Mathematics Thread

[Guest]

I've really been loving math/maths lately. Anyone else into it? Share cool math things in this thread!

Euclidean puzzles: https://www.euclidea.xyz

[auxien]

I've been watching a ton of Numberphile, Computerphile, and 3B1B lately. ^saw that one a few months ago, love the graphing of it on the end (relation to the Mandelbrot set of course!) 

 

Binged on the cards and dice playlist with this guy most recently:

 

[KovalainenFanBoy]

[Braintree]

I watched The Story of Maths recently and found it fascinating (even though it can be really dry and dorky at moments).

 

https://www.netflix.com/title/80093836

[YangYing]

I'm pursuing a career in engineering and am currently stumped in applied mathematics, them vids sure are fun but man I can tell you.. working with it can b a real bitch

 

It's rlly a discipline worthy of respect tho, the most fascinating thing for me is how incredibly abstract problems map onto reality as we perceive it

 

 

prime numbers also are rlly rlly weird

[dingformung]

subtraction is really hard imo

[Guest]

So many Numberphile fans! This video ignited it all for me and I had to understand what was happening:

 

I'm pursuing a career in engineering and am currently stumped in applied mathematics, them vids sure are fun but man I can tell you.. working with it can b a real bitch

It's rlly a discipline worthy of respect tho, the most fascinating thing for me is how incredibly abstract problems map onto reality as we perceive it

 

What exactly are you working with? I've been eating up algebra, trigonometry, and calculus in between things and loving it. But it's kind of a lonely endeavour since it's a little hard to find recreational math geeks who want to get together and discuss math.

[Guest]

Something to add as a recent math enthusiast: learning algebra opens up most of what is needed in a lot of math. 

[YangYing]

Partial differential equations, modelling things w them and methods to solve them

 

Is rlly quite algorithmic processes but it can become rlly rlly time consuming and tedious (which is why u usually have computers do the job, but u kno.. gotta know the ins and out of it)

 

more practically is modelling things like how the temperature on a meatball varies depending on place and time, or how a guitar string oscillates when u pluck it.. precisely

 

v powerful stuff

[Guest]

Very cool! I'm working my way to differential calculus, but I'm more interested in theory than applied maths at the moment. More precisely, on Khan Academy, I'm playing with trigonometric identities to rearrange calculus functions to keep them from dividing by zero. Which is kind of bonkers sometimes as it forces you to realize how functions involving SIN, COS and TAN can be morphed into seemingly very different functions but they now give valid results.

I compare all this stuff to playing puzzle games, except these puzzles apply to the underpinnings of the Universe! It really blows my mind.

[joshuatxuk]

I need to brush up on my math skills. I keep hearing how US schools are dropping multiplication tables and condensing a lot of the drill / repetition based stuff like long division and such, I have little kids who will one day go to school - if this indeed the case I suppose I could use Khan Academy and other resources if that's the case?

 

A few years ago (I'm 32 now) I took math classes at a community college in conjunction with my land surveying sources and it reminded me how much I studied in school. Def can't calculate stuff in my head like I used to but I got back in form ok  - so it freaked me out to think how lost I'd be otherwise.

Edited June 27, 2018 by joshuatx

[diatoms]

symmetrical:)

[Soloman Tump]

Anyone looked into the Millennium Problems? (pdf link)

 

The Riemann Hypothesis

The Yang-Mill Theory and Mass Gap Hypothesis

The P v NP problem

The Navier-Stokes Equation

The Poincare Conjecture

The Birch and Swinnerton-Dyer Conjecture

The Hodge Conjecture

[zlemflolia]

 

 

 

 

I'm no expert, just have a plebeian CS degree, but a good place to start out if you want to self study math is basic set theory, it will open up a lot of the lingo and are really low hanging fruits and is cool

[KovalainenFanBoy]

Anyone looked into the Millennium Problems? (pdf link)

 

The Riemann Hypothesis

The Yang-Mill Theory and Mass Gap Hypothesis

The P v NP problem

The Navier-Stokes Equation

The Poincare Conjecture

The Birch and Swinnerton-Dyer Conjecture

The Hodge Conjecture

a good way to pass the time is reading the 2 or 3 P vs. NP proofs that pop up twice a year then reading the inevitable follow ups where someone finds the flaw in the proof

[zkom]

I have a master's in applied mathematics and unfinished from theoretical. Sadly I haven't been able to use mathematics much in my work in the last couple of years except for occasionally solving some matrix equations for my coworkers. This might get fixed soon though.

 

Anyway, I really love mathematics. I tried to read some metalogic also but been stuck with a book on it for quite some time now. Philosophy of mathematics is also very interesting.

[Soloman Tump]

 

Anyone looked into the Millennium Problems? (pdf link)

 

The Riemann Hypothesis

The Yang-Mill Theory and Mass Gap Hypothesis

The P v NP problem

The Navier-Stokes Equation

The Poincare Conjecture

The Birch and Swinnerton-Dyer Conjecture

The Hodge Conjecture

a good way to pass the time is reading the 2 or 3 P vs. NP proofs that pop up twice a year then reading the inevitable follow ups where someone finds the flaw in the proof

 

 

I never did finish reading Godel / Escher / Bach... I gave up about page 500 when there were more symbols than words on each page.

[KovalainenFanBoy]

^ that book is a mess. He goes into needless, very specific detail just to make a more general point later on, but there's so, so many random digressions and self indulgent filler that the broader points just get lost. He spends like a hundred pages later on describing the process of DNA replication in cells. That book's in serious need of editing

 

it gave us that awful pitchfork review that's written as one of the achilles / tortoise dialogues though so it was all worth it

Edited June 28, 2018 by span

[Bodhidharma]

I've really been loving math/maths lately. Anyone else into it? Share cool math things in this thread!

 

Euclidean puzzles: https://www.euclidea.xyz

 

theres a book "chaos theory" by james gleick that goes into feigenbaum constants, not too many equations and stuff in it, more like a look at how things in the maths community evolved from when these things were discovered and how they came into the mainstream and talks about the people behind them. rly good read. i think a paper titled "period three implies chaos" by yorke and li touches on it, cant remem tho

[mcbpete]

So many Numberphile fans! This video ignited it all for me and I had to understand what was happening:

 

It's bit of a lengthy one but have you seen the counter video that shows the shenanigans behind such an 'proof':

 

[zkom]

Yeah, that 1+2+3+... =-1/12 has been an example in a bunch of books how to NOT to do infinite series.

 

The simple fact that integer set is closed under addition (adding integers together can only produce integers) already tells you it's dead wrong. The second hint is that the series definitely doesn't converge.

[YangYing]

hehe if you start delving into that rabbit hole you come into the definition of real numbers p quickly which is one hell of a thing to wrap your head around

[Guest]

 

So many Numberphile fans! This video ignited it all for me and I had to understand what was happening:

 

It's bit of a lengthy one but have you seen the counter video that shows the shenanigans behind such an 'proof':

 

 

Yes, that was a fun week. I was watching Mathloger vids for a while, but I didn't understand the finer details of what he was explaining yet, so it pushed me to go deeper with the basics.

 

Dr Padilla did write about this infinite series in more detail: https://www.nottingham.ac.uk/~ppzap4/response.html

 

And Dr Copeland's proof goes into more detail with the Riemann zeta function: 

 

But I can't really give an informed opinion since I'm still a math novice really. I can directly point to that original video in sparking my renewed interest for math, so I'm a bit of a biased romantic about it. 

[zkom]

The basic problem is that it's a divergent series so it does not have any definite sum since it does not converge toward any value.

 

For convergence you should be able to pick a value arbitrary close to -1/12 so that a finite subsum of the series 1+2+3+4+...would be closer to than the picked value and then adding any amount of values from the rest of the series wouldn't move the sum further away from.

 

So, let's see the series 1/2+1/4+1/8+1/16+...=1: We can pick a value arbitrary close to 1, like 0.99. There's now a finite subsum 1/2+1/4+1/8+1/16+1/32+1/64+1/128=127/128 that is closer to 1 than 0.99 and adding up values from the rest of the series to that, for example 127/128+1/256+1/512=511/512, will only get us closer to 1.

 

Going back to the original series in question, I should be able to pick a value like 0 that is 1/12 away from the -1/12. Now how do I pick a finite subsum of 1+2+3+4+.. that is closer than 0 to -1/12? Any finite subsum like 1+4+6=10 or 1+2+3+..+100=5050 is higher than 0 and definitely further away from -1/12 than 0. Adding any number of values from the rest of the series is going to move the sum even further away from it. The series does not converge towards -1/12 or any other value.

[phudoshin]

 - I love the numberphile guys

 - recently bought a friend "Fermats Last Theorem" as shes a math lover

 - I did Applied Physics in Uni but ended up in IT... a remember in optics there was a physical explanation for the concept of square root of -1 and i was so excited ......but now ive forgotten!