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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)

#41
post #39
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...

Yes, you can't do something if you chose to do something else instead. Clearly you find earning/spending money more appealing than math.

What a ridiculous oversimplification of life...

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

#42
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'm still grumpy that I accepted I knew what real numbers were just because I could recite back the definition given by the teacher. There is so much depth there if you go looking...

I contend no one understands real numbers if they can’t explain (without resorting to essentially purely symbolic rigor) why you can cover the rationals with intervals of arbitrarily small total length, but you can’t do the same with R.

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

#43
post #13
post #8

Earlier quoted context omitted.

One of my biggest regrets is not having studied (more) math. But would I regret not studying CS had I studied math? You really can't win :/

CS is math...

I’d argue math is actually (a proper subset of) CS.

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

#44
post #31

Earlier quoted context omitted.

A proof that no one would understand in not a good proof. The ideal approach to proving theorems, at least according to how Grothendieck did it, is to build a beautiful theory in which the proof becomes elementary.

It's quite a big assumption to think truth can always be bent so as to satisfy our ridiculously limited cognition. And math has been used instrumentally from the very beginning, so results are often much more important than the process. Theoreticians may still value elegance because that gives them pleasure or whatever, but few other people care about that as long as they can use the results.

The results aren’t often nearly as useful as the techniques used to find them. For example, a completely opaque proof resolving P vs NP is completely useless to theoretical CS.

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

#45
post #22
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 mor…

Impressive :)

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

#46
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...

You can’t really learn Math at school. Not really from the perspective of understanding mathematical beauty deeply. I wish there was an outlet or means to do so. I always found schooling to be woefully inept at assisting in learning the craft.

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

#47
post #22
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 mor…

This is a bit tangential, but was the lack of a STEM degree ever an obstacle in getting those jobs? Just asking because I'm currently in a similar position, regular SWE job, but I'd like to eventually move to something more mathy.

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

#48
post #16

Earlier quoted context omitted.

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…

About the simulation hypothesia, how is that different from Descartes evil demon? https://en.m.wikipedia.org/wiki/Evil_demon (apart from saying that the evil demon is a future type computer)

The simulation stuff is just “Plato’s Cave”:Reloaded for people who never understood the concept of the cave in the first place. At a basic level you can interpret it from Gödel’s incompleteness theorems, which state that systems of logic need some form of observer to function. That observer concept reaches way back across different philosophical domains and authors as well.

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

#49
I understood math much better after following the Software Foundations tutorials:

https://softwarefoundations.cis.upenn.edu/

Another good starting point (for mathematicians) would be the Lean community group and the Math lib project:

https://arxiv.org/pdf/1910.09336.pdf

https://github.com/leanprover-community/mathlib

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

#50
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...

https://arxiv.org/pdf/1910.09336.pdf
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