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Let me think of a counter-example: Ramanujan comes to mind.

http://www-groups.dcs.st-and.ac.uk/~history/Mathem aticians/Aristarchus.html

laugh, its funny.

It might make some wonder what really these rocket scientists know, behind their rocket science math, used to frighten laymen ;)

Any explanations?

• R, including several add-on packages (such as tseries, RODBC, coda, mcmcpack, gtkdevice, rgtk, rquantlib, qtl, dbi, rmysql), out-of-the box support for the powerful ESS modes for XEmacs as well as the Ggobi visualisation program;
• A complete teTeX, TeX, and LaTeX setup for scientific publishing, along with TeXmacs and LyX for wysiwyg editing;
• Perl and Python with loads of add-ons, plus ruby, tcl, Lua, and Scientific and Numeric Python;
• The Emacs and Vim editors, as well as Gnumeric, kate, Koffice, jed, joe, nedit and zile;
• Octave, with add-on packages octave-forge, octave-sp, octave-epstk, and matwrap;
• Computer-algebra systems Maxima, Pari/GP, GAP, GiNaC and YaCaS;
• the QuantLib quantitative finance library including its Python interface;
• GSL, the Gnu Scientific Library (GSL) including example binaries;
• The GNU compiler suite comprising gcc, g77, g++ compilers;
• the OpenDX, Plotmtv, and Mayavi data visualisation systems;
• it includes apcalc,aribas,autoclass,

I suppose it really depends on how granular you're being with your definition of trivia. It also somewhat depends on your direciton of study, as trivia to an EE could well be holy writ to an arts major.

I guess I segregate factoids into trivia categories depending on how relevant they are. Of course something I call trivia is probably relevant to someone, but --well, for example, knowing how to do a laplace transform on a circuit is something I do, and highly technical, but knowing when Laplace first published a paper (1771) isn't really useful in any sort of context without more information--trivia.

I hope that made some sense.

You can analyze puzzles like this using GAP. Here is an example using Rubik's cube(Google cache since the site seems down to be down at the moment.)

Mmm. While Ada was cool and described how Babbage's Analytical Engine could be programmed, she never actually programmed a computer.

Every piece I've read by Schneier over the past few years hammers on the same theme: software is fallible, no system ever works that fails to retain a phalanx of expensive security wonks. He's more right than wrong, but he sometimes delivers injustice to the details.

Let's think back a ways, a long ways to the original tabulating machine.

Counting votes is not rocket science. If ever there was a category of software that could be substantially more correct rather than less correct, it would have to counting. If, after 100 years and trillions of dollars, we still can't build a machine that counts correctly, let's fold up shop and go home.

Now, if the source code remains concealed, it certainly becomes much easier to build a machine that does not count correctly, but that's not a software failure and let's not blame that on an inherent imperfection of software.

No

See the Architas (428 BC) mechanical bird, or the Antikyithera (87 BC)orbit calculator.

Babbage's analytical engine was entirely mechanical, and was designed well before the invention of any device providing a consistant flow of electrical energy. However it was never actually built until a hundred years after his death, as engireeing wasn't of a high enough standard in those days to build the parts he required.

Ada Lovelace described the methods for programming the analytical engine and wrote a program for it (ie literally wrote it). da Vinci didn't actually write a program at all, he just designed a working robot.

More on Ada Lovelace, (daughter of Lord Byron)

If you have the chance to lobby to members of your government to stop software patents before they are even started in the first place, please do so. Let your political representatives know how you feel on this issue, and read up on the damage that it is doing to the software industry in the USA. While not "THE" issue that is destroying software developers, it certainly is a major factor and IMHO a major reason to why I have personally had difficulty in the past couple of years trying to find work. I fear that I need a Juris Doctorate just to be able to program effectively. that should not be the case.

I also think 20 years is too long for a software copyright. I mean, should the original software developed for the ENIAC in 1947 by Adm. Grace Hooper still be under copyright in 2067? By the Bern Convention and U.S. Copyright law that is currently the case. The earliest that any computer software will enter the public domain due to copyright expiration will be 2022, unless you count the software developed by Ada Lovelace. And even that could still be questioned.

Although I believe there are some books written in the 1970's (and referred to in the parent application) that refer to the fundamentals of computer graphics. I would bet money that they detail the matrix functions in one of those books. BTW, when did Microprose first start on FlightSim 1.0? Let alone any cad program used by Boeing or some other aviation/military firm.

From the Google answers:

So, to the shortcut. It turns out when all the dust settles that the multiplication among rotations is isomorphic to multiplication of unit quaternions. Quaternions, in case you've not seen them before, are a kind of four-dimensional generalization of complex numbers. They were "invented" by William Hamilton in 1843:

Dr. John Wilkins, the Jacobean scientist in question, was quite an interesting chap really.

For example, with his book, A Discourse concerning a New Planet, he tried to popularise the view of the universe according to Copernicus, Kepler and Galileo. He attempted to explain in the book that the Moon is not purely a shiny, cut out disc but rather it is a world with a landscape like that of the Earth.

Fairly radical stuff for the time, though admittedly he did publish the book annonymously.

For more info, try this or this

Certain aspects of calculus were developed two centuries prior to Newton in India by Madhava of Sangamagrama. This seems to be widely accepted now. A few links to Madhava and other Keralese mathematicians are also present here.

Certain aspects of calculus were developed two centuries prior to Newton in India by Madhava of Sangamagrama. This seems to be widely accepted now. A few links to Madhava and other Keralese mathematicians are also present here.

Certain aspects of calculus were developed two centuries prior to Newton in India by Madhava of Sangamagrama. This seems to be widely accepted now. A few links to Madhava and other Keralese mathematicians are also present here.

The Pope is reminded that the Church cannot have another "Galileo incident," science's first "martyr." Galileo presented his correct heliocentric views to the Church, and the Church clung onto dogmatic tradition -- incorrect scientific views.

Also note, it was Copernicus's heliocentric view that Galileo was presenting. Copernicus was an Orthodox Monk - so the Orthodox church at the time did not have a problem with the 'Heliocentric' view of the Universe. It was Catholic Doctrine and not the Bible which stated that the sun went around the Earth.

Galileo refered to himself as being a Copernican when stating his belief. The Catholic Churches beliefs at the time, were not based on the Bible, but upon the teachings of Aristole and Ptolomy. All part of the 'Renaisance' as the 're-birth' of knowledge once lost was re-found by the Western-world.

Another thing to note, was that the writing which Galileo used to present his view was in the form of two people having a discussion. He made the mistake of using something the Pope had said to him in a discussion as part of the arguement of the 'Sun revolves around the Earth' view. The character making the arguement was given an name equivalent of 'Ignoramus'. Something the Pope and Catholic Church at the time considered rather insulting. {And wouldn't we all if our words were put in the mouth of an ignoramus and used against us.}

Even Fundamentalism is a relatively new thing to the Church.

I am glad you posted what you did, it was nice to see this expressed in this forum. It is something I have a hard time getting across to both athiests and Christians alike (and anyone else). As I always try to tell them, Science is about HOW the earth was made, the Bible is about WHO made the earth. Both are answering two totally different questions ... those who look for the answer to the wrong question in the wrong place you will always get wrong opinions.

Those who choose to believe or not believe the bibles teachings are free to do so.

Nani mo hoshii mono ga nai

I hope Europe and America can do the same a few more years down the line to leap forward on the backs of Indian technology developed...

Err.. I think we did that already..

The number system we use today originated 4000 years ago... in India. http://www.scit.wlv.ac.uk/university/scit/modules/ mm2217/han.htm

And while we're at it, important developments in mathematics were made 1000 years ago in Baghdad, in what was then Babylon. http://www-gap.dcs.st-and.ac.uk/~history/HistTopic s/Arabic_mathematics.html. Mind you, all the looting of museums and important sites which has happened since Iraq was invaded may mean a lot evidence for that has been lost.

Abel's proof, and related proofs by Galois, have stood the test of time for 200 years. It would throw most of abstract algebra and modern mathematics on its head if true.

<URL:http://www-gap.dcs.st-and.ac.uk/~history/Hist Topics/Zero.html>

<URL:http://www-gap.dcs.st-and.ac.uk/~history/Hist Topics/Zero.html>

+5 and no one bothered to check.

The exceptions were the mathematicians who were involved in recording astronomical data. Here we find the first use of the symbol which we recognise today as the notation for zero, for Greek astronomers began to use the symbol O

History of zero

There is the Fields Medal.

In the same way that Europeans in the middle ages could deduce that the earth is round from seeing ships sink in the horizon

The fact that the earth is round was proven around 200 bc by a greek scientist, and it had nothing to do with seeing ships sink over the horizon. Even before that, everyone was pretty sure it was round.

If only I could have have gotten 271828 as my UID.

Nitpick: it's Karl Schwarzschild

The NAME, I say I say the NAME, son is Christiaan Huygens. Associate of the Protestant Defender and natural philosopher.

Where are you getting your infromation?

Gallileo BROKE THE LAW asserting the world isn't flat.

No! Look!

Born 1564... after Columbus, and even before Columbus, we knew the world was round.
If you're going to make a shitty argument, at least make your shitty claims seem plausible.

And how did this get modded insightful?

The Lagrange points, at least the first two, are about 1.5E6 km from us. These are named after Joseph-Louis Lagrange. He is a pretty fameous mathematician, though by now I suppose the bordello in LaGrange is pretty fameous too.

Do we pronounce "2" as "two", as what the Arabic word for "two" looks like, as "one zero", or as the Roman "II"? Rather than Arabic, perhaps we should have the written word in Babylonian, or what preceded the Arabic: the Brahmi "=" or Nagari "2".

Here is another interesting link:

http://www-gap.dcs.st-and.ac.uk/~history/Mathemati cians/Turing.html

Not only did he (amongst others) crack the German Luftwaffe enigma codes, but those of the German navy, which were far more difficult. His work was pioneering on several fronts. Surely the world is a far better place for his having lived in it.

i know it's OT but you might like this site about various beautiful curves. regards, my dear xYoni69x

a better article:

http://www-gap.dcs.st-and.ac.uk/~history/HistTopic s/Prime_numbers.html

Greek astronomers had figured out that the Earth was round several centuries before Cladius

Eratosthenes for example is often credited with measuring the earth with a stick, a pretty accurate measure of it's circumference. For him to do this B.C. he would have already got the idea the earth was a sphere earlier, or atleast want to use what he knew about geometry to prove the theory.

Now there were much in the way of educated Greeks, in fact I believe one of the earlier versions of the christian bibles was in Greek. I believe also, at least according to my catholic upbringing, it was translated into Latin simply because a hell of alot more people were literate in Latin. But whether Greek or Latin... it was seen by comon folk that someone who knew either or was smart, or at least literate. I imagine this is why it sounds better to say intelligent a word with Latin roots then smart which likely has Germanic orgins.

To be honest, I've been kind of disappointed by the lack of response for this topic. In fact, I'm rather upset at some of the snide remarks. I was a horrible student in high school. I had little skill in math. I hate to see someone give up their future profession over a few math classes. For the sake of disclosure, this post is coming from a guy whose now finishing his math degree. You're probably thinking "way to go with your strengths". However, you'd probably be right.

To give you an idea of where I'm coming from, I'm the guy who spent all of discrete math complaining about the lack of rigor. I'm the guy who yells "CHURCH'S THESIS" at the first sign of any "what is programming debate". I hate programming, but I've been doing it for years. In fact, there's a pretty good chance I'll end up being that egghead CS prof, who's really just an unemployed logician. I'll probably torture my students with abstract mathematics and unnecessary proofs.

I walked out of high school with a 2.5 GPA. I hated school. I remember telling my high school math teacher, if she even deserves that title, that it would be a cold day in hell before I'd ever study math. [To give you an idea of how bad this teacher was; she didn't understand the concept of base ANYTHING arithmetic. Certainly she used base 10, but she really had no idea what she was doing.] I figured I'd go to art school. However, being poor, I attended a local college instead.

Being the son of a math professor, who surprisingly never encouraged my interest in mathematics, upon entrance to college I was immediately thrust into a multi-variate calculus course. My father had a reputation for being a mathematical wiz. I guess they figured that this would have rubbed-off on me. In one of my ever-rare moments of reason, I decided to enroll in Calculus I instead. This was good, because my calculus-free high school math background was vastly inadequate.

During the third week of class, we had our first test [this was done to weed out people before the last day of withdraws]. I got a 30. You could have doubled my score and I still wouldn't have passed. Only one student got a decent grade and that was a B. Surprisingly, I actually did the homework for my calculus class. To this day, I still don't know why? I finished the semester with a B. I got an A for second semester calculus. Of course, I still didn't have the vaguest understanding of analysis, but neither does anyone else at this stage [okay, maybe this guy does....].

While taking a physics class, I wanted to understand the concept of energy. The definitions in the book were severely lacking [we used Resnick and Halliday]. So, I ventured to the library in search for an answer. I ran across an odd collection of books. It was the Feynman Lectures on Physics. I immediately knew these books was different. I was transfixed. Hours had passed and the sun had set. I didn't realize long I sat there reading the first few chapters. He made explanations accessible. He used Dennis the Menace to describe the conservation of energy. Feynman made sense. Thanks to Mr. Feynman, I managed to get an A in physics as well.

I still had bad study habits, but I spent quite a bit of my free time writing code in the computer lab. Eventually I got a job working for the school, doing a little IT and a little programming. I picked up work in town. Eventually I left school during the dot-com boom to write code full time.

Somewhere, during that time, I began a serious self-study of mathematics and science. I attribute such auto-didacticism to a general dissatisfaction with philosophy and religion. It was tough going at first, but after a while, I got use to the rigor. Unfortunately, it had the side effect of making me a pedantic smart-ass. Sometimes, I'm not sure if that's all bad.

My point is that anyone can learn to do math. You may never become a professional mathematici

First - yes, the US must change to meet the new global economy. I support outsourcing, at the expense of my own salary and living conditions. I imagine my stance will change over time. Disclaimer - I'm not an economist, I'm current taking a macroeconomics class but it's really just a skim overview of economics.

And GDP numbers I bring up below are from the world bank Total GDP 2002 report.

The E.U.s GDP is approximately the same as the U.S. About $10 trillion if I recall.

6,648,492 million. About 1/5 of the world economy. Part of the reason, I suspect, for the US's huge GDP is the cultural acceptance of high personal debt, which I understand is not a cultural similarity to many nations in the EU, though it is slowly creeping in over there. Home ownership and low cost mortgages, federal bank insurance, tax credits on various debts, etc early on in the 20th century provided a fertile field for today's economy in the US.

China's GDP was around 6 trillion...it will eventually pass the U.S. and not in the so distant future.

To be pedantic, China's GDP is 1,266,052 Million. I agree that it eventually must pass the US GDP if 1) China remains one cohesive state and 2) Any societal/cultural/governing revolution is started, mediated, and controlled by the gov't. I don't think China can withstand any of those revolutions economically, despite state efforts to do so. Further the gov't must spend so much money training and keeping their citizens in line it may be difficult to sustain any temporary growth.

Its true the U.S. GDP is growing again but that is almost entirely due to very low interest rates and the massive fiscal stimulus the Federal government is injecting in to the economy...This deficit spending is leading to near term prosperity at great future risk.

Well, at least you agree that the current administration's plan is working, albiet extremely risky. When the depression struck the gov't tried all the 'normal' methods to get the economy going, and then a guy by the name of Keynes wrote several treatises on the subject of economics which effectively said that then current theories were no longer applicable to then current economies. The economy only did well when aggregate spending, private, busines, and public, was up. It is his model of the economy which we use. Therefore, when the economy is bad the gov't must increase its spending, and encourage private and business spending. Further, deficit is a tool to be used to increase spending. Whether the rich or poor should be the ones receiving the encouragement is up for debate.

Personally, I hope to see more foreign investment and outsourcing. I hope that I can personally stay ahead of the curve and make myself valuable as an employee, but in the end the relationship I have with an employer is a business relationship. If he can get a better deal on milk at KMart, then he might stop shopping at Kroger. If I don't step up to the challenge and make a better offer then I can't reasonably force them to choose me over a better/cheaper product. I think too many people are fairly prideful on this point - as if it were their right to be making more than 80% of the world's population at the expense of other employees and businesses.

Besides, as companies get burned by outsourcing, and others have great success many jobs will move back here and other jobs will leave. This cycle will find another equilibrium just as past outsourcing 'emergencies' (cloth mills, steel, cars, etc) did. It's just another decade in the global economy - nothing to see here, move along. If one really didn't agree with outsourcing, one would have to forego buying any products made elsewhere.

Our economy already depends too much on outsourcing of goods and services. The real shock will be when we're forced t

For your information the concept of a numerical zero originated in India

In a recent paper Alonzo Church[2] has introduced an idea of "effective calculability", which is equivalent to my "computability", but is very differently defined. Church also reaches similar conclusions about the Entscheidungsproblem.[3] The proof of equivalence between "computability" and "effective calculability" is outlined in an appendix to the present paper.

Actually, while Ada Lovelace saw the potential of Babbage's Analytical Engine, her inspiration for this was Joseph Jacquard's punch-card-progammable Jacquard loom. Jacquards invention was also later copied as Hollerith's computer punched cards.

The distinctive characteristic of the Analytical Engine, and that which has rendered it possible to endow mechanism with such extensive faculties as bid fair to make this engine the executive right-hand of abstract algebra, is the introduction into it of the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs. It is in this that the distinction between the two engines lies. Nothing of the sort exists in the Difference Engine. We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.

Lovelace on Jacquard

Jacquard loom

Jacquard loom output

Paul Adrien Maurice Dirac.

We have a library named after him here at Florida State University. Is this the same guy?

How many thousands of years did the Greeks believe that a God named Apollo flew his chariot (that big bright ball of flame in the sky)? Hell, back then, people didn't even know the earth was ROUND.

Not to nit-pick, but "people back then", or at least the educated portions of the Greek population, were aware that the earth was round, and had even estimated its circumference with reasonable accuracy, given the limitations of the instruments available at the time. Eratosthenes of Cyrene (historical info), third librarian at Alexandria, conducted this experiment, using nothing more than a stick and a working knowledge of geometry.

There's even an "Eratosthenes Experiment" website for schools/students interested in repeating this classic experiment and comparing their results with other participants.

... except that he plagiarized Dirac's works...

That statement is plain stupid. Dirac finished school in 1918. Einstein published the Special Relativity in 1905 and the General Relativity in 1915. Can you back up your statement?! Beside, it is well known that Dirac was a great admirer of General Relativity, considering the Einstein equations the most beautiful in physics. That is the reason Dirac chose GR as a research topic in 1923 as a young student in Cambridge ...

The Dirac generation might have had more success in Einstein's project in his old age to unify the fundamental forces in nature. Since Einstein grew up with only gravity and electromagnetism as the fundamental forces, Einstein naturally focused on these two. In modern physics, electromagnetism has been unified with the weak interaction and strong nuclear force, but the problem still remains how to make a theory to include gravity with these three other forces. So, one can hardly blame Einstein for failing where modern physic is still searching for answers.

Sometimes, I wonder if some people's dislike of geeks is just something that has been imposed on us by society. How many of us secretly admire them, but are too afraid to admit it to anyone? Does this perceived dislike end up giving more intelligent people a lower self-esteem, making them less sociable, and re-inforcing the stereotype? According to this article, a geek started a business as a prank, but ended up becoming the richest man in the world, but was later disqualified because people preferred stylish furniture.

In the days of old, geeks used to be considered most attractive. Perhaps being intelligent was a symbol of fertility, and to maximise your chances of passing on your genes, you tended to look for a more intelligent man. Now-a-days, people just want to get laid, so maybe they subconciously look for men who are un-fertile.

Magic/Myth/Religion are all ways to explain the world to those who can't bother to be interested in the actual truth.

In 1843 Kummer, realising that attempts to prove Fermat's Last Theorem broke down because the unique factorisation of integers did not extend to other rings of complex numbers, attempted to restore the uniqueness of factorisation by introducing 'ideal' numbers. Not only has his work been most fundamental in work relating to Fermat's Last Theorem, since all later work was based on it for many years, but the concept of an ideal allowed ring theory, and much of abstract algebra, to develop.

This is not the only example of interesting math created by Fermat's Last Theorem, though it is certainly the most important.

Now, since Fermat's Last Theorem is solved, there is no reason to deal with all that anymore. So, all the interesting approaches to it that would've ultimately failed but created new things to study have also fallen by the wayside. Certainly, they might still be discovered, but it could take more time. Thus, he set math back a few decades.

OK, so the parent post was kind of silly, but it gives me a chance to mention Imre Lakatos, my favorite mathematical philosopher. (Yes, I have a favorite favorite mathematical philosopher. Don't you?)

He wrote a marvelous little book called Proofs and Refutations -- here's a very brief bit of summary and context -- which present a very interesting very of the process of mathematical discovery: instead of accumulating an ever-increasing series of perfect truths, he argues, mathematicians are constantly shifting their perceptions of what is true, because they're constantly shifting the very definitions of the things they're writing the proofs about. (This happened in a major way with calculus during the 19th century, for example, when limits, derivatives and integrals were redefined more formally, giving birth to the field of analysis.)

The book is a lot of fun, and actually not such a hard read. It takes place in an imaginary classroom, where the students and the professor, having just proved a simple little theorem about polyhedra, start coming up with counterexamples by "stretching" their notion of what a polyhedron is. (Should a cylinder be a polyhedron? Why not? What about a box with a box-shaped hole on the inside? etc.)

Through their arguments, they end up sharpening the definition of "polyhedron", eventually replacing their naive notion with something clearer and more formalized through a process of proofs and refutations.

So, Stan Wagon challenges our definition of "wheel" with an apparent counterexample: Does the bike have no wheels? Or are wheels not round? We might propose sharpening the definition of "wheel" to account for the new counterexample:

A wheel is a solid object designed to rotate about an axle, with its perimeter in constant contact with some other surface.

(Make a ridiculous post, get a ridiculous reply!)

Excel as a screen saver

I got the spelling wrong, that's: Zuse

Here's a general info link:
http://www-gap.dcs.st-and.ac.uk/~history/Mathemati cians/Zuse.html

He invented a mechanical computing machine that I think is most like what we think of today as a computer. It was programmable, digital, and stored data on a tape. It had memory similar to RAM. It didn't become famous because he did his work in Germany during the WW2 period. Others were independantly working on similar projects in Europe and America, which is why we tend to think of them first.

To my knowledge Babbage started working on theory prior to Zuse's first computer, the Z1, was completed. But Zuse had independantly created his own theory and language before Babbage. Furthermore, I don't think Babbage ever made a working Analytical Engine, whereas Zuse made the Z1, Z2, and Z3.

I could look up more if you're interested.

If I've gotten anything wrong, feel free to point it out.

The Abel prize is introduced as a sort of "Nobel Prize of math" where people are rewarded for results and achievements that have shown themselves to be of lasting value in the field. Alfred Nobel did not want there to be a Nobel Prize in math, since he himself saw little scientific value of math! The most prestigious prize in math before the Abel came into being is the Fields medal, but this prize is only given to younger mathematicians (belove the age of 40) that has made break-through results and also show promise for the future. The Fields medal is handed out every 4 years while the Abel will be handed out every year (first prize was handed out last year).

Must have been ironic for Abel if he were to know that such a huge money prize is to be given out in his name, when his whole life he had to live in poverty and fight to get time and money to do his scientific work. The irony of Abel's life is also that Abel himself finally got a professorship in Berlin but too late; the letter was sent to him two days after his death.