English speakers should learn math instead of a second language

You want to learn Mandarin to talk to people who cannot speak the languages you know, or because you’re interested in Chinese culture&#x2F;history.<p>You learn math because you want to be able to quantify scientific questions, or because you want to dig deep into quantitative logic for its own sake.<p>But what if you want to do something else? Such as getting to know your spouse, children or friends better. What if you simply want to make music?<p>I would say, then do that instead of learning math!<p>All this blog post highlights is that you should have a strong and clear learning goal, because if you’re learning Mandarin because it might seem useful on vacation to China, you might be spending your time inefficiently.<p>The idea of teaching children math as a language from day one is an interesting concept though. But even that still comes down to: start giving your kids amazing skills that you think will give them a fulfilling and good life from day one. Well yea, of course.

From article: &quot;So, really, there are only five global languages: English, Mandarin, Hindi, Spanish, and Arabic.&quot;<p>I would call all these &quot;big&quot; languages, but I would not call Mandarin, Hindi or Arabic &quot;global&quot; languages. There may be over 700M speakers of Hindi&#x2F;Urdu, but they live mostly on the Indian subcontinent and Hindi is not really a language of global business or education.<p>Spanish, and outside the above list, French, are more &quot;global&quot; languages in the sense that the language is a majority-dominant and&#x2F;or significant language of business on several continents.<p>(FWIW I do know English as second language and understand a few words of French and Spanish, and can get along with everyday things in Mandarin, though I am more fluent in a couple of other small languages (Swedish and German). I am certainly not belittling the mentioned big languages, I just do not think they are truly &quot;global&quot;.)

Another compelling point is that high school foreign language students almost never gain meaningful competence in the language they study: <a href="https:&#x2F;&#x2F;www.econlib.org&#x2F;archives&#x2F;2012&#x2F;08&#x2F;the_marginal_pr.html" rel="nofollow">https:&#x2F;&#x2F;www.econlib.org&#x2F;archives&#x2F;2012&#x2F;08&#x2F;the_marginal_pr.htm...</a><p>Math courses have a much better track record of actually teaching their students something.<p>However, I think individual students should still take foreign languages in high school to fulfill college application requirements. On a societal level, though, those requirements are a massive waste of time and money.

As someone who lived in China for 10 years, they aren’t wrong if we are just talking about earning potential. The number of bilinguals is pretty high, you would make more than a couple of thousand RMB a month if you knew English in addition to a native mandarin. On the other hand, a machine learning expert would easily start around 60k RMB&#x2F;month.<p>From a personal perspective, knowing another language is enriching, but don’t do it purely for the earnings gain.

The article reads a bit like a rather long way for the author to excuse avoid learning a few of the natural languages of which it seems he would have much use. (Like French that they mention half their family speaking, or Mandarin with which they say they have a fascination..)<p>But also predicating all learning on its &quot;objective usefulness&quot; (however way you try to quantify this) seems short-sighted, what&#x27;s the fun in learning something you know is useful but don&#x27;t enjoy?<p>Somewhere there&#x27;s a balance surely..

That&#x27;s like saying &quot;learn to play an instrument, not cooking&quot;. Everyone has different tastes&#x2F;needs.

Why not learn multiple? Why make a false dichotomy? Math, programming languages, and alternative spoken languages are distinct useful things you can learn.<p>Otherwise what if someone said, don’t learn Math, learn Modula-2?

&gt; Just as natural languages derive directly from our needs to do things with, and communicate about, things in, and state of in the real world, such as running away from lions, attracting mates, and (more recently) engaging in commerce, mathematics derives directly from our needs to do the exact same sorts of things: count chickens (or the number of lions you are running away from), mark time, distance, and rate (as you run from them) and their relationships, and so on.<p>This is a pretty half-baked comparison. Math is great for describing things which can be defined precisely and their interactions. Numbers, physical systems, economics, etc.<p>Human language can be (and is) used for these purposes as well, but more broadly is useful for an entirely different purpose: expressing emotions, sussing out the meaning of things, developing relationships, providing a voice for the human condition. Mathematics is ill-suited at best for these purposes. Both language paradigms may be able to quantify how fast one has to run to get away from a lion. Only one of them can express why you’d want to, or the terror you’d feel trying to do so.

«there are no studies that suggest that learning math as a “native speaker” does not have at least the same, and perhaps even more benefit», this reasoning is so flawed.

Basic math is _really_ important, and not uniformly taught well. Stuff like understanding compound interest would help a _lot_ of people avoid poverty or financial hardship. What&#x27;s surprising to me is that mathematics education (in many places) emphasizes things that are rarely useful _in daily life_ while ignoring things that are actually critical in many situations.

I would argue that an individual (and in turn, the entire world) would be benefit more from learning the &quot;languages&quot; of, or getting a good grounding in, logic and epistemology.<p>Logic, so you can think straight, and epistemology, so you are able to recognize when <i>your axioms are not actually hard facts</i>, which is where a lot of complicated fuzzy-logic style disagreements (anything related to complex systems (weather, economics, government), culture, gender, sexuality, etc) break down even between two people who have highly advanced logical capabilities.

I am sad I am not seeing a strong cultural push towards everyone learning a single common language (which, for historical reasons, could well be English) at least as a well-acquired second language. Instead, the received present-day norm is to insist on cultural and linguistic diversity. Learn Spanish. Learn Mandarin. Learn German. Learn French. Oh, and while you are at it, learn Welsh or Irish too... It’s bewildering. And those enormous corps of translators seem like such a wasted effort!

There is a lot of unique content in Chinese already, and the number will grow substantially in the upcoming years. It includes scientific and not-scientific content. So I wouldn&#x27;t call learning Mandarin a &quot;waste of time&quot;.

The author raises a good point that I agree with: math provides more direct value than learning a foreign language to native English speakers. The author talks about what children should be learning and I don&#x27;t know enough about children&#x27;s education to disagree, but if you&#x27;re an adult, I think it&#x27;s a good idea to learn at least one second language.<p>Language study and math are not mutually exclusive for me.<p>When I&#x27;ve learned math it&#x27;s through focused effort, sitting down and doing math problems, thinking really hard, and talking to people with a whiteboard.<p>When I start study languages I&#x27;m mostly filling time, things like listening to podcasts in the language, going through Anki flashcards while waiting in line or on the subway, or reading things about the language.<p>Learning the foundations of a foreign language is closer to brushing my teeth or going to the gym than it is to learning math. You just do some mundane things every day for a long time and suddenly you wake up with new skills.<p>Once you have a solid foundation, then it&#x27;s closer to having fun than studying. You just chat with people or read things you&#x27;re interested in, the same as you probably already do for fun in your first languages.<p>Anyways, my point is that if you have even a little free time or some downtime (like a commute), you can probably fit in time to learn a new language and not take anything away from your other pursuits like actively studying.<p>That said, I don&#x27;t think learning a new language is easy, but it&#x27;s rewarding and the improved cultural understanding, of both your target language and culture and your first culture and languages, it brings makes it worth it to people who live in a globally connected society.

Someone who&#x27;s studying these as a hobby is likely going to run into more uses for Mandarin in their day to day life than, say, Calculus. You&#x27;re more likely going to run into a situation where you&#x27;re saying &quot;I wish I could talk to that person&quot; or &quot;I wish I knew what that said&quot; than you are going to run into a situation where you go &quot;I wish I could calculate the second derivative of that formula.&quot; And though I doubt self-studying either of those is going to boost your career much, self-studying Mandarin is probably going to be more beneficial (it makes sense to stick &quot;I speak Mandarin&quot; on more resumes than &quot;I know calculus&quot;).<p>In the end, though, you&#x27;re best off either studying something to reach a specific goal (learning the math that engineers need in order to become an engineer) or studying something that interests you.

My read on this is pretty complex. On the one hand, my verbal ability is off the charts - I never scored lower than an 800 on a PSAT or SAT. My math ability is good but not great. For some time I&#x27;ve felt I&#x27;d have been better served by being the worst math or CS student at my college rather than one of the best foreign language students.<p>The reason is, our society has a number of clear paths for people with highly developed M ability, but fewer viable paths for highly developed V ability. Basically just law school, and that isn&#x27;t what it used to be. I think that&#x27;s a problem for us as a society, but it&#x27;s not going away soon. I&#x27;m advising my son to major in something quantitative.<p>That being said, the author&#x27;s apparent advice not to take fl at all is insane. Especially for high school students. If you are not MIT&#x2F;CalTech material, Ivies like to see foreign languages.

I feel like it&#x27;s much easier to start learning Mandarin than Maths. I can&#x27;t really put into words <i>why</i> I feel this way, given that there are great resources like Khan Academy out there. Maybe it&#x27;s easier to gauge fluency in a language than it is in maths? When do you stop learning? Maybe you&#x27;re proficient enough when you can order from an all-Mandarin menu? As soon as you can&#x27;t read a bit on a menu, you know what you need to work on next. But what about maths? I know how to add and divide. I&#x27;m fluent at trig and pretty good at some bits of algebra. Pretty rusty in calculus and OK at stats. I&#x27;m sure having this knowledge makes parts of my job easier. But maths is such a huge and diverse field.<p>Not knowing what I don&#x27;t know, I find it very difficult to gauge whether I&#x27;d benefit from learning more, if that makes sense.

I don&#x27;t get the point they&#x27;re trying to make.<p>I think the analogy between math and a language that you can learn as &quot;native language&quot; is quite far-fetched and flawed, but let&#x27;s accept it for the sake of argument.<p>Then, I&#x27;d say that in most developed societies, we already learn math as a native language since birth. Many toys for babies are focused on counting (among other skills, like recognizing colors, shapes and basic words). Parents routinely ask their kids to count things, just as they help them learn the language. Then, once you go to preschool and then school, there are always math lessons alongside the language lessons.<p>So in my view, what they&#x27;re advocating already happens, so I&#x27;m not sure what change they&#x27;re proposing.

I like learning languages because I like learning. There doesn&#x27;t need to be a reason. This is a very engineery perspective, I don&#x27;t like it.

Actually, math is not an universal language. There are several different languages within math, see <a href="http:&#x2F;&#x2F;math.ucr.edu&#x2F;home&#x2F;baez&#x2F;rosetta.pdf" rel="nofollow">http:&#x2F;&#x2F;math.ucr.edu&#x2F;home&#x2F;baez&#x2F;rosetta.pdf</a>

Note that the Wikipedia claim about total speakers, the Wiki page notes that &quot;Speaker totals are generally not reliable because they sum estimates from different dates and sources, usually uncited.&quot;

From my experience (and I emphasize on that) I can tell you from us (I&#x27;m from East Africa, speaking English, Swahili, French and two other natives languages) being proficient in at least English&#x2F;French is an existential question. I really understand why a US citizen may think twice before starting learning a new language. For us, if you want a &quot;normal&quot; life, you do have to learn other 2 languages. We do not have that luxury.

The author&#x27;s argument immediately fails at the fact that math papers are written in natural language and you&#x27;ll have no chance of understanding the paper if you don&#x27;t speak that language.<p>Just because I can read a math paper written in English or German I don&#x27;t harbor any illusions I&#x27;ll be able to understand one written in Mandarin.<p>On top of that there&#x27;s that mathematical notation really isn&#x27;t as standardized as one would hope. Neither is basic terminology (which already isn&#x27;t consistent between different disciplines&#x2F;schools within the same language).<p>So unless a Chinese mathematician deigns to translate the paper into a language I understand, I&#x27;ll just be screwed.<p>The underlying concepts may be universal, but the language and notation of mathematics today just isn&#x27;t.<p>Edit: For those who want to have a taste of what mathematics in a foreign language is like, have a look at this Chinese Wikipedia article on a very basic topic: <a href="https:&#x2F;&#x2F;zh.wikipedia.org&#x2F;wiki&#x2F;%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0" rel="nofollow">https:&#x2F;&#x2F;zh.wikipedia.org&#x2F;wiki&#x2F;%E8%BF%9E%E7%BB%AD%E5%87%BD%E6...</a>

I collect math, machine learning, statistics, etc urls. The ones discussed on HN have the HN discussion below the article:<p><a href="https:&#x2F;&#x2F;github.com&#x2F;melling&#x2F;MathAndScienceNotes&#x2F;blob&#x2F;master&#x2F;math.md" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;melling&#x2F;MathAndScienceNotes&#x2F;blob&#x2F;master&#x2F;m...</a><p><a href="https:&#x2F;&#x2F;github.com&#x2F;melling&#x2F;MathAndScienceNotes&#x2F;tree&#x2F;master&#x2F;statistics" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;melling&#x2F;MathAndScienceNotes&#x2F;tree&#x2F;master&#x2F;s...</a><p><a href="https:&#x2F;&#x2F;github.com&#x2F;melling&#x2F;MathAndScienceNotes&#x2F;blob&#x2F;master&#x2F;machine_learning.md" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;melling&#x2F;MathAndScienceNotes&#x2F;blob&#x2F;master&#x2F;m...</a><p>This recent HN was interesting, for example:<p><a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=19811715" rel="nofollow">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=19811715</a>

Learning other languages has absolutely improved my life and changed the way I think, just as much as learning mathematics. It has opened my eyes to the world that exists outside the anglosphere.<p>Just make sure that you have native speakers to talk to, the benefit of learning a language is being able to talk to people!

Why are they mutually exclusive?<p>If you don&#x27;t know any maths there are things that are hard to describe or even conceptualise.<p>If you know only one language there are assumptions you make and things you don&#x27;t know that you don&#x27;t even know you don&#x27;t know.

Can&#x27;t disagree more. Learning a spoken language is much more than picking-up a communication tool - it opens a world of culture and thought that is bigger than the language itself. Yes, the same can be said of mathematics, and both are as valuable.<p>I&#x27;m European, speak 3 languages and use math every day, professionally. I&#x27;ve studied, lived and worked in the US for many years and am often shocked at some of my American friends&#x27; lack of perspective on international affairs.... keep-up with the math education but don&#x27;t do it at the cost of languages... you can&#x27;t afford to.

There&#x27;s no shortage of Math advocates, one of you needs to put together the Math equivalent of DuoLingo. A math textbook isn&#x27;t the only way to work on math daily.

Fun fact: more people speak English in China than in North America.<p>- - - -<p>In re: teaching math ASAP see Iconic Math <a href="http:&#x2F;&#x2F;iconicmath.com&#x2F;" rel="nofollow">http:&#x2F;&#x2F;iconicmath.com&#x2F;</a> and (the general idea of) &quot;Proofs without words&quot; <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Proof_without_words" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Proof_without_words</a>

What you should learn depends on your interests. Curious about metallurgy? Then German holds a great reservoir of hard won knowledge. Culture, aesthetics, and hard math? There French has profound influence. And so on. Buddhist wisdom is scribed in Sanskrit, Hindi, Chinese, and many others. Extend and spread your knowledge using whatever language and idioms are most appropriate and useful.

This sounds like wonderful advice to me. If you are an English speaker, I frankly don’t see the return on the immense investment of time and energy learning a language requires unless you will eg live there or do much business there. Unfortunately for the average person I’d imagine learning math might not be extraordinarily useful either.

The author makes a good point of course.<p>But I&#x27;d add that, for native English speakers writing to a broad audience, they should spend a little time learning how non-native speakers use and understand the language.<p>A few changes in word choice, sentences structure and idioms can make informal communication significantly clearer.

Before one has learned a foreign language one has not a deep understanding of their first language at all.

Maybe he should try studying math <i>in</i> Mandarin. It doesn&#x27;t have to be so zero-sum...

I like the comparison between learning the language of math and learning a foreign language. In both cases, learning the language gives you increased access to more culture, history, knowledge, and means to express yourself. This is a good way to answer &quot;Why do need to learn math?&quot; which people often ask me. As in &quot;What am-I going to use this for?&quot;<p>I don&#x27;t like the idea of learning math INSTEAD of a foreign language, since both are meaningful and interesting for different reasons.<p>In writing math books I often had to come up with various analogies to try to motivate readers to invest the time---look, if you get through these hairy equations you&#x27;ll have access to powerful math modelling skills and be able to read Wikipedia pages that have equations in them without going into panic. I&#x27;ll add the &quot;learn a new language for the culture&#x2F;history&quot; angle too, not sure which is more convincing...

Languages are overrated.I was born in a country with population of only 3M people,so I had no choice but to learn English.Later on in life I also learned Russian,because I ended up living with Russians for more than a year.Yes, it&#x27;s great to go out there and be able to talk to people but that&#x27;s about where it ends. That&#x27;s why, unless one has some useful skills(IT, engineering, plumbing,etc.), knowing languages won&#x27;t take you very far.In my previous company most people spoke at least 4 languages.And what? Everybody was on crappy salaries,even though most were very well educated but very few could do anything outside linguistics sector.In business, languages help, however I&#x27;m yet to see any jobs that&#x27;d pay more just because one can speak German and Italian...

So is there a better way to learn math now? I haven’t taken a course in over a decade and would love to understand proofs. I admittedly memorized a lot to get through math during K-12 and most of Uni.

The math in high school was more relevant 50 years ago than now, though. Most students who learn calculus will never, ever, integrate a function again in their life. Most people who don’t learn statistics will get bombarded with arguments based on statistical analysis, often done sloppily but only obvious to someone with training in the subject.<p>So, if your choice is between calculus or Spanish, Spanish might be the better choice.

Or walk and chew gum, like the rest of the world does.

Why not both?<p>Seems to work for the rest of humanity.

Math + Mandarin = X; Math + English = Y; Mandarin = 1.11; English = 1.12; Article Usefulness = Math(X-Y)

Seems a bit silly. Americans typically learn enough math for the example problems he lists by the time they graduate high school.<p>I don&#x27;t think learning Mandarin is such a bad idea, personally.