
English speakers should learn math instead of a second language - abrax3141
https://leosstemhacks.wordpress.com/2019/06/13/learn-math-not-mandarin/
======
mettamage
You want to learn Mandarin to talk to people who cannot speak the languages
you know, or because you’re interested in Chinese culture/history.

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.

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?

I would say, then do that instead of learning math!

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.

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.

~~~
asdkhadsj
> start giving your kids amazing skills that you think will give them a
> fulfilling and good life from day one. Well yea, of course.

You'd think "well yea, of course" but man do I feel parents rarely do that.
The majority, and I really do think the majority, seem to be content just
doing nothing with the most valuable years of the childs life.

Perhaps I take that too seriously, but I don't think so. I feel that is one of
our largest failings as a society. That and failing to encourage learning,
lessons from past mistakes, self growth, etc etc.

~~~
finaliteration
> just doing nothing with the most valuable years of the childs life

I was pushed pretty hard as a kid and I’m not a very happy adult even though I
excelled academically and have a lot of “skills”. All of that pushing made me
constantly criticize myself and I still push myself way too hard and feel like
I’m never good enough.

As a parent, sometimes I think it’s best to do “nothing” and let my kid enjoy
her childhood and do childish things without an enormous amount of pressure to
develop all of these skills and “get ahead”. Kids need time to have a carefree
life for awhile without adults constantly dumping pressure on them to be
prepared for adult life by the time they are five years old.

~~~
Apocryphon
I definitely agree that having too many "skills" pushed on someone earlier can
sometimes lead to self-criticism and other maladaptive behaviors.

I tend to think that parents should present to their children as many
different potential things to learn and excel at, but allow the children to
drive themselves towards what interests them. Parents can then guide them
accordingly. But the child should still feel themselves in control. Sort of
like when Tibetan Buddhists find the next Lama- they have the candidate choose
an item from the predecessor's possessions.

~~~
sosborn
Present to them a buffet and see what they come back with on their second trip
through the line.

~~~
bertjk
I know what my kids would do. They would take nothing but Jello, play with the
ice cubes in their water glass for the remainder of their mealtime and then
later they will lose their shit because they feel hungry.

~~~
Apocryphon
I'm not surprised that they would, sounds like what most kids would do. That's
why the buffet has to be curated, so that the easiest way out / path of least
resistance isn't just "empty calories". So limit the offerings. And maybe use
approaches like the Maya Method [0] to "trick" them into thinking what's
commonly regarded as work or chores, to be fun. It's not easy, but it can at
least be tried.

[0]
[https://news.ycombinator.com/item?id=17905657](https://news.ycombinator.com/item?id=17905657)

------
ptaipale
From article: "So, really, there are only five global languages: English,
Mandarin, Hindi, Spanish, and Arabic."

I would call all these "big" languages, but I would not call Mandarin, Hindi
or Arabic "global" languages. There may be over 700M speakers of Hindi/Urdu,
but they live mostly on the Indian subcontinent and Hindi is not really a
language of global business or education.

Spanish, and outside the above list, French, are more "global" languages in
the sense that the language is a majority-dominant and/or significant language
of business on several continents.

(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 "global".)

~~~
bilbo0s
I don't know man?

Having worked with Halliburton a while back it certainly seemed like Arabic
was a global language to me. Many nations where you just have to speak it when
interacting with people below the C level. There's also a lot of business you
have to do in Arabic, and a lot of times when the expertise you may need is
really only available from Arabic speakers. Like if you want a half way
accurate estimate of how much oil Cuba likely has in the North Cuba Basin for
instance. They have tools and techniques that others just haven't developed.
(Or hadn't at the time.)

But I do think that when we are not so dependent on fossil fuels, Arabic will
become a VERY unimportant language. I'm just not sure when that will be?

Oh, also, I'd imagine Mandarin is important too. A lot people who dealt with
the Chinese on the "gotta get shit done" level used it all the time there.
Also a lot of traders downtown were using that all the time when I lived in
Houston. You kind of just had to when you were dealing with things in China
because for many people in those sorts of positions, a lot of stuff is just
moving way too fast to not be able to find the chase and cut to it faster than
the next guy.

Or it was anyway? I don't know if business with China from the US is slowing
because of the Trade War? Been out of that game for a while now.

~~~
maximente
can sympathize here. not sure where outside of France + former colonies French
is used for "business", but we were throwing around $400-$600/hr for two
native English + North African Arabic speakers (who also had expertise in
other Arabic dialects) for logistics work in MENA years ago. was basically
impossible to get anything done without those 2 guys.

Arabic also suffers from serious fragmentation: we would need help even
between people Morroco, Tunisia, and Algeria even though they're basically
neighbors. i think they are the same "language" in name only.

------
alexhutcheson
Another compelling point is that high school foreign language students almost
never gain meaningful competence in the language they study:
[https://www.econlib.org/archives/2012/08/the_marginal_pr.htm...](https://www.econlib.org/archives/2012/08/the_marginal_pr.html)

Math courses have a much better track record of actually teaching their
students something.

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.

~~~
Kaveren
As far as the U.S. goes, I doubt students remember much of the math they
learn, or gain much more competency in math than they would via a language
course.

~~~
alexhutcheson
There are lots of standardized tests that evaluate students’ math proficiency,
and lots of research examining specifically how much math proficiency students
gain from each year of school. Learning and retention could definitely be
improved, but I’ve never seen research that claims it’s as low as it
apparently is for foreign languages.

~~~
nicoburns
Standardised tests are pretty terrible at measuring actual competency.
Standardised testing is one of the reasons _why_ the US's school system is so
poor. And I say this as someone who generally excels at these kind of
arbitrary tests.

------
seanmcdirmid
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/month.

From a personal perspective, knowing another language is enriching, but don’t
do it purely for the earnings gain.

~~~
Kaveren
If you're living in a country where you don't speak the mainstream language,
living there is more than reason enough by itself to learn it.

~~~
seanmcdirmid
A lot of foreigners working in China get by with only basic daily life
mandarin. Mine was better than most, but no where useable for work.

Again, don’t learn mandarin just for the money. English is much more
important, even in a country like China, at the upper tech echelon.

~~~
Kaveren
It's pretty embarrassing to live in a country for 10 years and not being able
to use it for work.

~~~
sho
You'd be amazed at the bubbles expats can live in, especially high-value
personnel like embassy staff, executives or subject matter experts. I've heard
of people with english-speaking house staff (who also do all shopping),
driver, everyone at the office, personal secretary who organises absolutely
everything, doctors, schools - and a 24-hour phone number to dial if there's
any difficulties outside that. People can go for years without ever actually
having to talk to a local in their own language.

Plus, there can be weird dynamics at work. Some people will actually look down
on you as having somehow debased yourself for making too much effort to study
the local language, both fellow foreigners and the locals themselves. As best
as I can understand, they think it comes across as too eager to please, or an
attempt to ingratiate, or that you obviously don't love your own culture
enough, or that you evidently have too much time and thus can't be all that
important... have heard some variation on all of them.

Especially in Asia, there's a kind of stereotype of the Big Important
Foreigner who has been Appointed to this Developing Country to do Important
Things. Suddenly breaking into fluent $LOCALDIALECT kind of shatters that
illusion and raises all sorts of questions. Sounds strange, but it's a thing.

~~~
wawaygfuyre
That attitude is definitely not a Chinese thing though.

In China, it’s the reverse. They think foreigners aren’t smart enough to learn
Chinese. That’s why they are always amazed when some expat can speak even the
most basic phrases.

The scary thing is that’s it’s often these “expat bubble” executives that are
making decisions. No wonder foreign companies in China get taken to the
cleaners.

~~~
seanmcdirmid
That really isn’t always true though. There was a solid glass ceiling for non
Chinese speaking managers at the senior level, and well, it was really just
Chinese (even 大山 wouldn’t be Chinese enough for promo).

A senior Chinese manager in America is much more normalized than a senior
western manager in China, (the former is an immigrant and has a green card,
the latter is an expat and will go back next year after their assignment is
done).

------
Profan
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..)

But also predicating all learning on its "objective usefulness" (however way
you try to quantify this) seems short-sighted, what's the fun in learning
something you know is useful but don't enjoy?

Somewhere there's a balance surely..

------
siwatanejo
That's like saying "learn to play an instrument, not cooking". Everyone has
different tastes/needs.

------
cromwellian
Why not learn multiple? Why make a false dichotomy? Math, programming
languages, and alternative spoken languages are distinct useful things you can
learn.

Otherwise what if someone said, don’t learn Math, learn Modula-2?

~~~
mpoteat
I've always had a suspicion that one person can't be a master of all things
due to the physical limitations of human memory. Isn't that why we specialize?

~~~
whatshisface
More like the physical limitations on lifespan.

~~~
coss
But probably memory as well. If I start specializing elsewhere I'll forget the
intricate details of the thing I'm already specialized in.

~~~
pen2l
Don't think it works like that.

Rather, it's that you have only so much time to dedicate to things... if
you're focusing very much on one, then you're not spending time with the other
-- and overtime, you'll lose that other thing. If you can manage to spend a
good amount of time on two things (let's say, learning a new instrument and
learning a language) everyday, consistently, then you will get both.

~~~
colordrops
It does work like that. As you get older your ability to retain information
wanes.

~~~
Apocryphon
That could be physical degradation from age, not necessarily the "running out
of disk space".

~~~
colordrops
Why does the cause matter?

~~~
Apocryphon
Because if it's simply because of physical degradation, that means someone can
keep on learning and not worry about running out of memory.

~~~
colordrops
If your memory doesn't work, what does it matter how much you have?

You can create ungrounded abstractions all you you want, but as an older
person who has commiserated with other older people, the common conception
that it's harder to learn and retain things in older age is a real thing

~~~
Apocryphon
Sure, but what you're describing is the difficulty of learning as age sets in.
That's very different from the original assertion- "If I start specializing
elsewhere I'll forget the intricate details of the thing I'm already
specialized in." \- unless that person was describing themselves as older.

~~~
colordrops
If you wish to exclude more than half the population from your statement be
explicit about it.

~~~
Apocryphon
Perhaps fixing degradation will prove to be a less difficult task than
increasing memory, as the growth of new neurons is still a very newly-studied
phenomenon compared to treatment into neurodegenerative processes, and soon
medical science will benefit the learning of all demographics.

------
thinkpad20
> 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.

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.

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.

------
finnjohnsen2
«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.

------
nneonneo
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'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.

~~~
marcolussetti
> 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'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.

Agreed. I remember asking in high school what the material we studied was
helpful for as I was struggling with motivation -- I was told to help shape my
brain which is the blanket reasoning used from everything from Latin to music.

I think in addition to the important areas you highlighted, statistics is so
fundamental to understanding the world around us and should be emphasized
alongside.

------
mistermann
I would argue that an individual (and in turn, the entire world) would be
benefit more from learning the "languages" of, or getting a good grounding in,
logic and epistemology.

Logic, so you can think straight, and epistemology, so you are able to
recognize when _your axioms are not actually hard facts_ , 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.

------
azangru
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!

~~~
Tharkun
Y Gymraeg is a lovely language. Music to my ears.

There have been several pushes for common languages. Latin once dominated at
least the sciences and clergy. French was the literal lingua franca for a good
while in various contexts. English has kind of taken over that role at the
moment. But those languages are all a bit shitty when it comes to ease-of-
learning. French with its complex grammar. English with its spelling oddities
and its absolutely mind-bogglingly vast vocabulary. Latin, well, who even
speaks Latin anymore.

Artificial languages like Esperanto are allegedly easier to learn, but they've
never taken off.

I've long held the belief that the EU should make English a mandatory second
language across all its member states. It's easily the most spoken second
language in the EU already, but there are _huge_ differences in proficiencies
across countries/regions.

~~~
azangru
> But those languages are all a bit shitty when it comes to ease-of-learning.
> French with its complex grammar. English with its spelling oddities and its
> absolutely mind-bogglingly vast vocabulary.

Well, every natural language that developed organically and was not
artificially created will, by necessity, have its quirks. But if it is learned
early enough in life and actually used on a daily basis, people will overcome
these quirks.

Latin’s use as an international language of religion, scholarship and science
occurred during the time when it was already all but dead. Only a tiny
minority of the population knew it; and there was neither a universal system
of education to teach it, nor mass media to provide continuous examples of its
usage. When French and German were tried as international languages, the
situation was somewhat better in the sense that they both were living
languages; but still there was no infrastructure in place to teach it to large
segments of the population. Now, I feel, the situation is very different. A
huge proportion of population receives primary and secondary education, which
offers a great opportunity to teach a common second language. A massive amount
of films, books, or radio programs offer examples of oral and written English
usage; and the Internet is connecting people at a previously unimaginable
scale. Now, I feel, we have a fighting chance of finally getting a common
language.

Of course, I understand that a language becomes international not only due to
its linguistic merits, but in a large respect due to the political and
economic power of the countries where it is spoken. And since China is on the
rise and the West is somewhat in decline, I fear that English may lose its
momentum, and we may lose our chance to have it as a truly universal language.

~~~
pessimizer
That English is extremely difficult to write is a serious issue, though. A
very large portion of English speakers are functionally illiterate.

------
xvilka
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't call learning Mandarin a "waste of time".

~~~
AFascistWorld
>It includes scientific

Chinese is rife with misinformation, alternative facts, sophistry and pure
garbage, any thing scientific is either translated to English already or
tranlated from English and other languages.

>and not-scientific content.

It's OK if you major in Asian studies or something, for an average guy the
overall quality of Chinese content is just not worth you time. Not to mention
modern Chinese only existed little more than a century.

I repeat what I said, I oppose spending too much time (more than dabbling) on
Chinese by any average person or student, Chinese is a very messy language,
for the people worth your time talking to they most likely already know basic
English.

~~~
slaslasla
With that mentality I doubt that you speak a foreign language. If that's the
case, of course you think that everything "important" is translated for you
already - it's not going to show up on Google if you don't search it in its
published language. Considering your tone I doubt I can convince you, so all I
will say is that you don't know what you're missing.

~~~
dang
Please don't cross into personal attack on HN.

[https://news.ycombinator.com/newsguidelines.html](https://news.ycombinator.com/newsguidelines.html)

~~~
slaslasla
Personal attack? How fitting on a post about languages that people can't seem
to read.

~~~
dang
Yes, seven "you"'s in a row coupled with negative statements crosses into
personal attack. Please follow the site guidelines so we don't have to ban you
again.

[https://news.ycombinator.com/newsguidelines.html](https://news.ycombinator.com/newsguidelines.html)

------
throwaway072019
Someone who'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're more likely
going to run into a situation where you're saying "I wish I could talk to that
person" or "I wish I knew what that said" than you are going to run into a
situation where you go "I wish I could calculate the second derivative of that
formula." 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 "I speak Mandarin" on more resumes than "I
know calculus").

In the end, though, you'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.

~~~
superkuh
Sure, you don't run into situations requiring math. Instead existing everyday
situations are perceived in new ways because you understand calculus.

~~~
throwaway072019
Can you give an example? I can't think of any everyday situation that most
people would run into where calculus comes in handy. It's definitely necessary
for certain specific applications, but not ones I'd call everyday situations.

~~~
im3w1l
A lot of things are governed by differential equations, so understanding how
they behave is helpful. Financial models, physics models, biology models
commonly use them.

~~~
throwaway072019
> Financial models, physics models, biology models commonly use them.

In what specific everyday situations would most people find these useful? It's
not like it's common for people run into situations where they say "if only I
could calculate the predator prey systems" or "if only I could calculate
radioactive decay." I've studied these, and I don't think I've ever run into
some everyday situation where I've said "Man, I'm really glad I can apply my
differential equations/vector calculus/etc. here." Even in the rare situation
where I want to calculate compound interest I opt to just use a interest
calculator since it's quicker and less error prone than doing it by hand.

~~~
im3w1l
> I don't trust the experts, if only I could build my own disease spread model
> with partial vaccination - then I could compute the nash equilibrium
> strategy for the vaccinate-don't vaccinate game.

------
unixbeard1337
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've felt I'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.

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't what it used to be. I think that's a
problem for us as a society, but it's not going away soon. I'm advising my son
to major in something quantitative.

That being said, the author's apparent advice not to take fl at all is insane.
Especially for high school students. If you are not MIT/CalTech material,
Ivies like to see foreign languages.

~~~
alexhutcheson
Yeah, even for state schools there is often a foreign language requirement.
For example, University of Maryland requires applicants to have taken at least
2 years of foreign language courses[1]. If you decide not to check those
boxes, you’re just making the college application process unnecessarily
difficult for yourself. Take 4 years of Spanish or whatever else and move on.

[1]
[https://admissions.umd.edu/apply/requirements/freshman](https://admissions.umd.edu/apply/requirements/freshman)

------
Tharkun
I feel like it's much easier to start learning Mandarin than Maths. I can't
really put into words _why_ I feel this way, given that there are great
resources like Khan Academy out there. Maybe it's easier to gauge fluency in a
language than it is in maths? When do you stop learning? Maybe you're
proficient enough when you can order from an all-Mandarin menu? As soon as you
can'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'm fluent at trig and pretty good
at some bits of algebra. Pretty rusty in calculus and OK at stats. I'm sure
having this knowledge makes parts of my job easier. But maths is such a huge
and diverse field.

Not knowing what I don't know, I find it very difficult to gauge whether I'd
benefit from learning more, if that makes sense.

------
Al-Khwarizmi
I don't get the point they're trying to make.

I think the analogy between math and a language that you can learn as "native
language" is quite far-fetched and flawed, but let's accept it for the sake of
argument.

Then, I'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.

So in my view, what they're advocating already happens, so I'm not sure what
change they're proposing.

------
iamvik
I like learning languages because I like learning. There doesn't need to be a
reason. This is a very engineery perspective, I don't like it.

------
js8
Actually, math is not an universal language. There are several different
languages within math, see
[http://math.ucr.edu/home/baez/rosetta.pdf](http://math.ucr.edu/home/baez/rosetta.pdf)

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

------
chmod775
The author's argument immediately fails at the fact that math papers are
written in natural language and you'll have no chance of understanding the
paper if you don't speak that language.

Just because I can read a math paper written in English or German I don't
harbor any illusions I'll be able to understand one written in Mandarin.

On top of that there's that mathematical notation really isn't as standardized
as one would hope. Neither is basic terminology (which already isn't
consistent between different disciplines/schools within the same language).

So unless a Chinese mathematician deigns to translate the paper into a
language I understand, I'll just be screwed.

The underlying concepts may be universal, but the language and notation of
mathematics today just isn't.

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:
[https://zh.wikipedia.org/wiki/%E8%BF%9E%E7%BB%AD%E5%87%BD%E6...](https://zh.wikipedia.org/wiki/%E8%BF%9E%E7%BB%AD%E5%87%BD%E6%95%B0)

------
maoeurk
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't know enough about
children's education to disagree, but if you're an adult, I think it's a good
idea to learn at least one second language.

Language study and math are not mutually exclusive for me.

When I've learned math it's through focused effort, sitting down and doing
math problems, thinking really hard, and talking to people with a whiteboard.

When I start study languages I'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.

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.

Once you have a solid foundation, then it's closer to having fun than
studying. You just chat with people or read things you're interested in, the
same as you probably already do for fun in your first languages.

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.

That said, I don't think learning a new language is easy, but it'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.

------
melling
I collect math, machine learning, statistics, etc urls. The ones discussed on
HN have the HN discussion below the article:

[https://github.com/melling/MathAndScienceNotes/blob/master/m...](https://github.com/melling/MathAndScienceNotes/blob/master/math.md)

[https://github.com/melling/MathAndScienceNotes/tree/master/s...](https://github.com/melling/MathAndScienceNotes/tree/master/statistics)

[https://github.com/melling/MathAndScienceNotes/blob/master/m...](https://github.com/melling/MathAndScienceNotes/blob/master/machine_learning.md)

This recent HN was interesting, for example:

[https://news.ycombinator.com/item?id=19811715](https://news.ycombinator.com/item?id=19811715)

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mantap
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.

Just make sure that you have native speakers to talk to, the benefit of
learning a language is being able to talk to people!

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gumby
Why are they mutually exclusive?

If you don't know any maths there are things that are hard to describe or even
conceptualise.

If you know only one language there are assumptions you make and things you
don't know that you don't even know you don't know.

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floki999
Can'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.

I'm European, speak 3 languages and use math every day, professionally. I've
studied, lived and worked in the US for many years and am often shocked at
some of my American friends' lack of perspective on international affairs....
keep-up with the math education but don't do it at the cost of languages...
you can't afford to.

~~~
bernardv
Totally agree. A second language expands your world dramatically.

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babayega2
From my experience (and I emphasize on that) I can tell you from us (I'm from
East Africa, speaking English, Swahili, French and two other natives
languages) being proficient in at least English/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 "normal" life, you do have to
learn other 2 languages. We do not have that luxury.

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carapace
Fun fact: more people speak English in China than in North America.

\- - - -

In re: teaching math ASAP see Iconic Math
[http://iconicmath.com/](http://iconicmath.com/) and (the general idea of)
"Proofs without words"
[https://en.wikipedia.org/wiki/Proof_without_words](https://en.wikipedia.org/wiki/Proof_without_words)

~~~
Apfel
Having lived in China for several years, it's very important to stress that
the average English level of those "English speakers" is lower than that of
your average American toddler.

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m0llusk
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.

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bigred100
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.

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TomMckenny
The author makes a good point of course.

But I'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.

A few changes in word choice, sentences structure and idioms can make informal
communication significantly clearer.

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

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malloryerik
Maybe he should try studying math _in_ Mandarin. It doesn't have to be so
zero-sum...

~~~
twelve40
haha that's very optimistic! I'm thinking about getting into gymnastics and
also maybe skiing, a cork 720 backflip seems like a good first step!

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ivan_ah
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 "Why do need to learn math?" which people often
ask me. As in "What am-I going to use this for?"

I don't like the idea of learning math INSTEAD of a foreign language, since
both are meaningful and interesting for different reasons.

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'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'll add the "learn a new language for the culture/history" angle too, not
sure which is more convincing...

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cosmodisk
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's
great to go out there and be able to talk to people but that's about where it
ends. That's why, unless one has some useful skills(IT, engineering,
plumbing,etc.), knowing languages won'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'm
yet to see any jobs that'd pay more just because one can speak German and
Italian...

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masayune
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.

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beenBoutIT
There's no shortage of Math advocates, one of you needs to put together the
Math equivalent of DuoLingo. A math textbook isn't the only way to work on
math daily.

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pimmen
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.

So, if your choice is between calculus or Spanish, Spanish might be the better
choice.

~~~
gshubert17
Steven Strogatz in his book "Infinite Powers" shares the story of author
Herman Wouk interviewing Richard Feynman about his role in the Manhattan
Project. Feynman asked Wouk if he knew calculus. When Wouk replied, no,
Feynman said "You had better learn it. It's the language God talks".

Strogatz writes, "It isn't necessary to learn how to do calculus to appreciate
it, just as it isn't necessary to learn how to prepare fine cuisine to enjoy
eating it." His book gives a broader view of calculus than any text--more like
calculus appreciation.

> Most students who learn calculus will never, ever, integrate a function
> again in their life.

This is true. But will they never, ever use the concepts of slope or area
under a curve? An appreciation for calculus (or mathematics in general) can
enhance one's life in other ways. To know enough math to appreciate the
mystery of unreasonable effectiveness of mathematics [0], is mind-expanding.

[0]
[https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.htm...](https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html)

~~~
pimmen
I agree, learning calculus does enhance one’s life. Statistics enhances your
life even more though since you will actually use it. I use calculus sometimes
at work and I use it when learning new mathematical concepts but it still
doesn’t even come close to how important statistics is to me.

Sometimes it just comes down to utility. If you live in Nevada and you’re
wondering whether you should learn how to drive or how to sail, pick driving.

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

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otabdeveloper2
Why not both?

Seems to work for the rest of humanity.

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

~~~
abrax3141
You need to factor in: “English is the de facto language of Business,
Engineering, Science, and, most influentially, The Internet.”

~~~
dvduval
Ok, but spend a little time on the Chinese internet. Sure, they use "some"
obligatory English, but the dependency is likely not what many imagine it to
be.

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draw_down
Seems a bit silly. Americans typically learn enough math for the example
problems he lists by the time they graduate high school.

I don't think learning Mandarin is such a bad idea, personally.

