Is memory unimportant in doing mathematics?

The title says it all. I often heard people say something like memory is unimportant in doing mathematics. However, when I tried to solve mathematical problems, I often used known theorems whose proofs I forgot.

EDIT Some of you may think that using theorems whose proofs one has forgotten does not seem to support importance of memory. My point is that it is not only useful, but often necessary to remember theorems(not their proofs) to solve mathematical problems. For example, you can't solve many problems of finite groups without using Sylow's theorem.

Solution 1:

I think all of us at some point will invoke theorems whose proofs we have forgotten. I would argue that memory is important for mathematics in the sense that it is important for practically every other field.

Certainly having good memory will not hurt you and several mathematical giants were undoubted aided by their prodigous memories (notable examples that come to mind include Euler, Poincaré and Von Neumann). But as is always said for mathematics, it is more important to understand and particularly the connections between subjects.

I don't think many people can hope to retain absolutely everything they learned, even for undergraduate mathematics. Instead what is important is the ability to rapidly recover what you have lost. If you learn a subject and subsequently forget about it, then you should be able to relearn the subject much faster on a second exposure. In fact, I would argue that it is these repeated re-exposures which ultimately contribute to your mastery of a subject.

What's more important than memory would be the ability to efficiently find relevant literature. If you forget a theorem, but through your understanding and experience subsequently find it in some book or journal then you may have lost a bit of time, but ultimately you have your result.

Should you be discouraged from going into mathematics if you have a poor memory? Well that depends. If you fail to remember your own name then I would indeed say that mathematics will be a struggle to you. So will life in general. But if your memory is average, or even slightly below-average, then I would say that you will do just fine. Mathematics is ultimately not as memory-intense as subjects such as history or medicine.

P.S. In this question here, there is an interesting comment by Bill Cook about this subject. Of course I didn't remember the comment word for word, but rather just remembering the content roughly was enough for me to recover it. The ability to find is as equally as important as the ability to retain.

Solution 2:

I feel it is very unhealthy to say that memory is unimportant to doing mathematics and it is even more dangerous to equate memory with rote-learning. Memory has an important place in understanding of a subject. Understanding is on a basic level refactoring your knowledge and creating helpful associations. Finally, you have to remember those associations. You might internalize those associations and hence in the process, remember them without any external effort, but it is memory all the same.

Hence, having a really strong memory is really helpful to doing good mathematics. I think of good memory as a complementary process, as a cache you use to acquire data at a rate while the brain is processing and internalizing the already accumulated data.

What you are probably talking about here when you say memory is rote-learning. Which is basic memorizations of symbols, which is bad for any kind of field, not just mathematics. But then, in other fields, you can get away more with it than in mathematics. Also, in some fields, like history and law, rote memory might be thought of as important just because the associations are even more complex to remember and even more weakly related. Instead, in mathematics, associations are generally very very strong.

Solution 3:

Your question reminded me of the following article (I happen to be very interested in research on math and cognition): Working Memory and Mathematics. It's a very long article, a review of the literature, citing a lot great references, and dated 2010.

You seem to be referring to "long term memory", though. So perhaps the article is not of any interest to you. Mathematical cognition (and thinking in general) involves many sorts of memory: working memory, long term memory, fluid memory, static memory, pattern recognition, etc., as well as the faculties of spatial ordering, temporal-sequential ordering, etc., each of which involves various parts of the human mind.

Here's a link to the abstract of a nice article that might be of interest Memory and Mathematical Understaning. The article discusses the correlation between learning, understanding, and memory. That is, memory can be a function of how well one learned and understood the material one is hoping to remember.

If it's of any consolation, I don't think that you are alone. (I can only speak for myself, here, in that I too wish I was able to recall many things, many times. That's where having access to good references and texts come to the rescue! It is better to know how to find what you need to know, than to simply rely on the hope that everything one has learned will surface when needed! Usually, one need only refresh one's memory, which takes only a fraction of the time spent having learned in in the first place.

On a light note:

I remember consoling myself a while back by visualizing "learning" as filling a suitcase(s), the contents of which is "what I know." The more you add to your luggage, (the more you learn and the more you know), the harder it is to locate any particular item amidst the cramped collection of what you've acquired!

Solution 4:

You're more likely to remember something if you've understood it than if you've memorized it.

In that sense, memory does not play the role in mathematics that it is thought to play by students whose reason for taking a math course is to get it over with.

I would also add that you're more likely to remember something if you've taught it five times or more.