
What the Next Generation Needs Is Math, Not Programming - npguy
http://statspotting.com/what-the-next-generation-needs-is-math-not-programming/
======
Delmania
What the next generation really needs lessons in: \- Humility \- Empathy \-
Patience \- Self restraint and control \- Mindfulness/Awareness \-
Disappointment \- Resilience \- Communication \- Listening \- Learning \-
Financial independence and literacy \- Critical thinking \- Problem solving \-
Self acceptance

Then we can focus on what area the person can best contribute in. Not everyone
is going to suited for a job in programming or mathematics, or STEM as a
whole.

~~~
cousin_it
What the next generation really needs is an economy where everyone can make a
decent living with a modest effort, without having to desperately "outcompete"
other job seekers. The US had that kind of economy at some point. Since we
haven't lost any arcane secrets since then, it must be still achievable today.

~~~
cynicalkane
The "decent living" of past generations is still available today, but past
generations were poorer than you think they were, particularly for those who
don't come from white and privileged backgrounds.

~~~
pavedwalden
Although almost everyone is better off in material terms than they were two
generations ago, I fear that the level of wealth required to live a
"comfortable" life may have outpaced that increase. How many hours does a blue
collar worker have to put in to live close to a grocery store and good
schools? How much time do the working poor spend commuting? If you break your
arm, what percentage of your income will be consumed by medical costs?

I don't have any data on this, but it's my hunch about why there's so much
economic resentment these days.

~~~
parasubvert
"How many hours does a blue collar worker have to put in to live close to a
grocery store and good schools?"

Depends if they work in a unionized industry.

"If you break your arm, what percentage of your income will be consumed by
medical costs?"

In most industrial countries, including the US after the ACA, very little,
because of health insurance.

"there's so much economic resentment these days."

That's inequality. When everyone around you is poor, except for a few rich
folks you don't see often, it's not as big a deal. When you're constantly
exposed to the things you don't/can't have, that can lead to resentment.

This goes back to your first sentence: "Although almost everyone is better off
in material terms than they were two generations ago, I fear that the level of
wealth required to live a "comfortable" life may have outpaced that increase."

In the US, Median Income peaked in the 1970's and has been flat.
[https://en.wikipedia.org/wiki/Household_income_in_the_United...](https://en.wikipedia.org/wiki/Household_income_in_the_United_States#/media/File:U.S._Hourly_Wages_-
_Real_or_Adjusted_for_Inflation_1964-2014.png)

The poor (in the U.S. anyway) are relatively worse off than they were 2
generations ago - the bottom 50% have seen very little growth in income in 50
years, while the top 50% have grown a lot more.
[http://www.russellsage.org/sites/all/files/chartbook/Income%...](http://www.russellsage.org/sites/all/files/chartbook/Income%20and%20Earnings.pdf)

Not all countries are as bad as the US, particularly Canada or Europe, because
they have strong redistribution systems (health and social insurance, etc.).
But the trends aren't great.

~~~
soccerdave
I am self-employed and pay $6000 a year for high deductible health insurance
for my family that has a $5000 deductible. So if my child breaks their arm and
that is my only expense that year, then I paid $11,000 for their broken arm.
Not cheap by any means. I'm sure lots of people on this forum work for
companies that cover their whole cost of insurance and are out of touch with
costs, but the "Affordable" Care Act has not made health insurance more
affordable.

~~~
infinite8s
Insurance doesn't work that way. If you had a heart condition which required
operation (so maybe 100k) you would also have paid 11k. You need to average
over all expected outcomes to calculate whether it was affordable or
expensive. In other countries (Europe and Canada) that 11k comes out as taxes
instead of direct and indirect insurance costs.

------
parasubvert
Why place one body of knowledge in front of the other like this? Everything
has to be a competition with some people.

It's always been a mistake to believe math is somehow more noble than
programming. Best explanation as to why comes from the preface of SICP by
Abelson and Sussmann:

"Underlying our approach to this subject is our conviction that ``computer
science'' is not a science and that its significance has little to do with
computers. The computer revolution is a revolution in the way we think and in
the way we express what we think. The essence of this change is the emergence
of what might best be called procedural epistemology -- the study of the
structure of knowledge from an imperative point of view, as opposed to the
more declarative point of view taken by classical mathematical subjects.
Mathematics provides a framework for dealing precisely with notions of ``what
is.'' Computation provides a framework for dealing precisely with notions of
``how to.''"

~~~
davidamarquis
Where did you get nobility from. This isn't the author's point at all.
Obviously knowledge about different areas of knowledge can be of more
practical benefit at different times. The point is that in the next few years
knowledge of math will become relatively more valuable and programming
relatively less valuable.

Regarding the quote, it is a best a great oversimplification. Mathematicians
have been interested in computation for a long time. See the Euclidean
algorithm for example. Interestingly its computational complexity was worked
out a hundred years before computer science was even considered a subject.
Many great mathematicians like Gauss also had a keen interest in computation.
A description of the fast Fourier transform was found in his notes after he
died.

It is true that mathematical theorems have historically not been written from
a computational point of view. But many many theorems can easily be turned
into an algorithm (anything based on induction for example). Mathematics has
many different subfields and the number of such constructive theorems varies
based on the area. However, constructive arguments in mathematics are so
pervasive that I think it is silly to even try and separate computation and
mathematics as separate ways of thinking.

~~~
parasubvert
"The point is that in the next few years knowledge of math will become
relatively more valuable and programming relatively less valuable."

Sorry, that's at best an opinion, and at worst, bullshit. There little
evidence of this. This article makes an assertion, provides a few anecdotes.

~~~
davidamarquis
I agree there is almost no content in this post. Reasonable cases could be
made both for and against the point I think.

~~~
parasubvert
Yeah, I accept that.

------
veddox
> Today, we can get away with ‘knowing’ how Google works without understanding
> what a ‘principal eigenvector’ is. Tomorrow, we need to absolutely know
> that.

Part of the advancement of technology is that fewer and fewer people actually
understand how stuff works. What percentage of the population has any notion
of how a computer works under the hood? How many people understand how our
national power grid works? Our sewage system? Our cars? As our world gets more
sophisticated, we specialize; we have to. Sure, there will be people who will
have to know about eigenvectors tomorrow - but do we all? Not by a long shot.

~~~
tzs
That reminds of some idle thoughts I had several years ago, when I lived in an
apartment, during a storm.

It was a dark and stormy night. The rain was coming down hard, and there was a
good bit of wind. It was not a night you would want to be outside in. As I sat
in my dry, warm, lighted apartment I got to thinking about how different life
was compared to my distant cave dwelling ancestors.

If they wanted a drink of water, they had to leave their cave and go find
running water. On a night like this, they would have to choose between thirst
and going out in terrible weather.

In my apartment, I simply turn the handle on a faucet, and as much water as I
want is instantly available. No need to leave the apartment when I get
thirsty.

If I want to be in rain for some reason, such as to wash, I simply step into
the shower and it will rain on my command, at whatever intensity I want, at
whatever temperature I want. My ancestors would have to wait for rain, and
accept whatever intensity and temperature that it happened to be.

If I get cold, I turn the thermostat up, and minutes later the temperature is
to my liking. My ancestors would have to move around in their cave and hope to
find a warmer spot, or build a fire and trade away clean air for some warmth.

If I want to do something that needs light and it is night out, I flip a
switch and I have light. I can adjust the brightness to anything from just
enough to get around to enough to do anything I can do in full sunlight. My
cave dwelling ancestors would have to use fire for light at night, messing up
the air of their cave and only partly lighting their home.

If I want to enjoy a gentle breeze, I turn on a fan. They had to go outside.

I then got to thinking about how if my ancestors could see me, they might
think I was some kind of god as I summon running water, rain, wind, light at
will, and control the temperature.

Then I realized that if they were put in my apartment and I in their cave,
they would be able to do all that I can do after a couple minutes
instruction...and I would have no idea how to actually make a fire.

I'm not a god compared to them. I just found a better cave.

~~~
JoeAltmaier
Ok, but 'we' are gods compared to them. We've build a better society together.
You can take some pride in your part in that!

------
haphazardeous
This depends on how people learn and perceive information. If I hadn't learnt
programming before I was taught Maths and Calculus, I probably wouldn't have
understood some of the basics like Functions, Matrixes and Series etc or it
would have taken me quite a while to grasp the idea.

For me Maths is boring. It's abstract and you don't have any interaction
whereas programming is more fun for me. I never truly understood some of the
physical and mathematical concepts I was taught in school and uni until I came
across programming/software development problems that are solved with those
and only then I realised how useful they can be.

~~~
DamnYuppie
I also find Math studies by themselves to be quite boring, at least that is
how I perceived it for most of my education. Yet I had one teacher who worked
really hard to show how Calculus is applied in reality. He made all of his
homework and test's real world problem solving oriented. He was also a part
time scout for the Seattle Mariners and he would do all of his in class
examples using either base ball or real estate. This really helped me put into
context many of the concepts and the multitude of ways they can be applied,
not to mention it was a really exciting and enjoyable class.

After experiencing that I saw Math in a new light. I simply wish that my K-12
education was more directed to the applicability of many of the concepts we
learned as I believe it would have made the subject not only much more
approachable but enjoyable.

------
codingdave
What students need is the ability to self-teach. They need to be able to
recognize when there is a gap in their knowledge, know how to find instruction
in those topics, and have the motivation to follow through on actually
learning it.

If children gain those skills by the time they are adults, they can correct
any faults in their educational paths.

~~~
fuzzieozzie
Is self-teach 'newspeak' for learn? You learn by observing, researching and
practicing. I guess I am getting old.

~~~
oberstein
I thought self-teaching, self-taught, and similar were jargon that has been
around for a long time. In the historically recent programming community
especially it's all over the place: people who never did formal CS education
teaching themselves how to program and are as or more effective than their
Stanford peers. The difference between self-teach and learn is that the former
is an attempt at learning through one's own will and direction, and the latter
is merely a state of understanding the path to which can be from many
directions (self-directed, teacher-directed, or just simple observation of the
world around you).

------
gizi
According to the Curry-Howard correspondence, all mathematical proofs are
actually programs. This is normal. A proof is a series of steps, and if you
unambiguously describe these steps, a computer will obviously be able to
execute them. Furthermore, since Alonso Church successfully proposed a Turing-
complete axiomatization based on just functions (even numbers are just
functions), a computer program is clearly a mathematical object. An
alternative axiomatization, Zermelo-Fraenkel, is based on sets. There is
probably no better playground for sets than using a relational database. SQL
is pretty much Zermelo-Fraenkel on steroids. In other words, large areas in
math go into supporting the discipline of computer programming already. I do
not believe that everybody would have to spend more time with areas in math
for which no useful applications exist and that we are therefore unlikely to
use in programs.

~~~
jandrewrogers
All things that exist are mathematical objects and programs. Algorithmic
information theory asserts that my cup of coffee is actually a program.

While mathematics is important to computer programming, for most practical
purposes it is of limited utility unless you are inventing new computer
science. Knowing how to use a relational databases correctly requires no
formal set theory. Understanding how to build a massively parallel relational
databases requires understanding the topological equivalents of relational
operators, which is much more mathematical, but very few programmers design or
build parallel databases.

~~~
gizi
> Knowing how to use a relational databases correctly requires no formal set
> theory.

Very true, I guess. But the other way around, someone who has used relational
databases, will immediately understand formal set theory and find it
absolutely trivial. Another example would be regular expressions. Anybody who
has ever used them will immediately recognize what Kleene's closure is about
and effortlessly deal with it. I think that this is generally the case. If you
first solve problems with tools that embody a particular theorem, and if later
on you read up on that theorem, you will find that theorem trivially simple.
In other words, math and computer science are only hard, when you have never
used them. Since formal education does things systematically in the wrong
order, students tend to consider math and computer science to be hard.

~~~
ccortes
>someone who has used relational databases, will immediately understand formal
set theory and find it absolutely trivial.

This is simply not true, you may understand the very basics of it, but by no
means you will understand set theory and much less find it trval by just using
relational databases.

------
paulojreis
I'm going to deliberately try to be controversial, but in order to spur
discussion. What the next generation needs is more soft/social sciences, not
STEM.

tl;dr of my point: we know dangerously more about technology than about
people, their needs as individuals and their needs as a society. Somewhere
along the line we should stop throwing technology at people just because we
can, and start to focus on the right solutions - technological or not - to
real problems.

~~~
joeclark77
If by "soft/social sciences" you mean real substantive disciplines like
history, philosophy, civics, and the arts, I agree with you.

Currently "social studies" in school is a bit of a trash bucket into which
gets thrown every personal ideology and pet project that some teacher got her
feminism or social work or grievance-studies BA in. It's the worst subject in
most curricula, even worse than English. The problem is there's plenty of
those nonsense degree holders and far too few college graduates who have
studied the humanities.

~~~
chiaro
What kind of degree are you talking about when you say "social studies"?

~~~
joeclark77
I'm referring to "soft sciences" like social work, psychology, sociology,
[grievance] studies, poli sci, etc, as opposed to the humanities: history,
mathematics, philosophy, classics, fine arts, etc.

~~~
chiaro
Not sure what you mean by grievance studies but most of those, besides being
quite important, fit under the humanities label. Mathematics on the other
hand, probably not.

~~~
joeclark77
Most of those would be classified as "social sciences", not humanities. It has
to do with the methods and philosophies they use. Grievance studies is my
nickname for "_____ studies" where the "_____" is the name of some census
checkbox.

------
thewarrior
Every profession has a tendency to overstate it's own importance. In the eyes
of programmers , we are misunderstood , under appreciated and people don't
fully grasp our worth.

Management thinks that they're the real movers and shakers , having to take
all the risk , make all the tough decisions , while having to deliver results
while being saddled with sometimes recalcitrant and inefficient teams.

Mathematicians feel that they are the ones at the vanguard of progress and are
angered by the fact that people have the temerity to say that they don't "get"
math or have any use for it in real life.

Though Delmania's comment skirts dangerously close to what pg might call a
"middlebrow dismissal" , he makes a very important point. Our increasingly
unequal economy and limited opportunities are forcing us to increasingly push
ourselves harder and into a fierce cycle of competition that is destroying us.

Some lessons in Humility , Resilience and Self acceptance would do us a world
of good.

~~~
crimsonalucard
>Management thinks that they're the real movers and shakers , having to take
all the risk , make all the tough decisions , while having to deliver results
while being saddled with sometimes recalcitrant and inefficient teams.

It is by far easier to imagine something than it is to make that imagination
real.

It is by far easier to tell someone what to do then it is to do it.

Management is by far easier than engineering.

Management, however, is still a dramatically different skill than engineering,
and it is a skill that is important.

~~~
marcosdumay
> It is by far easier to tell someone what to do then it is to do it.

Only if you don't care whether it gets done, and if it gets done well.
Otherwise, it's far easier to just do it, and not rely on the known unreliable
"other people".

Problem is that a big share of management in fact don't care about those
things, and only manage the political game. But don't let that mislead you,
actual management is hard, quite on par with engineering.

------
kazinator
Misleading title: the actual message:

> _[I]ntelligent analysis of large scale data is the future. And for that
> future, what you need is Math, not Programming._

I don't agree; intelligent analysis of data probably requires the combination
of a large number of cases, stitched together with some hacks. And a principal
Eigenvector or two buried in there in some supporting role.

:)

------
vezzy-fnord
Of course, mathematics education in public schools is notoriously awful,
though quality obviously varies across jurisdictions.

I can't see programming education faring better, especially considering that
the emphasis is on "code". This is a _horrible_ thing to put at the forefront,
because it limits your view to the particular set of language constructs you
use as opposed to broader properties of computer systems and computation. It
is best to start by a rundown of high-level computer architecture (von Neumann
and Harvard) so as to understand basic machine instructions and types,
progressing into OS fundamentals (something like _The Design and
Implementation of the FreeBSD Operating System_ , though condensed), then
briefly into compiler construction and language VMs, onto practical usage of a
CLI shell, the various ways of representing resources and IPC, data structures
and how to use them in forming basic services (like a message/event broker bus
or publish-subscribe with named pipes and the file system under a standard
interface/toolkit), build systems and so forth. Ideas and concepts with code
on the side.

Obviously these are rushed examples, but the point is that code-centric
computing education in public schools will probably backfire by creating
people with just enough knowledge to have extremely warped views of software.
Unless your goal is to turn kids into ALGOL monkeys who can't see beyond the
mnemonics, I suppose.

You might say this would be too complex for public schools to implement. I
agree, which is why it should stay out. Do it right or don't at all. Bashing
out Java code alone is nowhere near as relevant as some people seem to think
it is.

------
copsarebastards
What the next generation needs (among other things) is for people to realize
that the world has become far too complex for the next generation to just need
one thing.

------
confutio
This article assumes there is no such thing as Computer Science, which is the
development of algos and the like which the author assumes is done by
mathematicians.

------
tempodox
The title already says it all. After “everyone must learn to code”, people
start returning to more sensible ideas.

~~~
agumonkey
Any interesting thing done on a computer will land into math territory anyway.
The current geek-fetish trend can't go away fast enough.

------
ThatMightBePaul
I agree the next gen needs Math. Not for the reasons in this article, though.

John Carmack's 2012 QuakeCon speech is almost a direct rebuke:
[https://blogs.uw.edu/ajko/2012/08/22/john-carmack-
discusses-...](https://blogs.uw.edu/ajko/2012/08/22/john-carmack-discusses-
the-art-and-science-of-software-engineering/)

 _In real­ity in com­puter sci­ence, just about the only thing that’s really
sci­ence is when you’re talk­ing about algo­rithms. And opti­miza­tion is an
engi­neer­ing. But those don’t actu­ally occupy that much of the total time
spent pro­gram­ming. You know, we have a few pro­gram­mers that spend a lot of
time on opti­miz­ing and some of the select­ing of algo­rithms on there, but
90% of the pro­gram­mers are doing pro­gram­ming work to make things hap­pen.
And when I start to look at what’s really hap­pen­ing in all of these, there
really is no sci­ence and engi­neer­ing and objec­tiv­ity to most of these
tasks. You know, one of the pro­gram­mers actu­ally says that he does a lot of
mon­key programming—you know beat­ing on things and mak­ing stuff hap­pen. And
I, you know we like to think that we can be smart engi­neers about this, that
there are objec­tive ways to make good soft­ware, but as I’ve been look­ing at
this more and more, it’s been strik­ing to me how much that really isn’t the
case.

Aside from these that we can mea­sure, that we can mea­sure and repro­duce,
which is the essence of sci­ence to be able to mea­sure some­thing, repro­duce
it, make an esti­ma­tion and test that, and we get that on opti­miza­tion and
algo­rithms there, but every­thing else that we do, really has noth­ing to do
with that. It’s about social inter­ac­tions between the pro­gram­mers or even
between your­self spread over time._

------
nateabele
Here's a concrete example of what this is about:

"Conventional programming languages are growing ever more enormous, but not
stronger. Inherent defects at the most basic level cause them to be both fat
and weak [...] inability to effectively use powerful combining forms [...]
lack of useful mathematical properties for reasoning about programs." [0]

It goes without saying that mathematics is at the root of computer science,
but we've gotten so far away from those roots, which is why we're reaching the
upper bounds of complexity that can be foisted upon our old, broken way of
thinking. Time to go back to basics.

[0]
[https://web.stanford.edu/class/cs242/readings/backus.pdf](https://web.stanford.edu/class/cs242/readings/backus.pdf)

------
gbachik
What the next generation needs is to stop being told what they need.

------
fuzzieozzie
Here's the challenge faced by strong students. At a recent science fair, a
strong 8th grader presented a simulation where you could fly a rocket around a
plant, with the ability to change gravity, thrust, etc. I asked if he had
explored the math (since this was a soluble problem.) The answer "The math is
too difficult - I do it numerically, much easier that way."

There is great advantage in re-using the work of others, but in order to
advance the frontiers of knowledge people truly need to understand the
underlying assumptions and mathematics.

~~~
nmrm2
There are whole subfields of mathematicians who would agree in spirit with "I
do it numerically, much easier that way" :-)

~~~
fuzzieozzie
Absolutely - numerically is they way to go in some fields, but without a deep
understanding of the underlying limitations there will be no expansion
understanding/knowledge. It's the old academic vs. practitioner argument.

------
bigtunacan
If we are breaking it down to something this basic I think a more accurate
statement would be, "What the Next Generation Needs Is Math AND Programming"

In traditional Computer Science there is already a focus on both of these
areas. The question I wonder is more, "Does the degree prepare us for either
of these areas?"

In the area of programming I believe the answer is a resounding NO. Most
students coming out of a 4 year CS program aren't ready to be programmers.
They've been taught a bunch of theory and fundamentals, but they haven't spent
time applying them on real problems at scale. Within the classroom setting the
fundamentals are applied to trivial problems that can fit into the constraints
of a classroom setting.

Like many programmers, my career path (until recently), has kept me pretty far
away from the math; so I don't think I can say for sure that the same is true
here, but I suspect it is.

I have argued for a long time that much like a doctor goes through a residency
program, something similar should be required of computer science degrees. At
least a couple of years of the program should include students working
together with experienced professionals building real systems that are
attempting to solve difficult problems.

------
S4M
As someone who has a maths degree, I find it sad that most of the jobs
advertised that require a background in maths are either jobs of Quants or
Data Scientists.

~~~
nmrm2
Actuarial work and accounting are both very accessible to mathematics majors;
you really just need one extra course worth of content (that you can work
through yourself) to be prepared for an entry level position in those fields.

~~~
S4M
For me Actuarial work falls into "Quant" work, and accounting has nothing to
do with maths.

~~~
nmrm2
_> accounting has nothing to do with maths._

Sure, but like I said, with a Mathematics degree you can self-study and get an
intro-level position pretty quickly.

Otherwise, I guess you can go to grad school or become a teacher? Or, certain
types of software developers get to do interesting math as well.

~~~
S4M
I am not interested in doing anything related to accounting, except for my own
business.

> Or, certain types of software developers get to do interesting math as well.

Yes! But sadly, those type of positions are rarely advertised - well, you
could say that Quants and Data Scientists are some kind of software developers
as well, but the maths needed in other fields are kept very secret.

Now, I am not looking for a job at the moment - I graduated in 2006 and am
working on my own thing now (maths related) - but I was just lamenting that
people complain that more mathematicians are needed without providing concrete
jobs for them.

------
sanoli
Teach kids basic arithmetic WELL, teach them logic in a fun way, find a way to
get them to like reading and think critically about what they read. That's
fine for me. I'd do away with all the rest of math (algebra, trig, etc) and
have it as optional in high school. Really, if you got the stuff above right
as a kid, you don't _need_ to learn trigonometry if you don't want to at the
time.

~~~
yellowapple
I'd personally throw in something like geometry, which (at least when I took
it back in my middle school days; maybe my experience was atypical) had a
heavy emphasis on mathematical proofs, how they worked, why they were
important, the differences between postulates and theorems, how to prove
theorems, etc. Whereas most of my prior and future math courses (particularly
algebra) ended up feeling like an endless barrage of busywork, geometry forced
me to actually _think_ about what I'm doing.

~~~
sanoli
Now that I think of it, I remember having lots of fun with geometry, trying to
figure things out on my own. I still remember the first time I got to prove
Pythagora's on my own, or the formula for the volume of a pyramid. It felt so
awesome that I still long today for a math course where you start from zero
and the teacher just guides you into figuring stuff out yourself, one by one
(Pythagora's, Pi, formulas for volume, etc).

------
0xdeadbeefbabe
Nah it needs history as demonstrated by the OPs myopic stance. Ever hear of a
liberal arts education? I wonder why that became popular?

------
PSeitz
Why do I need to know tomorrow what an ‘principal eigenvector’ is?

~~~
JoeAltmaier
Sort of like knowing what the complexity of an algorithm is - so you can know
if your solution to a big-data problem is going to scale.

------
graycat
Here is some of why the OP is correct:

From 50,000 feet up, we take in data, maybe already have some other data,
manipulate all that data, and get results we want to be powerful, valuable,
etc.

This little process is more important now because computers let us do much
more in the data _manipulations_.

That said, there is a remaining question: What manipulations should we have
the computers do?

Shockingly often in the past, we understood the manipulations well enough to
program them because we were largely just programming what we had done or in
principle knew how to do just manually.

But, as we have programmed more of what we knew how to do manually, we will
want more powerful, valuable manipulations.

Well, often the best approach to more powerful, valuable manipulations will be
via mathematics. There, we can look at reality, see some situations or
properties that appear to hold, let those be _assumptions_ for some
mathematics, that is, _hypotheses_ for some theorems, proceed with theorems
and proofs, get some mathematical results, and use those to say what
manipulations to do.

E.g.: (1) Statistical hypothesis tests. (2) Systems of ordinary differential
equations as growth models. E.g., what would happen if we released 1000
healthy US bobcats into the outback of Australia? (3) For real time local
delivery, which vehicle takes the next order that comes in so that we can meet
promises to customers and minimize expected delivery cost? (4) Pick a part of
the ocean, drill a lot of oil wells; now, what should the sea floor oil
pipeline network look like to carry the oil to where we want it meeting safety
standards and minimizing cost, e.g., expected net present value over the life
of the oil wells? There are many more such.

For such problems, data manipulations from theorems and proofs, sometimes new,
can knock the socks off any other approach, e.g., intuitive heuristics.

That's some of the future of math, especially in what gets programmed.

------
jhardcastle
Is it not possible that students need both?

In the same way that students were offered home-ec and shop in previous
generations, to learn the real-world applications of their "cerebral"
subjects, are we not teaching programming today as the real world application
of mathematics?

Eigenvectors, great. But what can I do with them? Now, software that uses
those eigenvectors to control the motions of a robot, that's something kids
can get excited about, and can turn into a career (not to suggest pure math
can't lead to careers, but the combination of the two opens up _more_
careers).

~~~
rz2k
While I appreciate not everyone is the same, I am not fond of the idea that
young students are always more interested in practical applications than they
are intellectually curious. Making things blow up, or controlling something
with a few lines of code is fun and exciting, but so is discovering something
that previously seemed hidden about how the universe works at a fundamental
level. For a lot of students math is exciting because they feel that they are
imagining how reality itself is working, and even how reality might have
functioned if some seemingly arbitrary rules had been decided differently.

I don't mean to say that practical applications are not inspiring, rather that
the good intentions are misguided when they imply that very young students
aren't capable of abstract thought or ever motivated by purely intellectual
subjects. Becoming an engaging teacher of theory may not even be attainable to
as many people as who are able to encourage a student through a practical
demonstration, but that is different from children not being receptive to
both.

------
0xDAVE
> “Google works without understanding what a ‘principal eigenvector’ is.
> Tomorrow, we need to absolutely know that.”

This is total BS. Even in the present day, most programmers can survive their
entire career without knowing this.

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louden
Not everybody needs to know how to do math beyond arithmetic (though the
opportunity should be provided).

The focus should be making sure everybody can understand the math, and
especially statistics, they are presented with everyday.

~~~
gizi
Wow. You are projecting us back to the mid-12th century, before we got hold of
Algoritmi's famous book: Kitab Al-Jabr, i.e., Liber Algebrae. Before that it
was only arithmetic and bits and bobs of Euclid's Elements (=Geometry). That
was all they had.

------
fapjacks
... says mathematician.

