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[转载]数学还相关吗? 或许有一天科学的皇后会失去她的皇家地位

已有 22637 次阅读 2012-4-18 22:43 |个人分类:书海拾贝|系统分类:观点评述|关键词:100,皇后,background,white,color| color, background, white, 100, 皇后 |文章来源:转载

数学还相关吗?

或许有一天科学的皇后会失去她的皇家地位

 

http://spectrum.ieee.org/at-work/education/is-math-still-relevant

IEEE Spectrum, Vol.49, No.3, p23

OPINION

Is Math Still Relevant?

The queen of the sciences may someday lose its royal status

By Robert W. Lucky / March 2012

 

Long ago, when I was a freshman in ­engineering school, there was a required course in mechanical drawing. “You had better learn this skill,” the instructor said, “because all engineers start their careers at the ­drafting table.”

This was an ominous beginning to my education, but as it turned out, he was wrong. Neither I nor, I suspect, any of my classmates began our careers at the drafting table.

These days, engineers aren’t routinely taught drawing, but they spend a lot of time learning another skill that may be similarly unnecessary: mathematics. I confess this thought hadn’t occurred to me until recently, when a friend who teaches at a leading university made an off-hand comment. “Is it ­possible,” he suggested, “that the era of math­ematics in electrical ­engineering is coming to an end?”

When I asked him about this disturbing idea, he said that he had only been ­trying to be provocative and that his graduate students were now writing theses that were more mathematical than ever. I felt reassured that the mathematical basis of engineering is strong. But still, I wonder to what extent—and for how long—today’s under­graduate engineering students will be using classical ­mathematics as their careers unfold.

There are several trends that might suggest a diminishing role for mathematics in engineering work. First, there is the rise of software engineering as a separate discipline. It just doesn’t take as much math to write an operating system as it does to design a printed circuit board. Programming is rigidly structured and, at the same time, an evolving art form—neither of which is especially amenable to mathematical analysis.

Another trend veering us away from classical math is the increasing dependence on programs such as Matlab and Maple. The pencil-and-paper calculations with which we evaluated the relative performance of variations in design are now more easily made by simulation software packages—which, with their vast libraries of pre­packaged functions and data, are often more powerful. A purist might ask: Is using Matlab doing math? And of course, the answer is that sometimes it is, and sometimes it isn’t.

A third trend is the growing importance of a class of problems termed “wicked,” which involve social, political, economic, and un­defined or unknown issues that make the application of mathematics very difficult. The world is seemingly full of such frus­trating but important problems.

These trends notwithstanding, we should recognize the role of mathematics in the discovery of fundamental properties and truth. Maxwell’s equations—which are inscribed in marble in the foyer of the National Academy of Engineering—foretold the possibility of radio. It took about half a ­century for those radios to reach Shannon’s limit—described by his equation for channel ­capacity—but at least we knew where we were headed.

Theoretical physicists have explained through math the workings of the universe and even predicted the existence of previously unknown fundamental particles. The iconic image I carry in my mind is of Einstein at a blackboard that’s covered with tensor-filled equations. It is remarkable that one person scribbling math can uncover such secrets. It is as if the universe itself understands and obeys the mathematics that we humans invented.

There have been many philosophical discussions through the years about this wonderful power of math. In a famous 1960 paper en­titled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” the physicist Eugene Wigner wrote, “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift [that] we neither understand nor deserve.” In a 1980 paper with a similar title, the computer science pioneer Richard Hamming tried to answer the question, “How can it be that simple mathematics suffices to predict so much?”

This “unreasonable effectiveness” of mathematics will continue to be at the heart of engineering, but perhaps the way we use math will change. Still, it’s hard to imagine Einstein running simulations on his laptop.

 

Glen Oakley
As a software engineer, I resent that remark about mathematics; I would be so, so very dead without linear algebra.

2012326, 10:55:21

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Neil Higgins
My question: How much pure maths must a person be taught in order to understand the subtleties that will break everyday tools? I can now do symbolic maths on my iPhone - stunning - but how much immunity from inappropriate use does this tool confer? Not much, I suspect. In the end, the user must still understand the application to which the tool is being put, and he/she or his/her employer must have a QA system that applies sanity checks to the results.

2012324, 11:10:02

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ALIJUMAAH
i think studying mathmatics has an embedded benifit which is how to think correctly

2012317, 2:20:09

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Bono Nonchev
Yes, a good question, rather revealing of the knowledge what mathematics is on the part of the author. Mathematics is NOT doing sums or calculating weights and whatever any more than music is a thing to silence noisy neighbours.

Mathematics is a study of the relationship between objects, and not only is it increasingly useful, elegant mathematical theories underlie quite a lot of the world we use. Yes, if you only apply the tools you rarely need to lift the hood and twinkle with the stuff inside, but that doesn't diminish, or even decrease, the usefulness of the knowledge of how it all works.

2012316, 17:54:15

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john.a.thompson.2.0@gmail.com
Good math skills will help debug and verify the simulator. Sometimes simulators make mistakes, give questionable results.

2012313, 3:50:03

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Farangis AMANI
Based on the current Market requirements for an Engineering Student the question is, can a person seeking a degree justify going over the required material with the full knowledge that most of it will proved to be useless!

May be the question should be rephrased as "Is Theoretical Math still Relevant?" which I believe it is. And will remain so until such time that dissemination of new ideas becomes Standard and the Nobel Prize committee accept it as a relevant endeavor.

On a different note, I must add that Drafting Art is still alive, well and in demand! Technical drafters are in short supply and a Skilled one who knows how to use the current industry standard tools is highly sought after in the industry I am familiar with.

2012312, 5:28:26

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Joe Citizen
Logic is one of the many forms of classical mathematics, and is essentially indistinguishable from classical mathematics (e.g., skim a book on "philosophy of logic" if you don't believe this sentence). The premise that there is "a diminishing role for mathematics in engineering work" would be valid if current and future engineers need less logical thinking to be successful as engineers. My experience is that there is a one-to-one correspondence between the technical excellence of an engineer and the person's logical abilities. So if tomorrow's world involves increasingly sophisticated products to address increasing complex problems, then it will need engineers who are stronger in logic and mathematics.

The three "trends" used as evidence are great examples of the lack of logical thinking associated with bad engineers. While it is true that a bad software engineer doesn't need mathematics, all of the best software engineers (the ones who write code that is highly reliable to solve challenging problems) are excellent at logic and mathematics. The existence of a lot of crappy software engineers who are weak in mathematics is an example that more mathematics is needed, not less. The increased use of Matlab and Maple shows nothing. If you don't know classical mathematics then you won't be able to do any useful engineering with Matlab or Maple. Regarding "wicked" problems, my experience is that these problems are primarily due to having too many people involved who lack skill in mathematics/logic and/or due to incentives that encourage too many people to act against what would be in the best interest of society.

I have consulted a lot with industry over the years while working in academia, and every problem that I have encountered was solved by combining logic/mathematical thinking with knowledge.

201237, 13:20:36

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Shaw
The mathematical core will change over time, but it's truly hard to conceive of engineering cut free from the power and richness that mathematical methods bring.

I think we'll see new mathematics being applied in more sub-specialties. I wouldn't be surprised to see some of the wicked problems addressed with innovative methods.

As to the software engineering situation, the answer is right here on the page next to the blog: "No clear boundary between math and software exists". I couldn't agree more.

201237, 12:36:17

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Ambroise
I am a software engineer and I use advanced mathematics on a regular basis. Not because it's necessary but because it allows me to make good software instead of just making software. As a student, I used to believe I would never have any practical use for topological spaces, Lipschitz matrices, analytical optimization, solving polynoms of degree 3+, diagonalizing matrices of any size, etc. Year after year, I used all of that. And undoubtedly I'll be using more math tools in the upcoming years.

201236, 21:14:41

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4 位訪客

Brooks
I say it depends on what you want to be when you grow up. If you want to be a “real” Engineer, and be paid an Engineer’s wages and contribute to a project as an Engineer, then the answer is obvious. Of course you will need not only the standard math courses, but more and more math. There’s not enough time to get all you really need! Different Engineers approach the same problem in different ways, often reflecting different capabilities and the results follow. You want to be sure you’ve got the best shot at success in whatever vocation you choose. You can only hope to get the best core of mathematics that will allow you to take on the challenges you will really face in whatever field you find yourself in. Engineers never stop learning (math too!) after graduation. You need the tools to enable that learning (which often involves math you’ve never thought of) or you may falter. Has the author never been around a real Engineering project? Would you like to keep the gate to graduate studies open? Better have the math! There are many electronic “tinkerers” who hook digital and analog circuits together and make neat things happen, but the best of electronic tinkerers are able to study and learn math to make even neater things happen. Here’s to the tinkerers! They have fun, invent some neat things and make a lot of people happy. When you are in school, you can’t possibly guess what area your Engineering career will take you into. Would you pay the cost, and spend the time for an Engineering education that dooms you from the start of your career? I think not.

201236, 11:06:02

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Maths_genius
Mr Robert,

Mathematics is ever relevant. Many phenomena in Nature are modeled by Mathematics and Scientific Computing relay on Mathematical Modeling for simulation.

Software Engineering is neither science or engineering. It is in-fact an art.
It doesn't require Engineering discipline to do Software Engineering.

There is huge difference between Computer Science and Software Engineering. Fundamental Principles of Computer science - automata theory is borrowed from Abstract Algebra.

Mathematics is Great. Long Live Mathematics

201236, 0:27:25

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Gordon Munsche
When I graduated college we didn't even have 4 function calculators. Now I can't work without a PC. but I'm sure glad I learned some math at least so I can make quick calculations in my head and tell the client if something is at least feasible and makes logical as well as monetary sense. No I don't use a sliderule anymore but at least I can do quick reasonable estimates.

201235, 9:06:23

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Keith Sketchley
Catchy title but wrong notions.
Reality is that definitions of parts and assemblies is still required, how to show them to those implementing the design was an essential part part of drawing (many people can make nice lines and print neatly etc, that’s not mechanical drawing as taught to engineers).

Similarly, programmers have to deal with mathematics. Yes, much of the rote it is being _further_ automated (as was done by the slide rule, electro-mechanical calculator, hand-held calculator, and personal computer).

What is not taught well in school is how to think. Engineers are usually good at thinking for their technical work, but the many engineers supporting the anti-engineering notions about humans shows lack of critical thinking skills. That’s the key to supposedly “wicked” problems – logic, ability to weigh options, and observing what is proven to work rather than following someone’s pet theory. Much of IEEE’s publication and activism lacks that.

201235, 1:46:44

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javierN
I got my BSEE two years ago, and I decided to do a second BS in Math. I couldn't be happier. I think engineers need to take more math than the required courses. I believe engineers benefit from taking theoretical math courses, it makes us better thinkers and analyzers. Applied math is fun but learning to prove theorems and learning formal math language makes people communicate better in an engineering environment. Not much fun but good.

You can argue than operating systems don't need much math, but the hardware and most of the algorithm research in based on math. Numerical methods, graphics, compression, encryption, etc. all are based on math. Even if you have Matlab, if you use the inappropriate method your solution will be compromised.

Are you really an engineer if all you do is use tools other people designed?

201234, 15:40:18

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Steve Bouton
The whole notion of math becoming irrelevant is pure and utter nonsense. Electronics is essentially applied physics, and math defines everything.

201234, 9:10:31

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Roger Graves
A long time ago a senior engineer I worked with said to me "computers are not a substitute for thought". Running computer simulations or tossing the problem into Matlab is fine, provided you already have a fundamental understanding of the problem. Doing so without really understanding the problem is just asking for trouble. And understanding the problem usually involves understanding the underlying equations.

201234, 4:17:57

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Soori
I have seen engineers with incompetence in mathematics, unable to explain the results they are getting from simulation softwares. It is frustrating some engineers rely completely on "computer says no or yes". The understanding of the mathematics is very important to validate your work. More and more you have mathematical understanding, more and more you your simulations are reliable. Engineering is a balance between mathematics, physics and practice.

201233, 2:58:26

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Distracted Voter
I don't understand the direction that IEEE is taking with their technical articles lately. Everything is green and math doesn't matter. It's almost as if this is politically motivated and that rational thought processes have not been applied. Sweet and Lucky, the pair to draw to for the new generation. No thanks.

201233, 0:33:34

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Dorn Hetzel
Using tools is fine, but engineers need to have enough math skills to sanity check the output of those tools. Modern airliners can almost fly themselves, but we still like our pilots to know how to do it without the automation, just in case :)

201232, 22:32:59

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Gordon Munsche

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Robert L. Baber
Software “engineering” is truly a separate discipline. As it is practiced today, it is not an engineering discipline – it is far from an engineering discipline. If the real engineering disciplines ever do take the direction that software development is taking, human society is in for big trouble.

Software developers do great things, but they do not do them as well as they could and should. They make far too many avoidable mistakes. They are not yet ready to call themselves "engineers".

Robert L. Baber

201232, 20:21:46

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wjteegarden
There are a great many software developers who refer to themselves as "software engineers", but whose grasp of the discipline and responsibility behind such a title is tenuous at best, and non-existent at worst.

There are also true software engineers, who have the education, experience, and innate ability to truly "engineer" software systems, and understand the totality of their creation and application. These, Mr. Baber, would take exception to your comment.

201233, 0:32:35

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Robert L. Baber
The true software engineers to whom you refer in your second paragraph are in the minority. They may produce engineering quality software, but their impact on the practice of the discipline as a whole is small, too small.

I was referring to the great majority of the software developers to whom you refer in your first paragraph, with which I agree. They like to claim the title "engineer" without earning it. They eschew mathematics, the very language of engineering, and hence cannot be engineers.

201233, 3:37:11

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Robert L. Baber
Until my retirement a few years ago, I was one of the "true software engineers" to whom you refer in your second paragraph above. As such, I do not take exception to my comment.

201233, 11:11:39

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James
As a software engineer, I spend a great deal of time creating work-arounds for hardware created by "engineers" who make so many avoidable mistakes.

201236, 1:01:56

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Philip Machanick
The disturbing thing about taking the existence of tools that can "do the math" as an excuse for not understanding it yourself is that a tool doesn't know when you set up the problem incorrectly.

A tool can only be made sharper. It can't be made smarter. If you know what you are doing a tool amplifies your ability. If you don't, a tool amplifies your incompetence.

201232, 16:20:54

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5 位訪客

Joe Citizen
Your last paragraph is poetry! Copyright that.

201237, 13:29:12

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Duane Dizon
good arguments folks, but no one thought of the use of math in finances and the economy...

201232, 16:20:53

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Phillippe
This article seems very incomplete to me. I'm not sure what the author's goals were with it. If they were to get a bunch of engineers riled up about the importance of math, then it very much succeeded. However, I think there could have been more done to point to a very scary mindset that is growing out there about the way math is both taught and used. Guesswork and computer simulations are replacing critical thinking and analysis, and person can only do this for so long before they get burned.

This article reminds me of the only TED talk that truly upset me. It was Conrad Wolfram talking about teaching students "real math" using computers which was really a thinly veiled advertisement for Mathematica: http://www.ted.com/talks/lang/en/conrad_wolfram_teaching_kids_real_math_with_computers.html

The question isn't if math is still relevant, the answer is a resounding yes. As the language of nature and physics, it's something that will always be relevant. The real question is how to adapt man's use of math to the 21st century and how to keep true mathematical reasoning while taking advantage of modern technology?

201232, 12:58:42

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Soori

Nirjhar Prakash
One needs to relate the mathematics with the physical picture. Mathematics without corelation will not be of much help. John is his example did exactly this, he could co-relate the missing pole which mathematics helped him find.

201232, 12:48:18

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Jonathan McGuire
"Programming is rigidly structured"

I've been writing software for more than 30 years and nothing could be further from the truth. You have to do certain highly structured things while your programming, but programming itself is highly interpretive. Most of the time, a given group of programmers will come up with a variety of solutions for even relatively simple tasks.

This is also the reason I disagree with the urge to treat programming as an engineering discipline. I've run hundred million dollar (plus) projects, I've been in small start-ups, I've done software architecture for Fortune 50 companies, and I've won one-liner magazine contests. I assure you that experience is dramatically more important than training.

201232, 9:26:48

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Dr. Graeme Gwilliam
I am disturbed that anyone should contemplate the demise of mathematics. How would the wonders of Maxwells's Equations be explaine in mere words, and when one considers the large variaty od languages that prevail in the world to-day, which language would be used. The point is, of course, that mathematics is a language, and in many ways is the language that separates the engineers and scientists of the world from our non-technical fellows. The benefit of mathematics is it gives discipline to the mind. If logic is accepted as falling within the boundaries of 'mathematics' where would we be without digital logic. All of those engineers and scientists who devote their days to computing would possibly be sweeping the streets or doing some other menial task which dulls the intelect and destroys the soul. I find the subject fascinating and would be delighted to debate this in a controlled forum.

201232, 8:19:30

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說讚的人

kais

Soori

Rami kanhouche
Interesting question for debate. Personally I have been faced to many problems at which there was no precise mathematical solution. In many situations numerical simulations was good to get better mathematical insights. Should we use Matlab or mathematical formulation? I say it should be a dialect for better understanding, control, and optimization.
Mathematics "weak" point is in its inherent generalism. It deals with abstract structure flowing in some space. When contextual modelization is required formulae become very difficult and near impossible. That is why, using maths, it is relatively easy to model fluid mechanics or atoms and very difficult to find an optimum airplane form. In conclusion I think we still needs maths to "put us" closest possible to the solution. Even when mathematics is not necessary the mathematical mind giving us a global understanding of a phenomena will remain crucial. And we need to put students to solve more maths exercises even if they are not going to actually use the given equations.

201232, 7:30:08

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Maurice Castro
Software packages encapsulate methods of doing things well but rarely address the question of when to do something. Statistical packages are particularly good examples of this phenomenon. A large number of common statistical tests require the input observations to be independent i.e. not correlated to each other to produce a valid result (If you are lucky the package mentions in its documentation these constraints). It is not uncommon to see people who aren't trained in the underlying maths of these tests ignore or not understand these constraints, and apply an inappropriate test. Packages can't really protect you from these types of errors as they require an in depth understanding of the experimental design - something that is abstracted away when you pass the data into a stats package.

201232, 6:50:35

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kais

Maurice Castro
Operating systems are filled with uses of mathematics - we use statistics to analyse performance, logic and proofs to validate models (most easily seen but not exclusive to computer security), and queuing theory all over the place. On top of calculus we have to add logic, symbolic and finite mathematics to even start covering the maths used in computer related disciplines.

201232, 6:38:29

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David Fernández Piña
Math will always be relevant, but knowing how to manually solve some tedious computations is not so relevant since we have calculators and computer algebra systems. Free and open source software like SpeedCrunch, Octave, Mathomatic, wxMaxima or SAGE makes this available to anybody.

201232, 6:26:29

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Tony
Pt 2....It's time to put computer control squarely under mankind's interests through taking on board that fashion isn't mankind's destiny and that once control is relinquished to "the devil"...you cannot get it back unless you control all sources of produciton.Speed has become our god and technocracy our church...there IS a better world and we who came through the immediate post war (11, not 111...that's still afoot!) well know it.

Finally, Maths is a mind maturing science with spin off into musical comprehension and architecture for example...things mankind can excel at with a slide rule and calculator, or a pencil and paper and a log-book (remeber those??) not necessarily capitulate to utter reliance on a computer.

201232, 5:38:49

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Tony
Pt 1There are many, for sure, who are happy not only to have computers answer all questions but to be controlled by them. Tragically such imbeciles might be cloned whereas at present they gravitate to subservience through one of several lazy minded methods. In the question of maths becoming irrelevant one might muse over what's reuired to service programming errors or aquuired defects and the effects of them before discovery...airplane crashes are a prime example but so also are the results of errors in military applications ...not only in "accidental" wipe-outs of families at dinner but in the Israeli expertise in making sure the 'early warning devices" they sell at vast profits don't work or can be controlled by Israel , designs usually stolen from the USA. The question we have to face is a simple one made difficult by the 'lemming" mentality encouraged by the Central bankers in their NWO need to keep people suppressed and depressed..."is science of this type to further relinquish mankind's dignity and essential self purpose or will it be made to stay as a tool and not a controller"? We already have the idiocy of children attending kindergarten being require to bring a calculator and computers being an essential tool for students...and even older people are expected to own access to the internet..".can you tell me XYZ" or "please tell me my account balance"...response "you can get that from the internet...go into html:/ etc..." Lunacy...capitulating our world to political aliens and ego-mania scientists who's fuutres depend on 'grants' from the government (taxpayer) or from industry. When computers go screwball and the sum of the squares on the other two sides = a(xpwr 2) +bx+ c we are no further advances and systems depending on it crash. Lets solve the world's peoples real problems as a priority and disable the sciences and programmes and the creations made to harness their "power" then used to mass murder, torture and control millions for the benefit of the very few. Gravity/magnetism is used to discover even more of the earths secrets so governments can behave irresponisbly, individuals accumulate hundred of billions power-brokers can accumulate stockpiles of production materials and energy at prices they dictate to us. In Australia we'd sell our mothers if the price were right...and we are so simple minded we sell off our assets as though there is no tomorrow, and to our commercial and philosophical enemies who specialise in crimes against humanity, eco-rape (CIA and the IMF/WB for example) and reducing wages.... BDS is not the only boycott this world needs to get off its wobble

201232, 5:36:47

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Ken Krechmer
Thanks Bob, good thought provoking article. I find the issue you raise to be related to the difference between how? math and why? math. The how? math fills most textbooks. That is, for a certain class of problems this text book explains how to solve them. It is this kind of information that is encapsulated in Mathlab so well. However, the why? problems require us to think. Why do a computer simulation or a mathematical analysis? Why a specific form of simulation or analysis? The why questions are often the ones where the big mistakes are made. Teaching math based on a specific form, e.g., differential equations and then learning how to solve problems that have been pre-selected to be applicable to differential analysis does not teach why? questions. So I think the issue is that different approaches to teaching mathematics are needed now that the how answers are more readily available.

201232, 4:07:05

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William Boykin
Developments of both rigid structure and, evolving art form require organized thinking based upon historical information —all of which is benefit from mathematics and analysis.
Otherwise, garbage in - garbage out.

201232, 4:00:18

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John Grevious
A provocative article that generates interesting responses of the historical roles math plays in predictive science and solid engineering. It also hints at the growing use of "black-box" trial and error engineering that is possible with new higher level tools. These are attractive for their "get-the-job-done" design capacity but raise risk of embarrassing or even tragic results. I cannot forget Roger Boisjoly’s explanation of how the proven O-ring joint seal of the successful Titan rocket was picked based on it’s record by Morten-Thiolkol and scaled up for the solid rocket booster concept. Had the engineers modeled the required tolerance limits with proper math (or checked assumptions as good math practices dictate) they would have seen the design cross a +-0 tolerance point as the diameter was expanded. Roger would have been spared his heroic efforts to stop the launch at the improbable 11th hour based on statistical (mathematical) arguments to an audience more inclined to believe anecdotal evidence of past launch success.

It is not just avoiding failure, math can reveal solutions not apparent in I/O simulation methods. I began my career as a technician but after engineering school in the 80’s I immediately applied a mathematical approach (-as I understood engineers were expected to do) to the design of a digitally programmable PPL for a computer based demodulator to eliminate the short comings of typical integrated PPL IC circuits. After significant time with equations I finally breadboarded the design and checked the output at the node commonly used in PLL circuits. It came up heavily overdamped. I almost accepted my attempt as a failure except that the closed form equation gave me something to study and it revealed that I was missing a pole cancellation by not tapping off a node in the feedback path. I returned to the lab and moved the probe to find the ideal response I was looking for. Saved by the math.
(PS: When Goggling for the spelling of Roger’s last name I discovered this. “Boisjoly, 73, died of cancer Jan. 6 in Nephi, Utah, though news of his passing was known only in the southwest Utah community where he retired.” Los Angeles Times.) An engineer’s hero.)

201232, 3:54:21

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說讚的人

Josh Romero (IEEE Spectrum editor)

Michael Hagedorn
I already see the impact of the de-emphasis of mathematics in engineering. Without an understanding of mathematics tools like Matlab, Maple, Mathematica, etc. are useless. Software tools cannot, by themselves, cannot perform tasks such as: develop new algorithms, calculate design requirements for specified performance, or calculate performance limits. (There is also the question of understanding design failures.) I am surprised at the number of software and computer engineers who don't know how to calculate the number of digits required when switching number bases.

201232, 3:51:00

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Richard
Um... But doesn't someone have to understand maths to write the Matlab functions we're using? What a bizarre article.

201232, 3:36:38

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Jeff Richard
If math is not needed, then how does an enigneer or scientist communicate results and ideas?

Math is the language of science and engineering.

201232, 3:05:20

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Enrique Aviles
Is math still relevant? It is if society wants to keep making new discoveries and advancements. We would not be having this conversation on a computer connected to the web if 20th century researchers thought math was irrelevant.

201232, 3:05:09

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Jerry Brown
No way! Mathematics is at the very core of our understanding of nature. Tools like Maple and Matlab may improve our efficiency by, for example, eliminating the need for a table of integrals. But, they are no substitute for understanding the fundamental concepts of mathematics.

201232, 3:03:15

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Miron Cristea
Mathematics helped me to solve a problem unsoved for more than 50 years, and discover a new Physics equation along with that! Or... put your computers at work, but no new Physics equation will result. See my point? For details, see my site http://arh.pub.ro/mcristea

201232, 2:51:46

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George McAlpine
Most practicing engineers don't know this but about 50% of those graduating from engineering schools change professions after graduation (law, medicine, insurance, etc.) In my case (BSEE '57, MSEE'61, PhD(EE) '67), my foolish 20-year attempt at being an entrepreneur required delving into civil engineering. My EE training/education/mindset gave me a significant advantage over my CE colleagues/competitors because of the extensive mathematical requirements of my chosen EE field of Statistical Communications Theory. Although most of CE design in the area of my commercial interest only required fairly simple mathematics, partial differential equations are used extensively in the theory of elastic buckling (geometric instability of rings & tubes/pipes) and other advanced areas of engineering mechanics. And these areas were of commercial interest. My EE/math background also allowed me to perform some fairly complex thermal/heat transfer calculations in frequently encountered problems in the structural installation of my firm's product.
The above is a single example of the obvious benefits of our engineering education including emphasis on fundamental knowledge in math & science. Thanks again to Bob Lucky for another well written and thought provoking article.

201232, 2:43:12

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Luis Fonseca
I think the biggest mistake in this kind of reflection is not that it reduces the importance of mathematics to the ability to make calculations. The main damage comes from the fact that it seems to support a big trend of our days to think that it is ok to give an opinion or to decide about things without having to understand how they work.
One of the main benefits of a mathematical education comes from the ability to formulate a model of a phenomenon and to analyze its properties in order to try to predict its behavior under any given circumstance. This applies to technical as well as social fields.
The use of a mathematical model doesn’t guarantee the best outcome from a decision, but it is certainly better than having people in all kind of positions, in both government and private sectors, making decisions without a proper analysis and, worst, thinking that is not necessary to make one.

201232, 2:40:13

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jl77
Mathematics classes do not teach how to build models, instead they provide technical tools to answer questions about models generally build by physicists or engineers. Of course, these physicists and engineers need to be aware of the mathematical tools available in order to build useful models. A danger of putting too much emphasis on mathematics in engineering however is that these useful but often limited models built by engineers with a good understanding of the physics are later on used as ground truth in legions of absurdly mathematical papers and PhD thesis, where proving theorems is more important than solving real problems. Look at many academics in fields like finance, system theory, or theoretical computer science.

201232, 3:07:48

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Titi Trandafir
At the beginning of the last century they were talking about the end of ...physics with the same (rhetoric ?) attitude or platitude.I don't see the end of math until I see a set of equations describing the human cells behavior and interactions . All 100 trillion of them. them.!

201232, 2:38:18

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Ken Sherman
An engineer without math skills is like a carpenter without a hammer or saw. Imagine trying to understand maxwells equations without knowledge of vector analysis, or electric circuits without understanding differential equations and laplace transforms. I once met a tech who thought he had invented a way to put virtually unlimited data thru a modem. I asked how close he had come to Shannon's limit, but he had never heard of it and furthermore stated that it didn't apply to him because he didn't know about it. I could go on, but you get the point.

201232, 2:31:44

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Adrian Nastase
I cannot believe such an article appears in IEEE Spectrum. Math is the foundation of any engineering discipline. How can an engineer design anything without math? How can somebody believe that a person, without formal training in math, can go in front of the computer, start a program, and here is the design.

What the proponents of "math is irrelevant" (and seemingly the author of this article) lack to understand is that Matlab is just a tool that helps us calculate faster and with less mistakes. The tool, like any other, saves us time. Just give specialized software to somebody untrained in math and watch what he can do.

201232, 2:26:53

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Marco
One still needs to know maths, to understand how good an engineering thought can be.

201232, 2:21:14

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Tony Varghese
Asking whether any person uses calculus on the job is a superficial way of assessing the utility of a mathematical education.

Very few professions use algebra, trigonometry, and calculus directly. What mathematics give us are two very powerful ways of thinking that are not consistently taught anywhere else: inductive reasoning and deductive reasoning. Math also sharpens our minds so that we can analyze and understand the core of any problem.

201232, 1:51:09

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Engineering Prof.
Agree with most of the posts...
Don Knuth's texts on the art of programming are a testament to the fact that the queen of sciences resides at the heart of this "art".

201232, 2:00:18

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Tom
There isn't much evidence that practice in a particular subject sharpens the mind such that it is better adept at solving problems in other areas. This type of general mind sharpening is known as the doctrine of formal discipline. Thorndike (1906) examined this doctrine and found that practice in one subject area did little to improve performance in another subject area. People constantly make reference to this idea of general improvement of thinking, but there is scant evidence that the phenomenon actually exists.

Detterman (1993) reviewed a number of transfer studies and found, even when the subject areas are closely related and hints are given to encourage study participants of the possibility of transferring knowledge from difference subject areas, the participants failed to solve the problems in the latter subject area.


Thorndike, E. (1906) Principles of Teaching. Syracuse, NY: The Mason-Henry Press.

Detterman, D.K. (1993). The case for the prosecution: Transfer as an epiphenomenon. In D.K. Detterman, R.J. Sternberg (Eds.), Transfer on trial: Intelligence, cognition, and instruction (pp. 1-24). Westport, CT, US: Ablex Publishing.

201232, 2:42:36

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Giovanni Franco Crosta
This article was posted simply because we (still) enjoy freedom of speech and expression.
And people are allowed to express nonsense.
Period.

201232, 1:48:16

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SergioPi
I can't believe this. Is the author aware of the existence of the GUAPS, the Great Unsolved Problems of Software Engineering? They include, among many others, refactoring, systems integration, parallel programming, image recognition, the semantic web. These problems are "easy for humans but very difficult for computers" to solve. Several of them are said to exceed the mental capacity of humans, even with the help of the "powerful" tools that SE's develop. Who or what is going to solve these problems? If the tools are so powerful, how come humans are still needed?

201232, 1:46:21

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SergioPi
Oops! That's the Great Unsolved Automation Problems of Software Engineering.

201232, 5:29:22

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kais
this article, frankly, is more absurd than a Yahoo Snooki "news" article. Software Engineer is a term that is as broad as the software itself (obviously). Some engineers write GUI code mainly, some right code that implements mathematical algorithms for signal processing, image processing, gene sequencing... etc., some right device to device communication... the point is that ALL software engineers need good mathematical skills to varying degrees. Algorithm engineers obviously need a lot; I finished my MSc in EE 12 years ago, I work in image processing, and I constantly find myself needing to learn new Math topics: advanced linear algebra, numerical linear algebra, functional analysis, inverse problem theory and on and on.... I am a "Software Engineer". GUI people need a lot less.. people who right code that move machine parts simultaneously need a good understanding of coordinate systems and transformations etc. to make all work together. Math is simply the language of nature (this really not a grandiose statement or an overstatement), every engineer needs it, but at different levels of complexity depending on what they do.

201232, 1:45:37

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R
Why do you believe that designing a good operating system does not require mathematics?

It perhaps doesn't require the same calculus needed to describe electric circuits but that is an *extremely* restrictive view of what mathematics is. Indeed, there is a rich body of mathematical ideas associated with computing systems - just as there is a need for a mathematics that addresses social systems, in the absence of which one is just left with vague intuitions that can't be compared or prioritized.

201232, 1:32:08

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James Dalessio
I think this post and discussion are moot without a really good definition of what is meant by "math".

2012229, 8:17:30

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matthew krawczun
man did not invent mathematics anymore then man invented fire and mud. these are all simply things that existed long before us that we just found.

2012228, 11:24:17

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Ian Yorston
RT @walkingrandomly: Is math still relevant? http://t.co/Lq5jK3Yb - http://spectrum.ieee.org/at-work...

2012228, 1:52:17

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Rehab
Even from a software engineering perspective, a major way to validate software & get effectively assuring simulation results/analysis is to use mathematical modeling & verification methods. Math is still the key!

2012227, 6:29:34

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Lealand LaPoint II
Engineering is applied mathematics and applied science. If you don't understand either then you aren't an engineer. Anyone can sit at a computer and push buttons until the simulation finally works, but that isn't engineering at all. Math is still relevant and always will be, because it gives us a language to describe our systems. It is the language of engineering and the language of science as a whole. Once engineers stop learning mathematics and can no longer analyze their systems on their own, they are nothing more than technicians relying of instruments to tell them how something works. That will be a sad day in engineering.

2012226, 21:59:21

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Guest
Very well said!

201231, 0:57:25

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Yao Hong
One of the most fascinating things that classical mathematics can do is to prove a certain property of a system always hold provided that the assumptions are satisfied. This is something Matlab and Maple that can do yet. I do hope that day will come though. That would certainly advance engineering even further.

2012226, 11:33:26

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asdf
Math in software engineering is simply different; we don't use calculus as much as other disciplines because it's not as relevant to us as it is to other disciplines. However, from my understanding of other engineering fields, we draw more from statistics, probability and linear algebra. For example, in machine learning, support vector machines are an application of linear algebra and bayesian inference is a statistical technique.

And by the way, your comment form is horribly broken. I had to change browsers to post this comment.

2012225, 9:07:18

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Fahad
I thought math in Engineering is much more than just calculation. Mathematical expressions convey the relationships and patterns that engineers exploit to build their devices. Without mathematical language, tool, and methods engineering would be nothing more than day dreaming.

2012225, 5:21:02

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Rehab

 

 



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