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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.

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

Remember that Pluto was discovered, because some anomalies were detected in Uranus and Neptune's orbit. I think the official discovery was made once they had some photographs of a moving body over the starfield.

Gravitational influence made W. Clyde Tombaugh aim his camera towards the right direction. He already knew where to search.

It such a small planet like pluto can modify in a measurable way, the orbits of two giant planets, just imagine what a Jupiter-sized planet could do.

.... was the fate of Shannon. He is the father/creator of information theory which he shared with the world in a brilliant paper. He was afflicted by Alzheimer's disease, and he spent his last few years in a Massachusetts nursing home.

Aberations aside, its always cool to se new technology emerge in the field of visual optics. The field of optical science is realy realy old and still there are many more things to be discovered.

actually, Fermat's Last Theorem was proved. So really, the mystery of why IE still sucks so much has no rival in the modern world.

I do not think that word means what you think it means.

Over the past five years there's been a major research effort looking at primate cultures mainly under the guidance of Cristophe Boesch (Chimps - Pan troglodytes spp) and Carole van Schaik (Orang-utans - Pongo pygmaeus), and even Monkeys (the village idiots of the primate family) have been shown to have culture traits.

Anyway, a great webpage on this from Boesch's team Chimpanzee Culture

See also -
Whiten et al. Nature, 399:682-685
van Schaik et al. (2003). Orangutan cultures and the evolution of material culture. Science 299:102-105.
Perry & Manson (2003). Traditions in Monkeys. Evolutionary Anthropology 12:71-81

Oh, and it's not only primates - Fish biologists have also jumped on board -
Bshary et al (2002). Fish cognition: a primate's eye view. Animal Cognition 5:1-13

which shows that fish can do all sorts of massively complex social behaviors - e.g. predator avoidance and something which is very cool, inter-specific (ie: different species co-operating) co-operative hunting. For example: Moray eels (Gymnothorax javanicus) and Red sea coral groupers (Plectropomus pessuliferus). The Morays sneak through holes whilst groupers wait to catch escaping fish - they actually 'go hunting together' and signal each other by shaking their bodies.

Oh, and let's not forget the bird-people:
Corvus Moneduloides

Hunt & Gray (2003). Diversification and cumulative evolution in New Caledonian crow tool manufacture. Proceedings of the Royal Society of London, Series B, Biological Sciences.

Lefebvre et al (2002). Tools and Brains in Birds. Behaviour, 139, 939-973.

ph rocked :-) I used it quite a bit on the St Andrews university servers up until the end of 2002. looks like it's being phased out now though.

The fundamental question is this: is, or isn't, mathematics an extension of logic? A smart man named Frege (read about him here) said, yes, it is. He showed a way to connect formal logic with set theory, which is the basis for mathematics as we know it.

There was only one problem: Russell's Paradox. Bertrand Russell showed that, using Frege's axioms that defined set theory, we have a contradiction - Russell's Paradox. And as any student of logic knows, a contradiction can be used to prove anything at all, which means that mathematics as Frege defined it was not viable.

To make a very long and very interesting story short, Russell (with Alfred Whitehead) attempted to create a foundation for mathematics that would not give rise to Russell's paradox - the Principia Mathematica. And everyone thought the world was cool.

Then, in the 1930s, Kurt Godel came along and smashed a hole in Russell's approach by showing that, given a sufficiently powerful formal system, one will always find unprovable truths and irrefutible falsehoods. So mathematics was, by that line of reasoning, incomplete.

This leaves the door open to a variety of critiques, the most relevant of which is that it is automatically not universal. After all, how could it be - there are things missing! We can't prove everything that is true, and we can't disprove everything that is false!

Godel's argument tells us that we are unable to describe the universal laws of nature using non-universal and incomplete mathematics. That dosen't make mathematics useless - it just places a limit on what we can or cannot do. For instance, we cannot use deductive mathematics to describe the laws of nature in their entirety, because we know that any effort to be complete is doomed to failure - by Godel's theorems.

Also, there are some specific areas of mathematics that lead to direct examples of non-universal, but nonetheless consistent interpertations of nature. Take, for instance, Euclidean and differential geometry. Euclidean geometry is the geometry of flat planes, whereas differential geometry describes abstract mathematical notions. It was once thought that Euclidean geometry is "sufficient", and that it is the simplest way of representing spacial relationships. However, as it turns out, differential geometry is actually much more simpler when it comes to dealing with, say, the theory of relativity - even though it is not intuitively connected to our perception of the universe.

So in short, we have two different "geometries", each of which can, supposedly, explain spacial representation. Both are valid, but one is much more useful. Neither is universal. And yet, there is no contradiction.

I don't know about anyone else, but I think this stuff is interesting.

The fundamental question is this: is, or isn't, mathematics an extension of logic? A smart man named Frege (read about him here) said, yes, it is. He showed a way to connect formal logic with set theory, which is the basis for mathematics as we know it.

There was only one problem: Russell's Paradox. Bertrand Russell showed that, using Frege's axioms that defined set theory, we have a contradiction - Russell's Paradox. And as any student of logic knows, a contradiction can be used to prove anything at all, which means that mathematics as Frege defined it was not viable.

To make a very long and very interesting story short, Russell (with Alfred Whitehead) attempted to create a foundation for mathematics that would not give rise to Russell's paradox - the Principia Mathematica. And everyone thought the world was cool.

Then, in the 1930s, Kurt Godel came along and smashed a hole in Russell's approach by showing that, given a sufficiently powerful formal system, one will always find unprovable truths and irrefutible falsehoods. So mathematics was, by that line of reasoning, incomplete.

This leaves the door open to a variety of critiques, the most relevant of which is that it is automatically not universal. After all, how could it be - there are things missing! We can't prove everything that is true, and we can't disprove everything that is false!

Godel's argument tells us that we are unable to describe the universal laws of nature using non-universal and incomplete mathematics. That dosen't make mathematics useless - it just places a limit on what we can or cannot do. For instance, we cannot use deductive mathematics to describe the laws of nature in their entirety, because we know that any effort to be complete is doomed to failure - by Godel's theorems.

Also, there are some specific areas of mathematics that lead to direct examples of non-universal, but nonetheless consistent interpertations of nature. Take, for instance, Euclidean and differential geometry. Euclidean geometry is the geometry of flat planes, whereas differential geometry describes abstract mathematical notions. It was once thought that Euclidean geometry is "sufficient", and that it is the simplest way of representing spacial relationships. However, as it turns out, differential geometry is actually much more simpler when it comes to dealing with, say, the theory of relativity - even though it is not intuitively connected to our perception of the universe.

So in short, we have two different "geometries", each of which can, supposedly, explain spacial representation. Both are valid, but one is much more useful. Neither is universal. And yet, there is no contradiction.

I don't know about anyone else, but I think this stuff is interesting.

The fundamental question is this: is, or isn't, mathematics an extension of logic? A smart man named Frege (read about him here) said, yes, it is. He showed a way to connect formal logic with set theory, which is the basis for mathematics as we know it.

There was only one problem: Russell's Paradox. Bertrand Russell showed that, using Frege's axioms that defined set theory, we have a contradiction - Russell's Paradox. And as any student of logic knows, a contradiction can be used to prove anything at all, which means that mathematics as Frege defined it was not viable.

To make a very long and very interesting story short, Russell (with Alfred Whitehead) attempted to create a foundation for mathematics that would not give rise to Russell's paradox - the Principia Mathematica. And everyone thought the world was cool.

Then, in the 1930s, Kurt Godel came along and smashed a hole in Russell's approach by showing that, given a sufficiently powerful formal system, one will always find unprovable truths and irrefutible falsehoods. So mathematics was, by that line of reasoning, incomplete.

This leaves the door open to a variety of critiques, the most relevant of which is that it is automatically not universal. After all, how could it be - there are things missing! We can't prove everything that is true, and we can't disprove everything that is false!

Godel's argument tells us that we are unable to describe the universal laws of nature using non-universal and incomplete mathematics. That dosen't make mathematics useless - it just places a limit on what we can or cannot do. For instance, we cannot use deductive mathematics to describe the laws of nature in their entirety, because we know that any effort to be complete is doomed to failure - by Godel's theorems.

Also, there are some specific areas of mathematics that lead to direct examples of non-universal, but nonetheless consistent interpertations of nature. Take, for instance, Euclidean and differential geometry. Euclidean geometry is the geometry of flat planes, whereas differential geometry describes abstract mathematical notions. It was once thought that Euclidean geometry is "sufficient", and that it is the simplest way of representing spacial relationships. However, as it turns out, differential geometry is actually much more simpler when it comes to dealing with, say, the theory of relativity - even though it is not intuitively connected to our perception of the universe.

So in short, we have two different "geometries", each of which can, supposedly, explain spacial representation. Both are valid, but one is much more useful. Neither is universal. And yet, there is no contradiction.

I don't know about anyone else, but I think this stuff is interesting.

Its actually Gaston Julia, not Julia Gaston

Radar Detector Detector Detector? George Boole would be proud. Or furious.

Nice troll but Germany made metric as compulsory in 1868 and both Germany and Russia signed the Metre Convention in 1875 long before Lenin and Hitler.

Nazi: A member of the National Socialist German Workers' Party, founded in Germany in 1919 and brought to power in 1933 under Adolf Hitler.

Helmholtz was born on 8/31/1821 in Potsdam, Germany. He ended his breathing on 9/8/1894 in Berlin, Germany.

Hence, he could not have been a Nazi...

PS, some info Helmholtz .

See for example, GAP, or Macaulay2.

> einstein suffered terribly in school, guess that makes him a moron too, eh?

While popular culture holds that Einstein was a drop-out, a lowly patent-office clerk, and an outsider who stood the scientific world on his head, he was in fact the equivalent of a modern PhD candidate in the last year of a PhD program. In 1900 he graduated with the equivalent of a bachelor's degree or higher, qualified to teach both math and physics at the university level. When he published his famous papers in 1905 he was what we now call an ABD ("all but dissertation"), and in fact he submitted his dissertation On a new determination of molecular dimensions that same year, earning a PhD in physics at U. Zurich.

More detail here.

More information about Neumann:

http://ei.cs.vt.edu/~history/VonNeumann.html
http://www.neumann.com/
http://www.mbi.ufl.edu/~vetneumann
http://www-gap.dcs.st-and.ac.uk/~history/Mathemati cians/Von_Neumann.html
http://www.math.columbia.edu/~neumann/
http://www.zyvex.com/nanotech/vonNeumann.html
http://www.karto.ethz.ch/neumann/
http://www.rit.edu/~drk4633/vonNeumann/
http://www.fsm-a.org/neumann

In the forward for "The Universal Computer" (by Martin Davis) there are a couple of quotes:

"If it should turn out that the basic logics of a machine designed for the numerical solution of differential equations coincided with the logics of a machine intended to make bills for a department store, I would regard this as the most amazing coincidence I have ever encountered."

Howard Aiken in 1956

Let us now return to the analogy of the theoretical computing machines... It can be shown that a single special machine of that type can be made to do the work of all. It could in fact be made to work as a model of any other machine. The special machine may be called a universal machine..."

Alan Turing in 1947

NOTE: In Mr. Aiken's defense, he is probably referring to a differential analyzer (which was an analog computer)

When I was in high school, my (supposedly) CS teacher read an article that stated, "the world would no longer need programmers". She attempted to persuade me from becoming a programmer because in the future no one would need programmers. It would be a dead profession. The year was 1994. Okay, she was half right (there won't be anymore jobs for a while, and they'll all go overseas...), but still.... You can't extrapolate. My teacher never would have imagined (or actually just read the other article) about the internet.

What if AI takes off? I think in the future even the soft sciences will become more computational. Look at fields like bioinfomatics or computational linguistics. There are all kinds of new areas opening up. The problem is that the world doesn't revolve around computers, but all the phenomena of our universe may be one really grand one. Programmers have to learn other skills. I see biologists, actuaries, and engineers (outside of EE/ECE) write code all the time. You need to attach an extra skill to your code.

All this just goes to prove, you shouldn't extrapolate about science or computing, unless your one of these guys:

Alan Turing
Albert Einstein
Kurt Godel
Nikola Tesla
Gordon Moore
Jules Verne

Of course, I'm extrapolating (and as you can guess, I'm not one of these guys...), so if you're a good philosopher you can safely ignore my post. Nothing to see here.... Carry on.

In the forward for "The Universal Computer" (by Martin Davis) there are a couple of quotes:

"If it should turn out that the basic logics of a machine designed for the numerical solution of differential equations coincided with the logics of a machine intended to make bills for a department store, I would regard this as the most amazing coincidence I have ever encountered."

Howard Aiken in 1956

Let us now return to the analogy of the theoretical computing machines... It can be shown that a single special machine of that type can be made to do the work of all. It could in fact be made to work as a model of any other machine. The special machine may be called a universal machine..."

Alan Turing in 1947

NOTE: In Mr. Aiken's defense, he is probably referring to a differential analyzer (which was an analog computer)

When I was in high school, my (supposedly) CS teacher read an article that stated, "the world would no longer need programmers". She attempted to persuade me from becoming a programmer because in the future no one would need programmers. It would be a dead profession. The year was 1994. Okay, she was half right (there won't be anymore jobs for a while, and they'll all go overseas...), but still.... You can't extrapolate. My teacher never would have imagined (or actually just read the other article) about the internet.

What if AI takes off? I think in the future even the soft sciences will become more computational. Look at fields like bioinfomatics or computational linguistics. There are all kinds of new areas opening up. The problem is that the world doesn't revolve around computers, but all the phenomena of our universe may be one really grand one. Programmers have to learn other skills. I see biologists, actuaries, and engineers (outside of EE/ECE) write code all the time. You need to attach an extra skill to your code.

All this just goes to prove, you shouldn't extrapolate about science or computing, unless your one of these guys:

Alan Turing
Albert Einstein
Kurt Godel
Nikola Tesla
Gordon Moore
Jules Verne

Of course, I'm extrapolating (and as you can guess, I'm not one of these guys...), so if you're a good philosopher you can safely ignore my post. Nothing to see here.... Carry on.

In the forward for "The Universal Computer" (by Martin Davis) there are a couple of quotes:

"If it should turn out that the basic logics of a machine designed for the numerical solution of differential equations coincided with the logics of a machine intended to make bills for a department store, I would regard this as the most amazing coincidence I have ever encountered."

Howard Aiken in 1956

Let us now return to the analogy of the theoretical computing machines... It can be shown that a single special machine of that type can be made to do the work of all. It could in fact be made to work as a model of any other machine. The special machine may be called a universal machine..."

Alan Turing in 1947

NOTE: In Mr. Aiken's defense, he is probably referring to a differential analyzer (which was an analog computer)

When I was in high school, my (supposedly) CS teacher read an article that stated, "the world would no longer need programmers". She attempted to persuade me from becoming a programmer because in the future no one would need programmers. It would be a dead profession. The year was 1994. Okay, she was half right (there won't be anymore jobs for a while, and they'll all go overseas...), but still.... You can't extrapolate. My teacher never would have imagined (or actually just read the other article) about the internet.

What if AI takes off? I think in the future even the soft sciences will become more computational. Look at fields like bioinfomatics or computational linguistics. There are all kinds of new areas opening up. The problem is that the world doesn't revolve around computers, but all the phenomena of our universe may be one really grand one. Programmers have to learn other skills. I see biologists, actuaries, and engineers (outside of EE/ECE) write code all the time. You need to attach an extra skill to your code.

All this just goes to prove, you shouldn't extrapolate about science or computing, unless your one of these guys:

Alan Turing
Albert Einstein
Kurt Godel
Nikola Tesla
Gordon Moore
Jules Verne

Of course, I'm extrapolating (and as you can guess, I'm not one of these guys...), so if you're a good philosopher you can safely ignore my post. Nothing to see here.... Carry on.

In the forward for "The Universal Computer" (by Martin Davis) there are a couple of quotes:

"If it should turn out that the basic logics of a machine designed for the numerical solution of differential equations coincided with the logics of a machine intended to make bills for a department store, I would regard this as the most amazing coincidence I have ever encountered."

Howard Aiken in 1956

Let us now return to the analogy of the theoretical computing machines... It can be shown that a single special machine of that type can be made to do the work of all. It could in fact be made to work as a model of any other machine. The special machine may be called a universal machine..."

Alan Turing in 1947

NOTE: In Mr. Aiken's defense, he is probably referring to a differential analyzer (which was an analog computer)

When I was in high school, my (supposedly) CS teacher read an article that stated, "the world would no longer need programmers". She attempted to persuade me from becoming a programmer because in the future no one would need programmers. It would be a dead profession. The year was 1994. Okay, she was half right (there won't be anymore jobs for a while, and they'll all go overseas...), but still.... You can't extrapolate. My teacher never would have imagined (or actually just read the other article) about the internet.

What if AI takes off? I think in the future even the soft sciences will become more computational. Look at fields like bioinfomatics or computational linguistics. There are all kinds of new areas opening up. The problem is that the world doesn't revolve around computers, but all the phenomena of our universe may be one really grand one. Programmers have to learn other skills. I see biologists, actuaries, and engineers (outside of EE/ECE) write code all the time. You need to attach an extra skill to your code.

All this just goes to prove, you shouldn't extrapolate about science or computing, unless your one of these guys:

Alan Turing
Albert Einstein
Kurt Godel
Nikola Tesla
Gordon Moore
Jules Verne

Of course, I'm extrapolating (and as you can guess, I'm not one of these guys...), so if you're a good philosopher you can safely ignore my post. Nothing to see here.... Carry on.

In the forward for "The Universal Computer" (by Martin Davis) there are a couple of quotes:

"If it should turn out that the basic logics of a machine designed for the numerical solution of differential equations coincided with the logics of a machine intended to make bills for a department store, I would regard this as the most amazing coincidence I have ever encountered."

Howard Aiken in 1956

Let us now return to the analogy of the theoretical computing machines... It can be shown that a single special machine of that type can be made to do the work of all. It could in fact be made to work as a model of any other machine. The special machine may be called a universal machine..."

Alan Turing in 1947

NOTE: In Mr. Aiken's defense, he is probably referring to a differential analyzer (which was an analog computer)

When I was in high school, my (supposedly) CS teacher read an article that stated, "the world would no longer need programmers". She attempted to persuade me from becoming a programmer because in the future no one would need programmers. It would be a dead profession. The year was 1994. Okay, she was half right (there won't be anymore jobs for a while, and they'll all go overseas...), but still.... You can't extrapolate. My teacher never would have imagined (or actually just read the other article) about the internet.

What if AI takes off? I think in the future even the soft sciences will become more computational. Look at fields like bioinfomatics or computational linguistics. There are all kinds of new areas opening up. The problem is that the world doesn't revolve around computers, but all the phenomena of our universe may be one really grand one. Programmers have to learn other skills. I see biologists, actuaries, and engineers (outside of EE/ECE) write code all the time. You need to attach an extra skill to your code.

All this just goes to prove, you shouldn't extrapolate about science or computing, unless your one of these guys:

Alan Turing
Albert Einstein
Kurt Godel
Nikola Tesla
Gordon Moore
Jules Verne

Of course, I'm extrapolating (and as you can guess, I'm not one of these guys...), so if you're a good philosopher you can safely ignore my post. Nothing to see here.... Carry on.

See this

"get binaries' checksums to match the old binaries' checksums (nigh on impossible, given how md5 hash works)"

It's so impossible that someone who could do it might win a Fields medal.

Back in my day we didn't have this abstract stuff [introduction to a book]. No sir. No turing machines and no compilers. We had to hard code our algorithms. We didn't have punch cards either. I had to manipulate the very laws of physics. My computers were huge, took large grants from the government to build. Heck, one of my employees (a woman) had to pretend to be a man just to find work.

--Charles Babbage

Back in my day we didn't have this abstract stuff [introduction to a book]. No sir. No turing machines and no compilers. We had to hard code our algorithms. We didn't have punch cards either. I had to manipulate the very laws of physics. My computers were huge, took large grants from the government to build. Heck, one of my employees (a woman) had to pretend to be a man just to find work.

--Charles Babbage

I'd rather say it was Hardy's hypothesis, although from what I know of his character, he was probably not a sexist or prone to any other form of bigotry;
He was an atheist and [most likely] a homosexual, and was therefore very much an 'outsider' himself in his times)

There simply weren't very many women in math 100 years ago.

And while I'm on the topic, it is interesting to note that Stockholm University was one of the first universites to give a chair in mathematics to a woman;
The great Sonya Kovalevskaya.

However, Andrew Wiles, who solved Fermat's last theorem, spent seven years in his attic to do so.

I guess broad generalizations don't work so well, eh?

Not to mention C. F. Gauss (1777-1855)

Look back a bit further, c. 1850-60.

I personally find the Jacquard loom's influence to be much more interesting regarding Charles Babbage, "the father of computing", and Ada Lovelace, "the first programmer".

The loom seems to have been a definite influence on his Analytical Engine (at least on the input design). Read the short bio linked above, it is really a must for anyone interested in computers.

Indeed, it's 'Quatre-vingt-dix neuf', which is 'Four-twenty ten-nine'... there is no explicit 'times'. (And if you're going to criticise, learn to spell first).

My point is that most languages do addition to express numbers - that's what the 'y' is doing in Spanish. I feel that 'dix-neuf' is pretty much equivalent to the Spanish 'diecinueve', so I suppose your difficulty is purely this 'quatre-vingt' construct...

Perhaps it would help you to look at the reason for this - which, as I say, is pretty much superseded outside mainland France by these 'septante', 'octante', 'nonante' constructs. Since Babylonian times, humanity seems to have had a habit of counting, rather than in hundreds, in sixties. (See 'Number words and number systems' by Karl Menninger, or this site). The link suggests a number of reasons for the popularity of the number sixty, including the two that I was given as a (British) child for the popularity of currently popular non-base ten systems like the foot or the dozen - firstly, that such numbers (12, 60...) maximise the number of divisors - secondly, that there are three joints on each finger, five fingers on each hand, allowing one to count up to 60 by pointing at one of the twelve parts of the fingers of the left hand with one of the five fingers of the right hand...

One can see the importance of the number 12 in Germanic languages, like English, whereas Latin languages actually inherit a simple base-10 system (undecim, duodecim, tredecim...) Germanic languages use 'one left after ten, two left after ten' - many hundreds of years of accent and erosion have simply hidden the meaning of the terms 'eleven' and 'twelve'.

The number 20 also has a special significance in English - it is the score, 'Three score and ten'. In fact, this 'score' is exactly the equivalent to the French 'eighty' that upsets you so much. The French are simply using a somewhat Biblical expression; "Four score".

Base sixty is indeed a little further from English-speaking experience, though, as I have said, it has a remarkably long historical pedigree. However, it was historically in use in Germanic languages, including English, where I believe sixty were given a special name (like 'score' - in the case of English, it was apparently 'shock'). Dictionary.com informs me that the term 'shock' is still in use in some Baltic ports to refer to a set of sixty loose items.

Until very recently, English included a good number of these peculiarities - and still does - English as a second language is full of irregularities, in and outside the language of mathematics. Remember, Americans didn't raise an eyebrow at the term when Lincoln said "Four score and seven years ago"... when the French say it, neither should you.

There is a disturbing historical precedent for this bizarre piece of nonsense. Francis Galton , the man who invented eugenics, wrote on 'Hereditary genius' by assigning what were effectively IQ scores to dead historical figures based on their biographies. He thought that he had found that these scores were heritable. He used this to argue for restrictions on human breeding.

Galton, by repute a kindly and pleasant man, was the unwitting intellectual godfather both of the Nazi exterminaiton programs, and of the disgraceful programs of forcible sterilisation in the United States and many other Western countries.

Galton's procedure was nonsense, based as it was on a completely circular defintion of "intelligence", a complete absence of data, and a deal of fuzzy thinking. Murray's appears to be equally nonsense, and probably for very similar reasons. What he has managed to show is that certain types of achievement are more likely to be recorded than others, which is at most mildly interesting, and that dominant social groups write about themselves, which is not very surprising, and entirely un-original.

Having read Murray's previous opus, I will not be parting with my hard-earned euros to read this one...

I wonder what John Horton Conway thinks about this ?

It is unfortuante that Raymond chose to appropriate that symbol without appropriate attribution.

I feel I should mention that Isaac Newton (or even Issac Newton, whoever the hell he was) wasn't a PhD - such things didn't exist in the UK educational system in the 17th century. According to the MacTutor History of Mathematics Archive he got his BA in 1665 and incepted MA in 1668, at which point he was elected a college Fellow.

There have been higher doctorates (which, unlike in the US, are not always honorary awards) in the UK for centuries - doctorates in Divinity, Law, Medicine, and Music date back to mediaeval times, while the DSc and DLitt came in in the late 19th century. But the PhD, being a degree somewhere between the first postgraduate degree (studied at the beginning of one's specialist academic career) and the higher doctorates (typically awarded late in a career, on the basis of a substantial published research record), is less than a century old in the UK.

The PhD originated in Germany sometime in the 16th century, migrated to the US sometime in the 19th century (I think) and was introduced in the UK (to some initial scepticism) in the early 20th century.

These days, it's pretty much impossible to get anywhere in (British) academia without a PhD, but that's only really been the case in the last thirty years. In Newton's day (and this seems to have been true at Oxford and Cambridge until the mid-20th century) things were less rigidly qualification-focused. Being elected a Fellow of a college was the important thing.

A few years later, he was appointed Lucasian Professor of Mathematics - a post held currently by Stephen Hawking, and at various other times by Airy, Babbage, Stokes and Dirac.

More importantly, though, Newton was a Fellow of the Royal Society which pretty much beats any other academic honour short of a Nobel Prize or a Fields Medal.

nicholas

John Nash was extremely eccentric but held down positions at MIT.

Ah, that would be the quantum computer on board the manned space expedition to Mars, power by a fission-reactor ion-drive. Back home we can watch it via our ubiquetous videophones, or our Linux powered desktops, which can run applications with true Artificial Intelligence. All our homes will be supplied by nuclear electricity that is too cheap to meter. There will be peace in Isreal.. etc..

We live in such interesting times that everyone is taking everything for granted. The idea of a quantum computer was born in 1982 (history of Quantum computing). Now, just over twenty years later, we already have brought bits of the idea into practice - that is stunningly fast, compared with history. Quantum computers are an extremely advanced idea.

Charles Babbage got the idea of a general computer around 1812 (Babbage), but one wasn't built until World War II.

So after only 20 years we already have done some tiny, extremely simple calculations involving a few qubits. Very far from being useful, and still totally amazing that we've come so far. Most ideas take twenty years to become widely known before they're looked at seriously.

So Slashdot readers compare it to Duke Nukem and flying cars, and laugh. These times are so interesting that everyone is jaded.

I'm not sure why this story is being posted now. "Galileo consumed by Jupiter" happened in around 1610. Galileo's consuming obsession with Jupiter ultimately led to his condemnation for heresy in 1633. This is a totally appropriate subject for Slashdot's righteous indignation, but is kind of late in coming, especially since he was exonerated (sort of, John Paul II waffled a bit) in 1992.

Don't forget, this is Slashdot, no need for me to RTFA.

This link [St Andrew's University, UK] credits Hooke with determining that Jupiter rotates and this link [Wikipedia] and [Encylopaedia Britannica] credit discovery of the GRS to either Hooke or Cassini around 1665. Schwabe was the first person to produce an accurate drawing and description of the GRS.

i've been using a computer for so long that i'm half convinced that the reals are a hoax invented by physicists to make their sums easier ;-)

Well, at least you are, or rather were, in good company. When Lindemann proved the transcendence of pi, Kronecker asked:

"Of what use is your beautiful investigation of pi? Why study such problems when irrational numbers do not exist?"

greatness, and it certainly is "masculine in its deranged egotism and orderliness," but I would not go so far as to say that there will never be a great female mathematician. On the other hand, there has not been one yet.

Emmy Noether was a great female mathematician.

You raise some valid points, but you need to come off your high horse. Back in the time when the USA was, what you call, a backward country, the US was all so pleased to get Fermi, Einstein fleeing totalitarian regimes in Europe (to name just a few). They did not come to their theories and research in isolation, but were a product of their environment and education in those countries. But they started or helped a developing industry and research in the US.

Later, the US even incited top leading researchers to go to the States, well in many cases, they had little choice, but it was better than being deported by the USSR.

In short, this has happened before (and was done by those that had little to protect or complain about, but are now the first to be scorned), and is happening again. Nothing new here, move along.

In times of world Economy, I am still dazzled to see that ppl seem to find reasons to protect their little countries (in fact, the country they are in can do anything they want, but everyone else should be good, unfair competition anyone?). I am just glad to see another alternative processor and in the long term, it can only benefit us with lower prices and better performance.

Gauss looks evil. I suggest that he knew that his math theories would eventually be used for cool weaponry.

Actually it was just around 1000 years ago that perspective was first formulated by al-Haytham, and a few hundred years later that people began to apply it to the arts.

There is no ether!

History . Learn it or repeat it.

I had always heard people refer to them as Newtonian Calulus and French Calculus, so I checked. See History of Calculus.

Pierre Fermat and Gilles Roberval were French.

Gottfried Leibniz was born a German, but his early contributions to Calculus happened while he was living in Paris. He returned to Germany in 1676, and did not publish until later. You are correct that I was thinking of his work.

I do not know why I believed it was referred to as French Calculus. Today it is called "Integral Calculus", or just "Calculus". Does someone know the correct name that distinguishes Leibniz's work from Newton's?

When visiting mathtutor one can see that even 200 years ago, many important discoveries were done in the later stages of the Mathematicians career. Stories like the ones about Abel or Galois distort the picture.

More and more discoveries of younger mathematicians are achieved through collaboration or by standing on the shoulders of people with more experience (who tend also to be more generous with sharing their ideas without expecting credit).

Mathematical knowledge continues to accumulate in a fast pace and only few of this knowledge has been absorbed in books. Chances grow that a young mathematician will discover something already known or to be a special case of a much more general result. Fortunately, there are better and better online databases but it also needs more and more time to dig through that material.

The most productive age for a mathematician will grow also in the future. The same will happen in physics or computer science (as a previous post has pointed out already).

They have to be an ancient Greek geometer?

Now, can someone tell me what practical applications there might be of this? Or is it strictly an abstract concept?

Hmmm, a lot of work in mathematics may not have immediate applications or uses. But down the line, they just might get used.

As many posters have already mentioned, Boolean algebra is one such case, and another example would be the work done by Fourier - particularly his integral transforms and series.

I mean, today these are used so much in DSP and the like, I doubt Fourier had these in mind when he worked it out in the early 1800s :-)

Although a lot of pure mathematicians may take pride in the fact that their work might just never get used, one can never be so sure ;-)