How I use Anki to learn mathematics

Memory is crucial. I got much better at learning mathematics when I started memorizing the statements and proofs of key theorems.

You also need the understanding, of course. The largest mistake in mathematics education is to think that memorizing a rote process is the same as learning mathematics (see: US high schools). The second largest mistake in mathematics education is to swing too hard in the other direction.

I had an absolute beast of an algebra professor who impressed upon us the fact that things are defined they way they are for a reason, and we, as mathematicians must know them. It is not enough to be able to remember the definition of a normal subgroup, for instance. We must know why we define it the way we do, and what happens if the definition is altered in the slightest, weakened, strengthened, negated etc. It is not enough to know that quotient groups are defined modulo normal subgroups only. You should know why defining a quotient group modulo a non-normal subgroup is meaningless. Even for much more complicated categories, like manifolds, one must absolutely know why all the bits and pieces are needed. Why do we require the transition functions for real n-manifolds to be C^r? What if r=0? What happens if two charts on some underlying topological space are not compatible? Why do we need the atlas to be maximal? Why on earth do we need a countable base? Hausdorff? What is this business about needing manifolds to be Hausdorff? [0]. Why is it that bijective homomorphisms are the isomorphisms in the category of groups - i.e. why is it that its inverse is not required to be a homomorphism as part of the definition? Learning definitions by rote is the surest route to mathematical mediocrity.

"Don't just read it - fight it!" - P.R. Halmos.

[0] Yes, I know these can be relaxed, but this is the standard presentation in Kobayashi-Nomizu/Spivak/Lee/Tu/Barden-Thomas/Do Carmo/Petersen etc etc.

Surprisingly - as stated by others - memory is crucial to math and problem solving. Most problem solving is just memory on a higher domain anyway. Break down a problem with first principles (hard part), and solve with a mental model gained from memory.

Euler - probably the greatest mathematician of all time - had an amazing memory. He memorized the entire Aeneid and could recite any line at will.

In that case you're learning foreign vocabulary, something Anki is more traditionally associated with.

I used handmade cards and it made all the difference. A good foundation was necesarry for me to make things click. I tried anki later on, but it was too cumbersome to create and work with digital cards for me.

Memorization and definitions go hand in hand. After all, you need a certain amount of memory to understand that epi means 'upon' or that mono means 'alone'. If I retain that, is it my understanding, or my memory?

That leads me to my next point, which is Anki is best used when you do what's called rote-memorization, but memorize simpler aspects -- so have one card that asks what does 'upon' mean in Greek, and another asking what 'mono' means in Greek - in addition to making more general questions regarding this subject.

Perhaps easier: if you can remember that "mono" means "one" (as in monophonic, monosyllable, monomania, monopoly, ...) then that should make it easy to remember it's for (the analogue of) one-to-one functions -- same as injective.

(But the OP is French and I don't know whether French mathematics terminology includes anything corresponding to English "one-to-one".)

Came here to say the same thing.

This won't give you an understanding of mathematics, just perhaps a memory of it.

I see it more like freeing up you active working memory to do other things, similar to how you can only become a better driver once you aren't constantly fretting over exactly how much to lift the clutch as you accelerate. You can (and must!) understand what/why you do what you want to do, but you can begin to abstract over it and find other patterns.

Yes, there is no substitute for developing intuition by doing exercises.

My comment does not contradict in any way the article: the problems of mathematics searchers are very different than the ones of students. I just disagree with many of the comments about this article: for me mathematics does not require a good memory. Perhaps a bad memory means the brain store more high level data instead of raw data and that may be useful for higher level of abstraction ???

purchased? I just had a look at the homepage and it says it's open source?

The flashcards class works fine for me. https://www.ctan.org/pkg/flashcards I specified a custom layout that I use to print on cardstock and then cut out the cards on a paper trimmer.

    \NeedsTeXFormat{LaTeX2e}[1996/12/01]                                                                   
    \ProvidesFile{letterCardstock.cfg}                                                                     
    \newcommand{\cardpapermode}{landscape}                                                                 
    \newcommand{\cardpaper}{letterpaper}                                                                   
    \newcommand{\cardrows}{2}                                                                              
    \newcommand{\cardcolumns}{2}                                                                           
    \setlength{\cardheight}{3in}                                                                           
    \setlength{\cardwidth}{5.0in}                                                                          
    \setlength{\topoffset}{1.25in}                                                                         
    \setlength{\oddoffset}{0.5in}                                                                          
    \setlength{\evenoffset}{0.5in}

I successfully used the example in this StackExchange answer [0]. And you could also take a look at the flashcard package on CTAN [1]. Another easy option would be using some kind of markdown tool [2] or even a Word template to generate a PDF and then printing it 8-up.

[0] http://tex.stackexchange.com/a/89347 [1] http://www.ctan.org/pkg/flashcards [2] e.g. http://pandoc.org

Some frequently mentioned blog posts:

Memorizing a programming language using spaced repetition software:

https://sivers.org/srs

Janki Method: Using spaced repetition systems to learn and retain technical knowledge:

https://www.jackkinsella.ie/articles/janki-method

Janki Method Refined:

https://www.oxbridgenotes.com/articles/janki_method_refined

Tips For Mastering A Programming Language Using Spaced Repetition:

https://www.smashingmagazine.com/2014/08/mastering-a-program...

For me, Anki reviews are a morning ritual. I do whatever it scheduled for the day. Then, I take time to review weaknesses. Then I move onto doing my actual projects. A combination of project experience and curiosity inform me as to what new Anki cards I need.

So yes and no to your question. Anki by itself isn't useful for learning to program. Anki as part of a larger personal development system can be pretty effective from my experience.

I did some experiments here: http://experiments.oskarth.com/srspractice/

A key thing is to differentiate between learning from scratch and retaining knowledge/a skill.

I've used it for many years, and for a short while threw some programming things on there. The main use case (I think) would be something like: you have interviews coming up, and you know a bunch of programming languages, but you aren't completely precise on the vocab for each, e.g. in python you might use len(someString) while in javascript you might use someString.length . Anki would be perfect for straightening all these out. For day to day programming, I doubt it would be useful (as if you forget that for some reason, you could just try it quickly on the interpreter)

Most computer programming languages have a simple syntax, so it's probably not so useful to memorise it. I find that having learned 10s of programming languages, I barely remember syntax anymore and rely on examples in the code I'm working on.

I think what's more interesting is using memorisation for learning short idioms. In fact, I recommend the same for human languages. Instead of learning vocabulary and grammar, memorising the translation of short sentences is much more effective in my experience.

As with the discussion of mathematics, memorisation will not give you insight or fluency. However, to have insight and fluency, you need comprehension and the first step of comprehension is memory. You still need to practice for fluency, though. Some people find that when they are practicing for fluency, they retain what they need automatically. I am envious of those people ;-)

Use Anki to memorize that gosh-darn block syntax. It's like the lord's prayer for me, used it 1000 times yet can't recall it for the life of me.

It doesn't seem like the sort of thing that would be useful for programming. I'm under the impression that the best way to become familiar with a language is to just use it. It wouldn't really occur to me to have a flashcard saying "define a function prototype that accepts 2 integers and returns a pointer to char".

Languages (vocab but also some grammar patterns), law cases, and other "fact" things is what I've used Anki for.

If instead you were thinking of using it to memorise algorithms, you'd get too caught up in the content of the flashcard while trying to learn it rather than the process of the algorithm itself. I think, anyway. I've never tried it :)