Mnemotechnics for mathematics

Are there are any mathematicians here that operate with memory techniques as an aid to the study of mathematics? If yes, how do you go about it?

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I guess the sutras in Vedic Math are a memory technique… Ekadhikena Purvena (one more than the previous) tells you how to do squares of 25, 35, etc.

For 35² you got 5x5 on the right hand side for a total of 25 and on the left hand side you take one more than the previous (i.e., 3+1 = 4) and multiply it with the original digit for 4x3 = 12. Together you get 1,225 as the answer.

For 45² you take 5x4 = 20 and for 55² it’s 6x5 = 30 which gives you 2,035 and 3,025, respectively. You can google “Sutras Vedic Math” to find more of these.

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Thank you for your reply, but I wasn’t referring to menial computation, but rather the “true”, proof-based and conceptually dense kind of mathematics.

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Lol… got an example then…?

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Yes, an example would be the proof of Taylor’s theorem with one variable, which you can find here.

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I’m not sure which proof you want to memorize, but it doesn’t matter, you will be able to extrapolate the process to the other proofs in general. I’ll just use the Theorem section of this website as an example: https://proofwiki.org/wiki/Taylor’s_Theorem/One_Variable

Whenever you want to memorize a proof or theorem, you often want to memorize the explanation of the proof as well. Oftentimes whenenver I do this, I just use the keyword method and memorize a word per sentence to remember the general idea of the paragraph.

In many math theorems, explanations are given in mathematical notation, as shown in the Theorem example I provided. To memorize this using the keyword method, I write down what the symbols mean in plain English, and then I use the keyword method to easily memorize the information.

Sometimes that’s not feasible to do, or you need to actually memorize a certain formula. In cases like this, you want to take the mathematical statement or formula and split it up into parts to be memorized separately. For example, I wanted to memorize the error term formula, some of my mnemonic images would be this:
Rn = Ren (from Ren and Stimpy), 1/(n+1)! = tie being cut in half by Ned Stark with an exclamation up his bum, and so on and so forth.

This is just a brief little description of my method that you can use. I’d put the whole method down, but this post is getting a little too long, and I don’t won’t to bog you down with soo much information at one time. If you have questions, I can help you and give you a more detailed explanation.

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Hi there,

so this is my first post ever in this forum. I am not quite sure what exactly you are asking for. But concerning on how to memorise math formulas, I can give you one short example of how I do it:

If I want do memories the formula to calculate the frequency of a simple pendulum:
f=1/2Ď€*sqr(g/l)

So I imagen myself going throw a room while holding two pies in my hand. Suddenly there is a wrecking ball swinging by that nearly hits me (that’s the simple pendulum…). Because it nearly hits me I flinch and want to drop both pies (1/2π). By stepping back I stumble over a root (sqr) and because of gravity (g), I fall down. And because of the heavy momentum, I have I fall down with a heavy smack at the full length of my body. (/l).

I don’t know if this is suited for everybody, but for me it works fine. Any thoughts on that?

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Whenever you want to memorize a proof or theorem, you often want to memorize the explanation of the proof as well. Oftentimes whenenver I do this, I just use the keyword method and memorize a word per sentence to remember the general idea of the paragraph.

I am sorry, I am not exactly sure (n.b. I am a newbie in this world) what you mean by keyword method: is it the same as described in this introduction? I’ll continue assuming that it is true.
How feasible is this method when considering you also have to memorise the conditions for a certain theorem to be true?

1/(n+1)! = tie being cut in half by Ned Stark with an exclamation up his bum, and so on and so forth.

I am not sure I quite understand the assocation there :rofl:

This is just a brief little description of my method that you can use. I’d put the whole method down, but this post is getting a little too long, and I don’t won’t to bog you down with soo much information at one time.

Please do! I would love to have something to refer to, I’m intent on learning mnemotechnics mainly as an aid to my studying method, I would love to have the reference of someone more experienced than me to on my particular use case.
Also, obviously, thank you for your post!

I find this method very creative indeed, how much time do you need to create a series of images like that?
How do you approach formulas that are more abstract?

P.S. I haven’t figured out how to reply to two people at once, does anyone have any idea? Is it alright to post two consecutive messages just to reply to two different people?

You can reply to both in one post or post twice – whichever you prefer.

If you want, you can quote parts of multiple posts by highlighting some text with the mouse and clicking the “quote” box that appears.

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The keyword method is basically using a word or phrase that encapsulates the whole idea of a sentence or paragraph. For example: “A token is the smallest part of a program”. To memorize the whole idea of this sentence, I would just memorize the word “smallest” and the ideas that this word signifies will flood my mind. The best explanation of the keyword method in my mind is Harry Lorayne’s and Jerry Lucas’s book on mnemonics. You can easily find a free copy online with a bit of searching.

Using the keyword method greatly reduces your memory load once you master it. You won’t have to contend with large palaces or overly long mnemonic links. Whenever I have to memorize “sub-information” like memorizing the conditions for something to be true or not, I memorize that information separately, and I can recall it whenever needed in the future.

Blockquote 1/(n+1)! = tie being cut in half by Ned Stark with an exclamation up his bum, and so on and so forth.

1 = tie. The division symbol I always represent by some kind of slashing or cutting motion. Ned = n1, which I translate into Ned. And the ! is just an exclamation. I combine all of these images to memorize 1/(n+1)!

Overall, that’s my method in full. It takes a bit of getting used to, but once you learn it, mathematics will be soo much easier. One word of warning I will say is that you should make sure you understand the material somewhat before you memorize it.

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I more work in IT but I do use mathematical formulas in programming. Seeing how I am now learning about these memorization techniques, I am now trying to create a system for memorizing formulas.

I think of formulas as an algorithm.

Below is what I have come up with so far:

Algorithm:

Finding if a positive number P is a prime number:

Set N=2.

( painting of tree with orange leaves falling My image for a variable N on one end of a scale perfectly balanced with a hen [my image for number 2 ] )

Divide P by N and find the remainder R.

(Papa Smurf being sawed into parts by variable N, Sherlock Holmes looking through a magnifying glass for forensic evidence [Romeo - variable R] at the scene of the previous crime )

If R is zero, P is not prime. Exit.

( Imagine choice of two tunnels/train tracks, one has variable R balanced perfectly with a sow [my image for 0] and leads to Prime the leader of the transformers with a big glowing red X scrawled across his chest, blocking the way, while the other leads to a train platform)

Set N=N+1.

(On the platform, variable N balances perfectly with variable N hugging a top hat [my image for number 1])

If N is greater than or equal P, P is Prime. Exit.

(the track continues and splits again.

- one side has an image of a large variable N towering above variable P, leading to transformer Prime posing triumphantly and blocking the way.

-the next has an image of variable N balanced perfectly with variable P , leading to transformer Prime posing triumphantly and blocking the way

Sorry for the long winded response. Understand I am still learning and trying to figure out how to apply these techniques to coding, or math.

What needs to be done:

  • Learn the Major method

  • Figure out images for each letter of the alphabet

  • images for mathematical operators (=,-, +, =>, …)

What do you all think?