Memory techniques for higher math

Out of curiosity I was watching one of the free university lectures on iTunes on Quantum Mechanics from Oxford University. I didn’t understand a word of it but it got me thinking as I was watching the professor scribble all kinds of cryptic Greek symbols on the board.

I thought if one took the time to translate all the operations, variables, symbols, and relations to very tangible objects would it be possible for an average mind to comprehend this stuff? And after working on it like memory training would they begin to follow this lecture like movie or cartoon animation (w/ understanding). Something like [meaningless] €-> ~^h would immediately bring up an apple being sliced under a tree and ~h^ -> € would be an apple hammering nails into a shoe (e.g., relation and operation changes objects and actions). This would require a complete comprehension of the subject and life-consuming amounts of time, but once done it would allow theoretical physics and the highest levels of abstract math to be taught to kids or right-brained adults.

I read somewhere on Ben’s blog that he participated in mental maths competition and that you can do mental calculations involving large numbers quite quickly if you know the methods.

I don’t know if he did it using images for numbers or using numbers only.

Would be curious to know if we can use images to to do calculations though.

I saw someone doing mental math on a video, and when he did a gigantic calculation at the end it looked like he was placing a couple of images to hold numbers in his mind will he worked on another aspect of the problem.

If I recall correctly, from the direction he looked and the way he moved his hands, it appeared that he might have had two or three loci that were right in front of him and slightly above him.

I found the video: Arthur Benjamin does “Mathemagic”.

I made a mistake about his placing loci. I think he just converted the numbers into images. The big calculation starts at 11:30.

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I was wondering about this too. Everything I’ve seen on mental math is just about doing basic arithmetic. Large multiplications or additions or divisions or subtractions. I’m an early Engineering student and was wondering if there is any type of mental math tricks for higher level maths. Algebra, Trig, Calc and so forth. It would be incredibly helpful with school, but I haven’t found much about it.


I would think that the suggestions for memorizing Chinese characters would help with advanced mathematical symbols as well.

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In his book, he recommends using the method of converting each number to a letter a la the Major System and converting those letters into words in a sentence with a combination of a 99 peg list and new words created situationally on the fly. e.g.
Ship my puppy Michael to Sullivan’s backrubber.
69 3 99 375 1 05820 97494

I’ve created a personal webpage using javascript to test-practice on each of his math tricks.

I don’t want to brag the slightest bit because I am not the kind of person to do so, but I have a very high IQ. During my free time I enjoy studying calculus, physics, and memory systems. I am an Honors student as well.

The point of giving my background was so that I can explain that even with me I don’t bother using loci systems for abstract symbols because it would be a waste of time since my photographic memory allows me to recall equations in fine detail. A lot of people such as quantum physicist that I know have the ability to recall equations rapidly and them precisely and they don’t bother using memory systems. I think it comes from how well you enjoy and UNDERSTAND what you are doing or maybe that those people are geniuses. By understanding i mean knowing the equation and what every variable is for and what would happen if you possibly deleted one.

Hope this gives insight since I didn’t include any techniques. For your information mainly.

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Careful with the ‘photographic memory’ claim. Many here think it’s a misused term, like me, can you explain a bit about what you mean? I’m a maths and physics student, too, and don’t have a problem recalling equations with detail either. But it’s certainly not because I have anything like a photographic memory!

Also, if you don’t want to brag, don’t mention it. It’s not a relevant detail. :wink:

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Obvious troll is a little too obvious.

BUT he does bring up a point worth considering:

Symbols are already quite easy to memorise because in each symbol hides a little picture and if you look into my old japanese kana post you can see why remembering them is a piece of cake.

Now the brain is good at remembering symbols/images (it’s why we’re all here on this forum after all), which is why you don’t always have to “convert” the symbol into another image before memorising it, but associating the symbol with something you already know still speeds up the process and allows you to add more information, like what the symbol actually MEANS. Because while anybody can recognise something they have seen before with ease, remembering the meaning or whatever other information comes along with the image is what mnemonics is for.

The symbols aren’t that hard to remember.

What is harder is remembering theorems exactly without leaving out seemingly trivial caveats and whatnot (non-empty set, etc.). Any ideas on memorizing theorems? I’m guessing some of the poetry or literature memorization tricks would come in handy. I’m new to mnemonics and have only just learned the linking system, but I’m guessing a memory palace will be most beneficial for this?

Also, do you guys have any tips on memorizing physical constants? I’m usually pretty good at it just from normal memory, but I often second guess myself and have to look them up anyway, so it would be useful to have a mental system in place which would give more certainty.

try ( if the constant is raised to a power which it usually is) make a peg system for powers so you don’t confuse them with number of course

then link the number with the peg.

I tried using palaces,but it doesn’t work very well.

Updated links


Anki Files

Remember to use the first word list while learning and reviewing.

If you use acrostics you can distinguish one symbol from another by using the first and last letters of a word or if necessary the second or second to last letter. I call this “letter matching”
ex: SiN SuN SquarE StorE LoG LeG LambdA LavA TwO TorpedO ThreE TimetablE or THere
I will use this in my Calculus acrostic system once it is done. Here is an example of a acrostic system for algebra


Anki Files

Remember to use the first word list while learning and reviewing.

I too am looking for a way to organize physics and mathematical knowledge in a memorable way. Dan’s original question especially highlights an essential underlying result/goal which to my mind need rely on simplicity to represent concepts, contexts and procedures, and perhaps even other texts other may deem essential. This need arises from having no grounding in higher math or physics, yet being require to not only understand, but even advance the thoughts or perform calculations solely from the system.

Such a system should by definition be teachable to children. I’ve just downloaded Mnemosyn, and I’m thankful that this has been made available and that others have donated their cards to share. But I intend to build my own cards linked to specific video lectures (So that contextual, and conceptual understanding may (but only if I think its needed) feature in the spaced card system, but the video lecture carry all the weight). But still, my system will require prerequisite knowledge, and it 'll be a system tailored for my benefit and to my way of memorizing and learning.
However, such a child friendly system most likely will need to establish some benchmark axiomatic starting references specific to the subjects to give contexts and concepts, but I think it can be done in a way that is memorable.

Any ideas anyone?

I think it is possible to develop a method to memorize theorems and other relevant scientific facts, even if I’m not sure it’s worth doing. If you need to memorize theorems for a final exam it might work, but when it comes to science, and especially physics, a deep understanding of what you’re studying is what helps you most remember formulas and theorems.
But the idea of substituting higher math with images, in order to make difficult topics, e.g. quantum mechanics, understandable for everyone, makes little sense to me. The very axioms of quantum mechanics are based higher math (hilbert spaces) and so it seems very difficult to me, to be able to leave them aside.
Moreover, the math is what allows you to make calculations and predictions, which is the main goal of a physical theory, and i see no way of substituting all the math in quantum mechanics, and still be able to use the theory itself to make predictions.

The benefit is the simplification and refinement of my own system/s with such clarity and simplicity as to make it easy to assign mnemonic aids. The secondary and tertiary benefits may help others.

granted, it is difficult to give a physical image to describe a Hilbert space i.e the potentially infinite dimensional complete inner product space; Defining this in a meaningful way isn’t easy for me at this time because my knowledge is still rather primary, but as soon as I can describe a Hilbert space, which may for example depend of describing the use of such space, then perhaps the easier I can assign a mnemonic aids in a meaningful way.

Having only a procedural understanding enables me to calculate the inner product of an n dimensional space, but doesn’t benefit my theoretical pursuits in the actual physics of things. I take the position that hopefully, if a child can understand it, surely I can understand it too.


  1. Memorizing theorems.
    I have to remember approximately 50 theorems and their proof for my mathematical analyses course. I use memory palaces. The most important task is to remember, what the theorem states. I estimate, how much base objects (objects which I use to attach new objects) I need to accomodate the statement of the theorem. It can vary from 2 to let’s say 8 objects. Most of the theorems I have encountered state that some mathematical objects are smaller that others. So we can use the base objects to illustrate a scale, where an base object positioned left from another object is smaller than the other.
    In my course, I have to deal with mathematical objects that are infinitely large or small. So this kind of object can be imagined as a top right object that expands rapidly to the right (or left, if it is minus infinite).
    Some values in mathematics are fixed, other are variables. For exapmple, character Thor represents a fixed point at a graph, but his fkying hammer represents varying point. Overall, when I encounter a new symbol, then I find a 3D person/object to represent this symbol. In math and physics, it’s really important that the representer carries the main idea of the symbol (flying hammer is certainly better symbol for a variable than for example a never-moving stone).

A therem has an assumption and deduction. Make sure, that the path in memory palace goes from assumption to deduction (can also use left->right / up->down placement).

The key aspect is to remember the most important parts of the theorem, not every word. Using memory palace, you can make it even more understandable through realistic (i.e not necessarily making a vivid palace, but trying to make the palace objects reflect the true idea of the theorem) visualitation of key parts/words of the theorem.

  1. Physical constants
    I use PAO to remember the 6 first numbers of the constant (using PAO, that counts as one locus: two first numbers as person, 3rd and 4th number as the action what the person does, 5th and 6th number as object, that is the subject to the action). For accomodating the power of ten that follows the number I use another base object.
    I usually don’t bother to remember the units. Usually before memorizing a constant I have already memorized a formula where this constant occurs. For example ideal gas law: pV = nRT which I can modify a bit and I get: R = pV/nT. I already know that pV unit is J, n: mol, T: K. So, R unit has to be J/mol*K. But if you want, you can also memorize the units.

Stephen Hawking has a suite of tricks for very very advanced math. But I have yet to see a compilation of them anywhere… :frowning: Although, to be fair, I haven’t been looking around the mental techniques fora that are parallel to .

“Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.”

“During the late 1960s, Hawking’s physical abilities declined once again: he began to use crutches and ceased lecturing regularly. As he slowly lost the ability to write, he developed compensatory visual methods, including seeing equations in terms of geometry.”