examsmanship, then suddenly after passing enough exams in graduate school he's told to do something original. That is, the research is work that is suddenly different, maybe for some people quite different and challenging, than all the academic work before. E.g., there are cases where a student made A's and was the darling of all the teachers from kindergarten through college but in all that time never encountered anything like having new ideas. Bad such cases can lead to stress, loss of self-esteem, crippled ability to work, more stress, burn out, clinical depression, and ... suicide. No joke. For me, part of what helps in research is some qualified respect for some of the existing material. So, I look at what is there as needing improvement and try to do that. If look at the existing material as some nearly perfect construction, then maybe won't feel confident should or could improve on it! One thing rarely taught in math is the importance of intuition: It is needed to do well at guessing, guess a suitable problem, broad outlines of a solution, attack, tools, etc. Good guessing is important since that's most of what there is to do, and good intuition helps with good guessing. Sure, when the results are obtained and in clean form with polished proofs, there can be little or no view of the sources, the intuition. There can be some question about how good some Ph.D. research is: The professors don't want to grant Ph.D. degrees for poor research but don't really know how to ensure good work, indeed, for either the students or sometimes themselves. So one standard that can remove some possibly painful ambiguity is that the Ph.D. research should be "an original contribution to knowledge worthy of publication" with the usual standards for publication being "new, correct, and significant". If a student does some research and the professors question if it is publishable, then the student can settle the issue in an objective way -- try to publish the work. E.g., computer science is concerned with computational time complexity, i.e., good algorithms where good means running time that grows no faster than some polynomial in the size of input data for the problem (rough statement -- more details in the famous Michael R. Garey and David S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, ISBN 0-7167-1045-5, W. H. Freeman, San Francisco, 1979. and more recent sources). IIRC that polynomial criterion came from J. Edmonds. More IIRC, he left his Ph.D. program early and did and published some of his work on networks. Eventually a committee of his former professors came to him and said that should he stack his publications and put a staple in one corner, that stack would be accepted as his Ph.D. dissertation and he would get his Ph.D.

mcguire 6y ago

"A PhD is less important for doing groundbreaking applied engineering and entrepreneurial work, especially in tech." I'm just going to sit here and ponder "groundbreaking entrepreneurial work" for a while. Is it like "financial innovation?" Anyway, I'll also point to Matt Might's illustrated guide: http://matt.might.net/articles/phd-school-in-pictures/ http://matt.might.net/articles/phd-school-in-pictures/

AnHonestComment 6y ago
I don’t read that quote as “groundbreaking” applies to both terms, but rather “groundbreaking applied engineering” and “entrepreneurial” as two kinds of applied domains where the knowledge gained in a PhD is perhaps less useful than 4-6 years of work experience. I’m not sure why you’re mocking “financial innovation” — do you think there aren’t new ways to do commerce or finance than what we have now? Also, that post is dumb: the topology of knowledge isn’t nearly so simple — and that’s worth remembering because the places where you can create new knowledge aren’t all at some boundary which only can be reached by a vaunted PhD. The oversimplification isn’t enlightening — it’s a self-serving justification for classism.

jokoon 6y ago

There's a difference between a degree and an education. The problem is how we consider the destination (the degree), to be a proof of competence and knowledge, while it's really the journey (the education) which actually matters. That's why degrees should be abolished, and a certificate of education be given to the student as long as he/she is present. School should not act as a social filter. As long as you go to school and go to classes, and shows motivation to learn, it's enough. There are no proper ways to evaluate how a student really learned and absorbed the knowledge that was given. There are many students who love the knowledge, but cannot accept scholasticism, the competition, the selection and the filtering. It often ends up being about "belonging to a group", and honestly it was never the goal of education. It's up to companies to really check if someone if competent and has the knowledge, it's not the job of universities. Higher education is an enormous source of inequality, and an immense social barrier. It's really easy for people with degrees to disagree with this, I can only answer with survival bias.

quickthrower2 6y ago
I have a degree, and I agree with you. At least for software engineering. What there could be is a standardised test, that is a national or international standard, not linked to a uni. Learn to program and do the test and that is your credential. Maybe it costs $200 or something. That way you can skip uni, self teach but be able to show you can code without employers needing to find novel ways to evaluate. Just spitballing!
- injb 6y ago
  Ultimately if you standardize something, people will gamify it. The point of employers finding novel ways to evaluate candidates is to win that game and beat the average. Good for them! It can't/shouldn't be otherwise (imo).
  - tprice7 6y ago
    They aren't mutually exclusive approaches, e.g. the standardized test could be used just to get past the initial resume filter.

LudwigNagasena 6y ago

This doesn’t prove that PhD is needed. This just proves that people prefer to get paid.

black_puppydog 6y ago
The author clearly articulated that it is needed in practical terms. That is, empirically (according to their small sample) people who don't do a PhD don't feature in the list of notable maths achievements.
- LudwigNagasena 6y ago
  Why then did he only mention money once in passing? Sounds like a very practical concern to me.

fizixer 6y ago

PhD is not strictly necessary, but the process and training that results in a PhD degree is. Case in point, Freeman Dyson, brilliant mathematician/math-physicist, never got a PhD degree, but did research work all his life. Note, he was deeply embedded in the research community, and pretty much everyone he collaborated with, was a PhD or eventually got a PhD (meaning he went through the motions just like other researchers). Final note, the process and training required to be able to conduct research is massively undernurtured, i.e., in my opinion, most PhD graduates are barely an iota better-trained than MS graduates these days. This is getting increasingly true as world population grows, and PhD diplomas get handed out willy nilly (a topic I could go on at for hours). In short, Sturgeon's law is in full swing.

leereeves 6y ago
> PhD is not strictly necessary, but the process and training that results in a PhD degree is. I was just about to post the same. I just finished a master's in math (in fact, with additional coursework in physics and statistics I've almost completed two master's) and I don't feel ready to tackle outstanding math problems. And the PhD students I knew were receiving a lot of help from their mentors as they learned how to tackle outstanding problems. There's just so much to learn to contribute to research math these days, it's hard to imagine anyone learning it all on their own.
mudita 6y ago
Freeman Dyson studied in very unusual circumstances and got more support than most PhD students. He was regularly playing billiard and discussing math with famous professors at age 17. From his collection of letters "Maker of Patterns": >I arrived as a seventeen-year-old undergraduate at Trinity College, Cambridge, in September 1941. It was a great time to get an education, in the middle of World War II. The famous old professors were all there, but there were hardly any students. >I have fixed up all my lectures now, they are: Hardy on Fourier series, Besicovitch on integration, Dirac on quantum mechanics, Pars on dynamics. The lectures are very select; Hardy has an audience of four, Besicovitch three, Pars four, and Dirac about twenty Here's a video of him speaking about the PhD system, part of a great interview series: https://youtu.be/DzC1IRYN_Ps?t=98 https://youtu.be/DzC1IRYN_Ps?t=98 (“It is an evil system and it has ruined many lives”)

deleted 6y ago

[deleted]

strikelaserclaw 6y ago

If u were gifted at math and wanted to do it all the time, would you a) get paid for doing it with peers while getting a PhD or b) work a job as a janitor to support yourself while doing math. With the amount of depth modern math has, i think to achieve results you need to be able to do it full time, so getting a PhD seems to be the most logical route for aspiring mathematicians. Not to mention that most pure math don't have much practical application at the moment, you certainly would not convince your manager in industry to let you solve random problems just for the sake of solving it.

formercoder 6y ago
There’s probably a middle ground given how little phds are paid. Consult as a software engineer for 1/3 time, make double janitor comp, 2/3 time on research.
- varjag 6y ago
  It never ends at 1/3 time.
  - andrewstuart2 6y ago
    I feel like at 1/3 time you'd spend most or all of it catching up on what happened in the 2/3 of the week you missed. Unless you're not on a team.
- quickthrower2 6y ago
  I think you would miss out on having a supervisor and peers to learn from. You’d need to replace that. Might be possible with IRC etc. but I don’t know.
  - sushshshsh 6y ago
    Imagine learning from a supervisor, yikes. It is almost always the individual contributors who have to explain things to the supervisor, who might as well be a child at that point.

adamsea 6y ago

It also depends on the person, no?

prionassembly 6y ago

I dropped from grad school with a Master's degree in applied math, and vowed to keep studying for the rest of my life. It's really hard to study "real maths" on your own. It's harder to understand materials without the aid of someone who has already deep-dove and built some intuitions, metaphors and visual schemas. More critically, it's very hard to know if you're doing proofs correctly without feedback.

nottorp 6y ago

If you're interested enough to do math research, you're likely to get a PhD in mathematics because it's, well, full time math research?

YeGoblynQueenne 6y ago

>> How many mathematical, biological, and physical discoveries would never have been made, if it weren’t for robotics (invented by someone with no higher education) and cheap compute (provided by the business sector)? Who does the article mean, by "robotics (invented by someone with no higher education)"? Wikipedia tells me that [in] 1948, Norbert Wiener formulated the principles of cybernetics, the basis of practical robotics [1], but Wiener had a PhD from Harvard [2] and certainly much education, at all levels. The wikipedia article on robotics has a number of other names of people who contributed in various ways to robotics from ancient to modern times, but I'm not sure who fits the article's description. Did Heron of Alexandria have a "higher education", sensu stricto? ____________ [1] https://en.wikipedia.org/wiki/Robotics https://en.wikipedia.org/wiki/Robotics [2] https://en.wikipedia.org/wiki/Norbert_Wiener https://en.wikipedia.org/wiki/Norbert_Wiener

eindiran 6y ago
It's really unclear who they could mean. A few of the people in the History of Robotics Wikipedia article[0] didn't have PhDs[1], but seemingly all of them had some higher education. Maybe they are referring to someone who wrote fiction about the idea of robots before robotics really existed: Karel Čapek (who came up with the word "robot") had a PhD though[2]. Perhaps it refers to L. Frank Baum, as he appears to have had no higher education[3]. [0] https://en.wikipedia.org/wiki/History_of_robots https://en.wikipedia.org/wiki/History_of_robots [1] See William Grey Walter for example: https://en.wikipedia.org/wiki/William_Grey_Walter https://en.wikipedia.org/wiki/William_Grey_Walter [2] https://en.wikipedia.org/wiki/Karel_%C4%8Capek https://en.wikipedia.org/wiki/Karel_%C4%8Capek [3] https://en.wikipedia.org/wiki/L._Frank_Baum#Childhood_and_early_life https://en.wikipedia.org/wiki/L._Frank_Baum#Childhood_and_ea...

Joof 6y ago

I'd agree with the hypothesis that a PhD let's you hang out and get paid to do a lot of math. My brain is pretty spent from writing code -- I don't have time to spend doing more math.