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Memorising formulas or deriving them? 
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#1
Dec712, 02:36 PM

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Hello,
I'm new here and this is the first thing I ever write on this forum, hence the question if this is the wrong place to post anything remains unanswered on my part. I came across this forum doing something on the internet, I can't remember what. I'm certain though that it was related to science, most likely got stuck with homework. Anyway, this question might seem idiotic and I don't really know where or how to start. However, many things are intuitive to me, why the definition of derivative looks like what it looks like, why 2+2=4, why you can add a 5x to the side of the equation that has 5x to make that side equal to 0, and add the 5x to the other side. What my point is that I don't believe that I would ever have come up with it, discovered it, that I had to learn it from someone else. Eventhough I understand it as well as anything else, I couldn't as a caveman have discovered it. Now, I'm alright at maths, I love learning maths and learn it rather quickly. What I want to know is how people on your level of intelligence and ability experience subjects such as maths or physics. Do you read books, go to classes and struggle to comprehend a new concept or have you already in your day dreams come up with a similar idea and just had it confirmed from your teachers? A maths Ph.D. for example, has he gone to classes to learn from others or did he already, eventhough he wasn't sure or had created sufficient proof, understand it from just thinking about it? I apologise for this question, yet I really wish to know how it feels for those who are at your level. 


#2
Dec712, 07:28 PM

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I've had that feeling many many times (how the hell is some genius come up with this?)
Not sure what your post has to do with your title. 


#3
Dec712, 07:56 PM

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Well, mainly what I meant with the title was that how do you "do math" without knowing the formulas... I guess the naming was off, sorry. :)



#4
Dec712, 11:07 PM

P: 784

Memorising formulas or deriving them?
I'm very young, at least for this forum, and I already know that feeling. Today in my Multivariable Calc class the professor asked us a question about a function. We all looked at it quietly for about 30 seconds until one person answered it in about 3 words.
Did the answer make complete sense to me? Yes. Was there a chance in a billion I would have answered that question correctly in comparative time? No. 


#5
Dec712, 11:26 PM

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P: 4,287

Some guy came up with the d'Alembertian and turned maxwell's four equations into one that allowed for gauge transforms. They were all "standing on the shoulders of giants" as Newton would say. That's why it's important to learn the field you want to contribute to, because a lot of work has already been done and lot of your intuitions may already be wrong. But if you go to the edge of research, you don't have to waste time testing all your hypotheses and you can focus your questions better and find the next step in understanding some obscure branch that nobody else cares about (unless you want to be a celebrity scientist... then you better be good at presenting. Might even try minoring in drama.) 


#6
Dec712, 11:45 PM

P: 5,630

Algebra, which you admire but don't think you could have invented, likewise, seems to have been the creation of a rare individual, Persian mathematician, Muḥammad ibn Mūsā alKhwārizmī. But there's another problem. Today I think science and math are bogged down in so many useful tools that a lot of people's creative energies are sapped just trying to familiarize themselves with those tools so they can get a job exploring some unbelievably specialized vein, or more likely capillary, of science. If there's a Galileo out there today he's probably anonymously making amazing headway in some minute subspecialty no one outside his workplace will ever hear about. 


#8
Dec812, 02:25 AM

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#9
Dec812, 04:18 AM

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It is not a question of either memorization or derivation.
If you should derive everything everytime, then you have barred yourself from doing any progress at all. 


#10
Dec812, 10:31 AM

P: 132

About memorizing or deriving, I have some rule of thumb about it. I 'memorize and not derive' if I'm in an unusual hurry, but would still insist that I have some intuition about what the theorem/formula says. Otherwise, I usually rederive and reprove pretty much most of what I am trying to learn. 


#11
Dec812, 11:06 AM

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P: 18,299

Al Khwarizmi certainly did make significant contributions to mathematics. As an example, he solved equations using geometric shapes. But it wouldn't be right to credit him with the entire invention of algebra. Needless to say that algebra back then and algebra now are significantly different. For example, the concept of 0 and the concept of negative numbers did not exist yet. 


#12
Dec812, 12:40 PM

P: 3

Thank you so much for your answers. I'm really feeling more confident in myself now, seeing that you aren't so different from me afterall, hehe.
So in plain words, it is NOT shameful to go to class and read books or browse the internet to learn new scientific or mathematical concepts... I guess. 


#13
Dec812, 01:24 PM

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#14
Dec812, 02:02 PM

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#15
Dec812, 03:28 PM

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#16
Dec912, 09:53 PM

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#17
Dec912, 09:56 PM

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