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**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.

2012年3月26日, 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.

2012年3月24日, 11:10:02

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ALIJUMAAH

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

2012年3月17日, 2:20:09

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說讚的人

訪客

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.

2012年3月16日, 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.

2012年3月13日, 3:50:03

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說讚的人

訪客

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.

2012年3月12日, 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.

2012年3月7日, 13:20:36

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說讚的人

訪客

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.

2012年3月7日, 12:36:17

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說讚的人

訪客

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.

2012年3月6日, 21:14:41

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說讚的人

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.

2012年3月6日, 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

2012年3月6日, 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.

2012年3月5日, 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.

2012年3月5日, 1:46:44

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說讚的人

訪客

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?

2012年3月4日, 15:40:18

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說讚的人

訪客

Steve Bouton

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

2012年3月4日, 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.

2012年3月4日, 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.

2012年3月3日, 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.

2012年3月3日, 0:33:34

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說讚的人

3 位訪客

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 :)

2012年3月2日, 22:32:59

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說讚的人

Gordon Munsche

訪客

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

2012年3月2日, 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.

2012年3月3日, 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.

2012年3月3日, 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.

2012年3月3日, 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.

2012年3月6日, 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.

2012年3月2日, 16:20:54

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說讚的人

5 位訪客

Joe Citizen

Your last paragraph is poetry! Copyright that.

2012年3月7日, 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...

2012年3月2日, 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?

2012年3月2日, 12:58:42

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說讚的人

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.

2012年3月2日, 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.

2012年3月2日, 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.

2012年3月2日, 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.

2012年3月2日, 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.

2012年3月2日, 6:50:35

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說讚的人

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.

2012年3月2日, 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.

2012年3月2日, 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.

2012年3月2日, 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

2012年3月2日, 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.

2012年3月2日, 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.

2012年3月2日, 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.)

2012年3月2日, 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.

2012年3月2日, 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.

2012年3月2日, 3:36:38

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訪客

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.

2012年3月2日, 3:05:20

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訪客

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.

2012年3月2日, 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.

2012年3月2日, 3:03:15

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說讚的人

訪客

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

2012年3月2日, 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.

2012年3月2日, 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.

2012年3月2日, 2:40:13

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說讚的人

2 位訪客

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.

2012年3月2日, 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.!

2012年3月2日, 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.

2012年3月2日, 2:31:44

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說讚的人

訪客

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.

2012年3月2日, 2:26:53

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說讚的人

2 位訪客

Marco

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

2012年3月2日, 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.

2012年3月2日, 1:51:09

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說讚的人

訪客

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".

2012年3月2日, 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.

2012年3月2日, 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.

2012年3月2日, 1:48:16

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說讚的人

3 位訪客

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?

2012年3月2日, 1:46:21

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說讚的人

訪客

SergioPi

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

2012年3月2日, 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.

2012年3月2日, 1:45:37

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說讚的人

訪客

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.

2012年3月2日, 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".

2012年2月29日, 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.

2012年2月28日, 11:24:17

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說讚的人

訪客

Ian Yorston

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

2012年2月28日, 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!

2012年2月27日, 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.

2012年2月26日, 21:59:21

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說讚的人

4 位訪客

Guest

Very well said!

2012年3月1日, 0:57:25

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訪客

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.

2012年2月26日, 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.

2012年2月25日, 9:07:18

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說讚的人

2 位訪客

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.

2012年2月25日, 5:21:02

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說讚的人

Rehab

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