What the Next Generation Needs Is Math, Not Programming

What the next generation really needs lessons in: - Humility - Empathy - Patience - Self restraint and control - Mindfulness&#x2F;Awareness - Disappointment - Resilience - Communication - Listening - Learning - Financial independence and literacy - Critical thinking - Problem solving - Self acceptance<p>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.

Why place one body of knowledge in front of the other like this? Everything has to be a competition with some people.<p>It&#x27;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:<p>&quot;Underlying our approach to this subject is our conviction that ``computer science&#x27;&#x27; 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.&#x27;&#x27; Computation provides a framework for dealing precisely with notions of ``how to.&#x27;&#x27;&quot;

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

This depends on how people learn and perceive information. If I hadn&#x27;t learnt programming before I was taught Maths and Calculus, I probably wouldn&#x27;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.<p>For me Maths is boring. It&#x27;s abstract and you don&#x27;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&#x2F;software development problems that are solved with those and only then I realised how useful they can be.

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

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.

I&#x27;m going to deliberately try to be controversial, but in order to spur discussion. What the next generation needs is more soft&#x2F;social sciences, not STEM.<p>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.

Every profession has a tendency to overstate it&#x27;s own importance. In the eyes of programmers , we are misunderstood , under appreciated and people don&#x27;t fully grasp our worth.<p>Management thinks that they&#x27;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.<p>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&#x27;t &quot;get&quot; math or have any use for it in real life.<p>Though Delmania&#x27;s comment skirts dangerously close to what pg might call a &quot;middlebrow dismissal&quot; , 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.<p>Some lessons in Humility , Resilience and Self acceptance would do us a world of good.

Misleading title: the actual message:<p>&gt; <i>[I]ntelligent analysis of large scale data is the future. And for that future, what you need is Math, not Programming.</i><p>I don&#x27;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.<p>:)

Of course, mathematics education in public schools is notoriously awful, though quality obviously varies across jurisdictions.<p>I can&#x27;t see programming education faring better, especially considering that the emphasis is on &quot;code&quot;. This is a <i>horrible</i> 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 <i>The Design and Implementation of the FreeBSD Operating System</i>, 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&#x2F;event broker bus or publish-subscribe with named pipes and the file system under a standard interface&#x2F;toolkit), build systems and so forth. Ideas and concepts with code on the side.<p>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&#x27;t see beyond the mnemonics, I suppose.<p>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&#x27;t at all. Bashing out Java code alone is nowhere near as relevant as some people seem to think it is.

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.

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.

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

I agree the next gen needs Math. Not for the reasons in this article, though.<p>John Carmack&#x27;s 2012 QuakeCon speech is almost a direct rebuke: <a href="https:&#x2F;&#x2F;blogs.uw.edu&#x2F;ajko&#x2F;2012&#x2F;08&#x2F;22&#x2F;john-carmack-discusses-the-art-and-science-of-software-engineering&#x2F;" rel="nofollow">https:&#x2F;&#x2F;blogs.uw.edu&#x2F;ajko&#x2F;2012&#x2F;08&#x2F;22&#x2F;john-carmack-discusses-...</a><p><i>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.<p>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.</i>

Here&#x27;s a concrete example of what this is about:<p>&quot;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.&quot; [0]<p>It goes without saying that mathematics is at the root of computer science, but we&#x27;ve gotten so far away from those roots, which is why we&#x27;re reaching the upper bounds of complexity that can be foisted upon our old, broken way of thinking. Time to go back to basics.<p>[0] <a href="https:&#x2F;&#x2F;web.stanford.edu&#x2F;class&#x2F;cs242&#x2F;readings&#x2F;backus.pdf" rel="nofollow">https:&#x2F;&#x2F;web.stanford.edu&#x2F;class&#x2F;cs242&#x2F;readings&#x2F;backus.pdf</a>

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

Here&#x27;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 &quot;The math is too difficult - I do it numerically, much easier that way.&quot;<p>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.

If we are breaking it down to something this basic I think a more accurate statement would be, &quot;What the Next Generation Needs Is Math AND Programming&quot;<p>In traditional Computer Science there is already a focus on both of these areas. The question I wonder is more, &quot;Does the degree prepare us for either of these areas?&quot;<p>In the area of programming I believe the answer is a resounding NO. Most students coming out of a 4 year CS program aren&#x27;t ready to be programmers. They&#x27;ve been taught a bunch of theory and fundamentals, but they haven&#x27;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.<p>Like many programmers, my career path (until recently), has kept me pretty far away from the math; so I don&#x27;t think I can say for sure that the same is true here, but I suspect it is.<p>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.

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.

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&#x27;s fine for me. I&#x27;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&#x27;t <i>need</i> to learn trigonometry if you don&#x27;t want to at the time.

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

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

Here is some of why the OP is correct:<p>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.<p>This little process is more important now because computers let us do much more in the data <i>manipulations</i>.<p>That said, there is a remaining question: What manipulations should we have the computers do?<p>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.<p>But, as we have programmed more of what we knew how to do manually, we will want more powerful, valuable manipulations.<p>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 <i>assumptions</i> for some mathematics, that is, <i>hypotheses</i> for some theorems, proceed with theorems and proofs, get some mathematical results, and use those to say what manipulations to do.<p>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.<p>For such problems, data manipulations from theorems and proofs, sometimes new, can knock the socks off any other approach, e.g., intuitive heuristics.<p>That&#x27;s some of the future of math, especially in what gets programmed.

Is it not possible that students need both?<p>In the same way that students were offered home-ec and shop in previous generations, to learn the real-world applications of their &quot;cerebral&quot; subjects, are we not teaching programming today as the real world application of mathematics?<p>Eigenvectors, great. But what can I do with them? Now, software that uses those eigenvectors to control the motions of a robot, that&#x27;s something kids can get excited about, and can turn into a career (not to suggest pure math can&#x27;t lead to careers, but the combination of the two opens up <i>more</i> careers).

&gt; “Google works without understanding what a ‘principal eigenvector’ is. Tomorrow, we need to absolutely know that.”<p>This is total BS. Even in the present day, most programmers can survive their entire career without knowing this.

Not everybody needs to know how to do math beyond arithmetic (though the opportunity should be provided).<p>The focus should be making sure everybody can understand the math, and especially statistics, they are presented with everyday.

... says mathematician.