Was a PhD necessary to solve outstanding math problems? • Hacker News Board

Re: Was a PhD necessary to solve outstanding math problems?

#31

Post by AnHonestComment » Sat, Jul 11, 2020, 3:57 PM UTC

mcguire wrote: post #15

" 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/

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.

Re: Was a PhD necessary to solve outstanding math problems?

#32

Post by injb » Sat, Jul 11, 2020, 4:00 PM UTC

quickthrower2 wrote: post #24

jokoon wrote: post #17

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 sc…

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 spitb…

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).

Re: Was a PhD necessary to solve outstanding math problems?

#33

Post by mudita » Sat, Jul 11, 2020, 4:04 PM UTC

fizixer wrote: post #3

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 researc…

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 (“It is an evil system and it has ruined many lives”)

Re: Was a PhD necessary to solve outstanding math problems?

#34

Post by btrettel » Sat, Jul 11, 2020, 4:07 PM UTC

formercoder wrote: post #12

strikelaserclaw wrote: post #6

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 do…

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.

I've thought about this general approach for funding my own research. Unfortunately it seems hard to do in practice.

If the goal is consulting specifically then it's going to take a while to build up the client base needed. I'm just starting consulting myself and I don't expect this to get me more than a couple thousand dollars over the next year.

Generalizing a bit, one could make money running a business, consulting being a possible example. The problem with this is that starting a business is usually more than a full time job. This is only viable in the long-term once all the hard work is done, and only if the business gets off the ground. There are no guarantees.

Another possibility is to work a more conventional job that offers reduced hours and still decent pay/benefits. I don't know of any such jobs and would welcome any recommendations.

Re: Was a PhD necessary to solve outstanding math problems?

#35

Post by i_am_proteus » Sat, Jul 11, 2020, 4:08 PM UTC

black_puppydog wrote: post #14

DanBC wrote: post #8

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.

* and don't care about why these results will go unpublished

Or you are comfortable with why they will go unpublished.

Re: Was a PhD necessary to solve outstanding math problems?

#36

Post by prionassembly » Sat, Jul 11, 2020, 4:17 PM UTC

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.

Re: Was a PhD necessary to solve outstanding math problems?

#37

Post by kkylin » Sat, Jul 11, 2020, 4:18 PM UTC

bo1024 wrote: post #9

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.)

Exactly. Getting a PhD means 1. taking some advanced math classes 2. hanging around some like-minded people for a few years 3. solving a problem or two, big enough to add up to a dissertation 4. publish, with professional help on learning to write 5. getting teaching experience Except for the last item, all these are things every aspiring mathematician would need / want to do anyway.

Now, not everyone wants to teach, and at some universities TAs are overburdened. But certainly not all, and I'd argue that teaching experience in a well-strucured programs can teach one a lot of useful communication skills.

Working on your own means you can get #3. Not everyone needs #4, and you can get some of #1 online or from books (but harder to find people to talk to). So no, a PhD isn't necessary. But most of the things one would do to get a PhD certainly is useful.

Full disclosure: FWIW I have a PhD and work as an academic mathematician.

Re: Was a PhD necessary to solve outstanding math problems?

#38

Post by tprice7 » Sat, Jul 11, 2020, 4:19 PM UTC

injb wrote: post #32

quickthrower2 wrote: post #24

Earlier quoted context omitted.

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 spitb…

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).

They aren't mutually exclusive approaches, e.g. the standardized test could be used just to get past the initial resume filter.

Re: Was a PhD necessary to solve outstanding math problems?

#39

Post by carlosf » Sat, Jul 11, 2020, 4:26 PM UTC

DanBC wrote: post #8

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.

Financial markets as well.

Re: Was a PhD necessary to solve outstanding math problems?

#40

Post by mathattack » Sat, Jul 11, 2020, 4:27 PM UTC

bo1024 wrote: post #9

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.)

I think you’re correct here. The author assumes you have the starting knowledge out of undergrad (or ability to self teach) and everything in grad school is sorting and signaling.

My view of school is more nuanced. Both undergrad and grad have a mix of signaling, sorting and learning. Since the financial barrier to entry to solving math problems is low, the easy problems are solved. To solve the hard ones, you need several more years of post-undergrad coursework to get to the edges of the field, and several more being mentored on how to push the edges. It’s hard to get there without the more advanced guided tour that grad school provides.