Take a look at the following maths problem, and see if you can solve it:

*x*= 2*y*=*x*+ 3*x*+*y*+*z*= 10

What does *y* equal? How about *z*?

Are you wondering where I’m going with this? Well, try the following language problem:

If…

*ha llamado*means “He has called”,*ha cantado*means “He has sung”, and*hemos usado*means “We have used”,

… then how do you think you say “We have sung”? What about “He has used”? “We have called”?

If you easily solved one of these problems, chances are you solved both of them. That’s because they can both be solved by *deduction*.

Deduction is the process of taking a set of known facts, such as that *ha llamado* means “He has called” and that *ha cantado* means “He has sung”, and reaching a conclusion, such as that *ha* must mean “He has”. Then you can use this conclusion to construct the new sentence, *ha usado* (“He has used”).

Similarly, if you know that *x* = 2 and *y* = *x* + 3, then you can deduce that *y* = 2 + 3, or 5. And if 2 + 5 + *z* = 10, then you can conclude that *z* must equal 3.

The similarity between maths and languages doesn’t end there though! It turns out they have a lot in common:

- They both require abstract thought to use.
- They both use logical patterns to communicate meaningful information.
- They both have well-defined rules about how to represent that information.
~~Neither one of them ever, ever has exceptions to those rules~~.

Okay, the last one isn’t strictly true!

As these two disciplines have so much in common, often people who are good at maths are also good at learning languages, and vice versa. The same goes for musically-minded people, but that’s a topic for another article.

Before I go any further, I should draw your attention to my use of the word *maths*. To my Canadian and American readers, this isn’t a typo. It’s how those of us from the British Isles (and Australia and New Zealand) say *math*.

## Warning: There is no Maths Gene!

If you enjoy either maths or languages, you’d probably enjoy the other, even if you don’t know it yet. At least, it was like that for me.

In high school, I was always enthusiastic in my maths and tech classes. I loved them! My German and Irish language classes, on the other hand? Not so much. They were always a struggle, and I didn’t find them particularly fun or useful.

Like many people, I assumed that these two disciplines were mutually exclusive, and that I just wasn’t born with the “language gene”. I abandoned language studies after high school and went on to major in electronics engineering. The time I spent in Spain, where I lived for many months without learning the language, served to confirm my earlier assumption that I was definitely not gifted in languages.

It took me quite a while to learn that I didn’t *have* to be gifted in order to love learning languages, and to get really good at it. I just needed to look at learning languages from a different perspective. In my case, this perspective was to take my language learning outside of the classroom entirely.

I also realized early on that I could apply the analytical skills I learned in engineering to better learn languages. With this approach, I discovered that I enjoyed learning languages.

This is basically what mastering any skill boils down to. If you enjoy something, you’ll want to do it a lot. When you do something a lot, you get good at it. It’s as simple as that. Notice how *natural talent* and *gifted* don’t enter the picture.

If you enjoy maths, logic puzzles or analytical problems, then chances are, you’ll enjoy learning languages as well.

Let’s look at why that is…

## Maths is a Language With Verbs and Nouns

All natural human languages (and some animal languages!) have a set of words to represent objects (nouns) and words to represent actions (verbs). You can’t really form an intelligible sentence in any language without them! Well, maths also has its own version of verbs and nouns! Think about the following equation:

*x* + *y* = 10

Try to guess which elements of the equation are analogous to nouns, and which are like verbs. It’s almost like a real sentence, isn’t it? In fact, in maths, equations such as this are called *statements*.

Hard-core mathematicians have given mathematical notation a name: “mathematese”, and it can get pretty complicated! If you can grasp the fundamentals of the complex language of maths, then the fundamentals of a foreign language won’t be much more difficult.

## You Can Apply a Maths Mindset to Language Learning

When you read about my language missions here on *Fluent in 3 Months* (*Fi3M*), you might think that I’m *against* the idea of taking a logical, methodical approach to language learning. It looks like I just dive in, ignoring the rules of the language.

To some extent, I do. But that doesn’t mean I’m not learning it methodically. In fact, the way I learn a language is similar in many respects to the way people learn maths.

When I start learning a new language, I tend to avoid explicitly studying grammar rules *at first*. I prefer to start *using* the language before anything else. I do this through learning some important phrases to help me communicate with a native speaker. I don’t know the specific conjugation rules that make up the phrases. I can speak the phrase and be understood without knowing these rules.

As I use the language, the grammar rules gradually reveal themselves. I *learn* the rules of grammar without *studying* them. For more complex rules, I do sit down and study how they work. But I only do this after I’ve been using the language for a little while.

Just like language, you were using maths long before you started studying the rules behind it. As a preschooler, you used concepts like subtraction, geometry, and even probability before you even knew what those words meant. You didn’t need to learn the specific principles behind these concepts to use them effectively.

Eventually, you started studying them in school. When you did, all those times you had observed these mathematical principles in the past started to make sense. Now you understood why you seemed to win more Connect Four games when you got the first move. Or why your basketball went farther if you threw it at a certain angle.

## Both Maths and Languages Use Logical Patterns

Many people, especially the arithmetically-minded, love doing puzzles and games where the goal is to find the pattern to solve the problem. But they may not realize just how useful this is in language learning.

Suppose I invented a new system of representing numbers that was different from our usual 0-9 system of representation. Instead of explaining to you the rules of this new numbering system, I’ll just show you a list of the first few numbers of our normal numbering system along with the translation from each old number to its representation in my new system:

*old →* *new*

0 → 0

1 → 1

2 → 2

3 → 10

4 → 11

5 → 12

6 → 20

7 → ?

You can probably work out the correct representation of the number 7 under the new numbering system without me needing to teach you the explicit rules. You can use the data given, and *infer* the correct value. And if you did, congratulations, you’ve just learned the ternary numeral system!

In language learning, you can employ a similar strategy to make new sentences. Think about it: you don’t need to know every single word in the English dictionary to make words that you *know* are correct (or at least, perfectly understandable). For instance, if you’re a native English speaker, did anyone ever explicitly teach you that you can change a verb into its past participle by adding -ed? Probably not! More likely, you heard some examples of this rule in action, and inferred the rule by yourself.

This is why you sometimes hear young children say words like “stealed” instead of “stole”; they’re using their past exposure to the language to construct different words. They don’t always do it perfectly due to the many exceptions that exist in most languages. It’s hard to be critical, though, since they *are* successfully communicating!

The first time you correctly form a new word (or sentence) in your target language that you’ve *never heard before*, but correctly guessed because you’ve observed the language in action for a while, is an unforgettable experience. It gets addictive once you realise that you have the ability to branch away from those canned sentences you memorised at the beginning of your language mission.

If you enjoy solving logic puzzles based on patterns for fun, imagine how much fun it can get if you apply it to an entire language.

## Imperfection is Everywhere – in Maths and Languages

A lot of maths purists might not think that they would enjoy language learning because of all the imperfections inherent in natural language, all of the irregularities, and the imprecision in meaning and semantics.

They’re overlooking the fact that applied maths, and so much mathematics used in engineering is full of imprecision and approximations of true values. From truncated Taylor expansions for approximating a mathematical function, to the Monte Carlo method of integration for estimating the area of an irregular shape, the mathematical world is bursting with imperfection.

So is language learning, of course! When you’re learning a new language, you’ll probably mess up and say phrases incorrectly, or stumble with tones or verb conjugations, but guess what? Getting the phrase 100% correct isn’t important as long as it’s close enough that you get the correct *meaning* across.

## Can Language Learners be Good at Maths?

I’ve shown you how an appreciation of maths can translate into a fondness for language learning. But it also works the other way. Language lovers can become maths lovers!

There’s a great deal of evidence that mastering a foreign language is one of the hardest things you can accomplish. Far harder than understanding complex arithmetic. Why, then, do so many language learners shy away from maths and assume that they’re “no good” at it?

I think the answer is the same as why many maths students don’t think they’re any good at languages. If it’s unfamiliar territory, or if they tried it a certain way a few times and didn’t excel, then they become afraid of making mistakes and decide to just stick with what they know.

Now that you see just how much these two territories overlap, don’t be afraid to delve into both of them if you’re currently only comfortable with one. You don’t need to have *either* a “maths brain” *or* a “languages brain”. Having one reinforces the other!

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