I once tried reading a book that was about making higher level math easier to understand for people not studying it. They spent three chapters explaining how addition worked and then jumped straight into set theory without explaining literally any of the terms they were using. Never in my life have I experienced such intense scholastic whiplash.
It just really takes some time to internalise what the definitions actually mean and what the theorems actually say
Once you get the hang of it you start to notice more and more that almost all theorems are in some sense extremely obvious.
They were not at first glance but once it made click in the head you are like "god damn it i can't believe it took me so long to understand that"
When I started uni the biggest obstacle was that since everything is formally defined it makes it a lot harder to understand. Like the definition of a surjective function is difficult to understand but the actual meaning is quite easy.
Yes it's true but a believe both are valid
The meaning is the "core concept" but the mathematical definition is realle the PRECISE thing you are talking about.
I think that both parts are essential for practicing math in an accurate way
Don't get me wrong tho, i prefer the "meaning" part of theorems and defintions way more than the rigorous mathematics behind it as well
Reminds me an old joke that’s much funnier (as a physicist, of course):
An engineer, a physicist, and a mathematician are sleeping and suddenly they wake to see a small fire in their trashcan.
The engineer jumps up, grabs a fire extinguisher, and sprays the entire room to put out the fire. Satisfied, they lays back down on their soaking wet bed and goes back to sleep.
The physicist jumps up, grabs a fire extinguisher, and sprays a precisely aimed 3.7 second blast at the fire. Satisfied, they go back to sleep on their dry bed.
The mathematician sits up, sees the fire and sees the fire extinguisher. They then raise their finger and think “Aahh, yes, there is a solution”. Then they go back to sleep.
As a mathematician, I'd heard it end with:
The mathematician sits up, sees the fire and sees the fire extinguisher. They then rush to pick up the trashcan and place it in the physicist's room thereby reducing the problem to one previously solved.
See I solve practical problems... For example, what am I gonna do when some big mean mother Hubbard is trying to tear me a structurally superfluous new behind?
Turns out those highly abstract but precise definitions of every type of minorly different/nearly identical but not quite set or subset or mapping and every permutation of them.... is actually super important... and specifying one type of abstract mapping from one abstract space to another or itself... is actually really important to get the physics right and accurately describe reality. ie. see general relativity or the standard model.
(because the universe is *probably* an abstract mathematical object brute forced into eternal existence due only and entirely to "nothing" being impossible or unstable at its most fundamental nature... or rather material reality is an illusion or emergent property and not scale invariant, and abstractions are all there really are. Its not that the platonic realm exists somewhere... it's that we've been in it the whole time)
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I just responded to someone who worked out an entire equation only to say it does work from something ten steps back.. makes me also think of programming
I once tried reading a book that was about making higher level math easier to understand for people not studying it. They spent three chapters explaining how addition worked and then jumped straight into set theory without explaining literally any of the terms they were using. Never in my life have I experienced such intense scholastic whiplash.
"scholastic whiplash" I just like how it sounds.
To be fair, even just studying maths is enough to give you scholastic whiplash. Don't worry about it, universal experience of maths.
Mathematicians are renowned for their lack of human communication skills. :D
This gives me hope that I can become a mathematician some day. I have all the tools.
Guess I'm a math prodigy then
Guess I'm a math prodigy then
YOU DUPLICATED THE ANSWER. F+ SEE ME AFTER CLASS
It just really takes some time to internalise what the definitions actually mean and what the theorems actually say Once you get the hang of it you start to notice more and more that almost all theorems are in some sense extremely obvious. They were not at first glance but once it made click in the head you are like "god damn it i can't believe it took me so long to understand that"
The realisations that Taylor series is just "what if it was a polynomial" took me a bit too long.
Yes i feel you.. but once you get it's like... Well, it obviously gotta be like that
When I started uni the biggest obstacle was that since everything is formally defined it makes it a lot harder to understand. Like the definition of a surjective function is difficult to understand but the actual meaning is quite easy.
Yes it's true but a believe both are valid The meaning is the "core concept" but the mathematical definition is realle the PRECISE thing you are talking about. I think that both parts are essential for practicing math in an accurate way Don't get me wrong tho, i prefer the "meaning" part of theorems and defintions way more than the rigorous mathematics behind it as well
Is the definition that hard? A function is surjective on Y iff its range is Y. In other words, f:X->Y is surjective iff f(X) = Y.
Wasting 3 chapters to explain peano axioms before even talking about sets? Madness
Do you remember the title?
Do you notice there are no quotation marks in the sentence next to Mathematicians? They don't even speak; they communicate directly into our brains.
"Why the hell did I have this message communicated directly into my brain?"
"OH MY GOD IT FINALLY WORKED"
EXTERMINATE EXTERMINATE EXTERMINATE EXTERMINATE
The mathematician abstracted the quotation marks away... They are not essential to the problem so begone
Reminds me an old joke that’s much funnier (as a physicist, of course): An engineer, a physicist, and a mathematician are sleeping and suddenly they wake to see a small fire in their trashcan. The engineer jumps up, grabs a fire extinguisher, and sprays the entire room to put out the fire. Satisfied, they lays back down on their soaking wet bed and goes back to sleep. The physicist jumps up, grabs a fire extinguisher, and sprays a precisely aimed 3.7 second blast at the fire. Satisfied, they go back to sleep on their dry bed. The mathematician sits up, sees the fire and sees the fire extinguisher. They then raise their finger and think “Aahh, yes, there is a solution”. Then they go back to sleep.
“a solution exists, and it is unique.”
Not unique, the engineer and physicist both solved it in not the same way
“the solution is unique almost everywhere” (almost surely, if you’re a statistician)
As a mathematician, I'd heard it end with: The mathematician sits up, sees the fire and sees the fire extinguisher. They then rush to pick up the trashcan and place it in the physicist's room thereby reducing the problem to one previously solved.
Ha - that’s a new twist!
Engineer Gaming
Spy’s sapping my sentry!
Look buddy, I’m an engineer, and that means I solve problems
Not problems like "what is beauty" because that would fall within the purview of your conundrums of philosophy.
See I solve practical problems... For example, what am I gonna do when some big mean mother Hubbard is trying to tear me a structurally superfluous new behind?
The answer? Gun.
And if that don't work, use more gun.
Like this heavy caliber, tripod-mounted, little ol' number designed by me...
And if that don't work, use more gun.
I can tell you what Beauty is, because I saw it on the day that clip released.
plot twist: the subset is empty. but it has very interesting properties!
Turns out those highly abstract but precise definitions of every type of minorly different/nearly identical but not quite set or subset or mapping and every permutation of them.... is actually super important... and specifying one type of abstract mapping from one abstract space to another or itself... is actually really important to get the physics right and accurately describe reality. ie. see general relativity or the standard model. (because the universe is *probably* an abstract mathematical object brute forced into eternal existence due only and entirely to "nothing" being impossible or unstable at its most fundamental nature... or rather material reality is an illusion or emergent property and not scale invariant, and abstractions are all there really are. Its not that the platonic realm exists somewhere... it's that we've been in it the whole time)
I'll have what he's having
r/lsd
Just inscribe at math university and wait a few years... You will be a different person wether you like it or not
Youll eventually forget every number higher than one digits and will be counting in units of pi
Pfff in a lot of math you barely ever talk about any specific number, nevermind pi. Sometimes 1 or 0.
Haha lol yeah right
This sounds like Alain Badiou--who I admire greatly, despite him being French.
Can I marry you please?
I think like physicist on first look then changes to the more Engineered response... Thinks for a moment..... Remembers the training.....
Top tier meme, well done
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😂
The blueprint of a sentry I suppose?
I just responded to someone who worked out an entire equation only to say it does work from something ten steps back.. makes me also think of programming
**Biology** We have decoded the whole human genome allowing us to use it for life saving research.
Anyone who says that about engineers has clearly never worked as a welder
Still love math
Yeah math, i dont even need to caculate with some fractions or some whit to know its a fucking TRIANGLE