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There’s more to mathematics than rigour and proofs (2007)

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Re: There’s more to mathematics than rigour and proofs (2007)

#21

Post by ffhhj »

paulpauper wrote: post #5
devnulll wrote: post #2

One day I'll retire and go back to school. The idea of learning Math - really learning & understanding Math - as a fun pastime is so appealing. What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...

keep the salary. if the goal it to change the world, to understand reality, to have an impactful life, have a good standard of living, etc. math is one of the hardest ways of achieving that. It's such a saturated field. Almost everything you can imagine has been done to the highest possible degree of abstraction. Every stone overturned except for things which may take a lifetime to even try to understand. Writing a b…

I couldn't wait that much, started researching stochastic processes a few years ago and been developing a theory for supertasks.

Re: There’s more to mathematics than rigour and proofs (2007)

#22

Post by stult »

devnulll wrote: post #2

One day I'll retire and go back to school. The idea of learning Math - really learning & understanding Math - as a fun pastime is so appealing. What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...

I’ve had a very similar experience and my solution was to incrementally move into more and more math intensive jobs, starting from regular old SWE working on a web app to working on an aerospace-related web app that involved lots of physics and geospatial calculations and then moving toward MLE/DS jobs. All without a STEM degree, teaching myself the math as I go. It hasn’t been easy but I enjoy what I do more and more over time.

Re: There’s more to mathematics than rigour and proofs (2007)

#23

Post by lordnacho »

paulpauper wrote: post #5
devnulll wrote: post #2

One day I'll retire and go back to school. The idea of learning Math - really learning & understanding Math - as a fun pastime is so appealing. What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...

keep the salary. if the goal it to change the world, to understand reality, to have an impactful life, have a good standard of living, etc. math is one of the hardest ways of achieving that. It's such a saturated field. Almost everything you can imagine has been done to the highest possible degree of abstraction. Every stone overturned except for things which may take a lifetime to even try to understand. Writing a b…

This is why I'm happy to simply read the well established facts of a variety of fields. There's more than enough to learn for a lifetime, and from what I read about research there's a heck of a lot of BS in the way for small incremental gains.

Having said that, if something does come along that interests someone, they should try it. A friend of mine is doing his 2nd PhD 40 years after his first, having found his way into it via a love of jazz music.

Re: There’s more to mathematics than rigour and proofs (2007)

#24

Post by lordnacho »

markus_zhang wrote: post #17
devnulll wrote: post #2

One day I'll retire and go back to school. The idea of learning Math - really learning & understanding Math - as a fun pastime is so appealing. What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...

In the same boat. One of my dreams is to go back to school, learn vector analysis, differential equation, differential geometry, classic mechanics, electromagnetic, special relativity and finally general relativity. Actually quite doable as long as one can grit through the Math, some of which do not need a back to back read.

Why would you need to go back to school to learn those things?

At best school is a syllabus telling you what people think you should know, fairly easy to get a hold of, and maybe a bit of accountability to make sure you actually learn it.

Re: There’s more to mathematics than rigour and proofs (2007)

#26

Post by peterhalburt33 »

ffhhj wrote: post #20

Which are the newest developments in math? Someone told me Geometric Algebra has been around for a long time but wasn't really useful until some recent theorems.

It really depends on which field you are talking about. I’d say it is very hard to find an area of math that’s completely new , but you will often find existing areas where novel perspectives are driving math forward. Geometric algebra may be a hot topic in some areas, but the ideas of exterior algebra go back more than a century at this point, so is it really new??

Just to humor you though, I think Deep Operator learning is a vastly exciting new field which combines ideas from functional analysis and deep learning in order to do things like solving PDEs.

Re: There’s more to mathematics than rigour and proofs (2007)

#27

Post by markus_zhang »

lordnacho wrote: post #24
markus_zhang wrote: post #17

Earlier quoted context omitted.

In the same boat. One of my dreams is to go back to school, learn vector analysis, differential equation, differential geometry, classic mechanics, electromagnetic, special relativity and finally general relativity. Actually quite doable as long as one can grit through the Math, some of which do not need a back to back read.

Why would you need to go back to school to learn those things? At best school is a syllabus telling you what people think you should know, fairly easy to get a hold of, and maybe a bit of accountability to make sure you actually learn it.

Yeah I agree with that. I can also buy a few books and go from there. But essentially O cannot do that now because of X, Y and Z.

Re: There’s more to mathematics than rigour and proofs (2007)

#28

Post by mbustamanter »

This is remarkably accurate and resonates with me a lot. I did mathematical olympiads in high-school, where intuition to crack problems plays a major role. Then went on to college to study an undergraduate degree in maths (concentration in analysis). Analysis requires, at least in its rigorous foundations, to be careful and have a skilled knowledge of logic/quantifiers (more than elementary abstract algebra in my humble and biased opinion), often very scrupulously. Then in my graduate studies intuition along with the maturity of rigor work to produce new theorems. I'm impressed that several times I look at a paper or series of results and can read them "diagonally" to get the motivation without scanning all the text (of course, if the aim is to cite/build on top of/generalize/apply it then close attention to reasoning should be paid).

Re: There’s more to mathematics than rigour and proofs (2007)

#29

Post by Koshkin »

devnulll wrote: post #2

One day I'll retire and go back to school. The idea of learning Math - really learning & understanding Math - as a fun pastime is so appealing. What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...

Be sure not to retire too late. At an older age, with all the experience you will have under your belt, picking up new concepts and methods will not be a problem, but retaining details in memory will. You have no idea how incredibly hard it will be. So start early.

Re: There’s more to mathematics than rigour and proofs (2007)

#30

Post by agumonkey »

devnulll wrote: post #2

One day I'll retire and go back to school. The idea of learning Math - really learning & understanding Math - as a fun pastime is so appealing. What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...

not alone, or more like the vast majority

I'm still trying to find a part time dev gig so I can just focus on graphs and advanced combinatorics

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