Right now, there appears to be an edit war starting up over at wikipedia on whether a particular prime number was created or discovered...

http://en.wikipedia.org/w/index.php?title=Illegal_prime...next&oldid=107425442

http://en.wikipedia.org/w/index.php?title=Illegal_prime...next&oldid=109031738



The prime number whose creation and/or discovery is being argued about here is

49310 83597 02850 19002 75777 67239 07649 57284 90777 21502 08632 08075 01840 97926 27885 09765 88645 57802 01366 00732 86795 44734 11283 17353 67831 20155 75359 81978 54505 48115 71939 34587 73300 38009 93261 95058 76452 50238 20408 11018 98850 42615 17657 99417 04250 88903 70291 19015 87003 04794 32826 07382 14695 41570 33022 79875 57681 89560 16240 30064 11151 69008 72879 83819 42582 71674 56477 48166 84347 92846 45809 29131 53186 00700 10043 35318 93631 93439 12948 60445 03709 91980 04770 94629 21558 18071 11691 53031 87628 84778 78354 15759 32891 09329 54473 50881 88246 54950 60005 01900 62747 05305 38116 42782 94267 47485 34965 25745 36815 11706 55028 19055 52656 22135 31463 10421 00866 28679 71144 46706 36692 19825 86158 11125 15556 50481 34207 68673 23407 65505 48591 08269 56266 69306 62367 99702 10481 23965 62518 00681 83236 53959 34839 56753 57557 53246 19023 48106 47009 87753 02795 61868 92925 38069 33052 04238 14996 99454 56945 77413 83356 89906 00587 08321 81270 48611 33682 02651 59051 66351 87402 90181 97693 93767 78529 28722 10955 04129 25792 57381 86605 84501 50552 50274 99477 18831 29310 45769 80909 15304 61335 94190 30258 81320 59322 77444 38525 50466 77902 45186 97062 62778 88919 79580 42306 57506 15669 83469 56177 97879 65920 16440 51939 96071 69811 12615 19561 02762 83233 98257 91423 32172 69614 43744 38105 64855 29348 87634 92103 09887 02878 74532 33132 53212 26786 33283 70279 25099 74996 94887 75936 91591 76445 88032 71838 47402 35933 02037 48885 06755 70658 79194 61134 19323 07814 85443 64543 75113 20709 86063 90746 41756 41216 35042 38800 29678 08558 67037 03875 09410 76982 11837 65499 20520 43682 55854 64228 85024 29963 32268 53691 24648 55000 75591 66402 47292 40716 45072 53196 74499 95294 48434 74190 21077 29606 82055 81309 23626 83798 79519 66199 79828 55258 87161 09613 65617 80745 66159 24886 60889 81645 68541 72136 29208 46656 27913 14784 66791 55096 51543 10113 53858 62081 96875 83688 35955 77893 91454 53935 68199 60988 08540 47659 07358 97289 89834 25047 12891 84162 65878 96821 85380 87956 27903 99786 29449 39760 54675 34821 25675 01215 17082 73710 76462 70712 46753 21024 83678 15940 00875 05452 54353 7.

So, what's your opinion? Was this prime number created or was it discovered?

Without knowing almost anything beyond high school math and not having read the links - I'd say discovery. The number has always been there. We just figured out how to find it.

Right?

quote:

Originally posted by MBM:
Without knowing almost anything beyond high school math and not having read the links - I'd say discovery. The number has always been there. We just figured out how to find it.

Right?

When an artist chisles away at a piece of stone, is he creating a sculpture, or discovering a sculpture that was there hidden inside the stone all along, just waiting for the derbus around it to be cleared away so that it could be revealed?

quote:

Originally posted by ricardomath:

When an artist chisles away at a piece of stone, is he creating a sculpture, or discovering a sculpture that was there hidden inside the stone all along, just waiting for the derbus around it to be cleared away so that it could be revealed?

But - unlike in sculpture where the artist is actually manifesting something from his/her mind onto the piece of clay - that number existed prior to the mathematician creating the means to find it. My favorite number is 13. In another universe, that prime number may be some being's favorite number. Who knows?

Created... and then stolen... Leading to a "discovery"...

THe way I look at it, you have many works of art which, if the artist doesn't create them, then they don't get created. So I'd say an artist CREATES his works.

In mathematics, I don't ask the question of would the theorem be there if I didn't prove it. But I ask, would the question that I asked that led to me proving the theorem have ever been asked. The part of mathematics thats creation is the part of asking the difficult questions that further your research. Once the questions have been asked, its a discovery to find the answer.

What exactly is the argument in favor of the number being created? A number represents a quantity. If the person who first, let's say, brought forth the knowledge of this prime number, had not done so, would the number not exist? Hmmmmm....

quote:

Originally posted by Vox:
What exactly is the argument in favor of the number being created? A number represents a quantity. If the person who first, let's say, brought forth the knowledge of this prime number, had not done so, would the number not exist? Hmmmmm....

I think that it is a mistake to associate a number with a quantity. Isn't math essentially a symbolic logic system and as such tautological. Moreover, like language, isn't the relationship between the signifer and the signified is arbitrary.

quote:

Originally posted by Vox:
What exactly is the argument in favor of the number being created? A number represents a quantity. If the person who first, let's say, brought forth the knowledge of this prime number, had not done so, would the number not exist? Hmmmmm....

True the number exists, but the person who discovered that this number is a prime number, probably did so through some (possibly new) advanced methods of number theory. And while we can easily say this number would have one day been proven prime, we cannot say that the methods he used to prove that this number was prime would have been discovered.

the universe already, and has already operated on supreme mathematics,what we are dealing with now is man trying to understand how the universe works. Its like saying Saturn wasnt there until man discovered it, or that the moon had water on it, it was always the case man just found out about it. Maybe many many millions of years ago, all of this happened before, and we are just reliving thoughts bounced around the universe, who knows?

quote:

the universe already, and has already operated on supreme mathematics,what we are dealing with now is man trying to understand how the universe works. Its like saying Saturn wasnt there until man discovered it, or that the moon had water on it, it was always the case man just found out about it. Maybe many many millions of years ago, all of this happened before, and we are just reliving thoughts bounced around the universe, who knows?

I guess the question really boils down to how do you define mathematics. Is mathematics the theorems themselves or the proof of the theorems? Is mathematics the numbers themselves or the proofs of properties of the numbers? In both cases I would argue that mathematics is the later. These proofs are the beauty of mathematics. Consider Turing for example - this is the guy who decades before the first computer came up with the concept of Turing machine, which is the technical formality which is used to judge the accuracy of an algorithm. Thats a beautiful mathematical creation. And while this creation has been used to discover many properties of computational problems, it is a creation in itself.

Look further at Godel and his completeness theorem. Its a pretty understandable theorem and one could easily conclude that the theorem itself was 'discovered' by Godel. However, the way he proved it - with the usage of Heinkin sets was so creative and illustrative that it only follows that one should call his proof a creation.

We can move it to a more basic principle like that of mathematical induction or dynamic programming. Both of these are concepts that somebody came up with to prove things on sets with certain properties. So while the statement that's being proved may be a simple 'discovery', the people who created the concept of mathematical induction or dynamic programming should get credit for being the creators of new mathematical concepts.

If you want to go as far as to say that a proof is 'discovered', then I'll follow up with the statement that that line of reasoning would make one say that DiVinchi's paintings or Langston Hughes's poetry were all discovered as well.

How fast does thought travel? how do you measure thought?

quote:

Originally posted by ZAKAR:
How fast does thought travel? how do you measure thought?

huh?

Answering the question, I say created.

Mathematics was created in order to explain, and have a reproducable system-of-proof.

The question is akin to the which came first question regarding music.

Which came first, the written score or the sound it can produce when used.

I always say the music came first.

Musicians who can produce music, but cannot read the notation of the music system are considered 'lacking', and they are.

Yet, they remain musicians.

So, does music exist before it is played?

Does music exist before it is written, and whether it is ever played or not?

Man-made systems are by definition...created.

PEACE

Jim Chester

After reading many of the responses and considering Kresge's question to me, I'm almost ready to conclude/accept that mathematics is created, rather than discovered. Basically, it's a system designed by humans to explain/predict the behavior or numbers and/or values. The values themselves may not be created, but the system designed around understanding them would have been created.

My only hesitation is due to this question: could there be another logic system, totally different from what mathematicians employ, that could just as reliably explain/predict/prove what our mathematics do? If a culture on some alien planet employed mathematics, could their system differ completely, with no resemblance whatsoever, to ours, and yet remain just as effective as ours? If the answer is "no," to that last question, then why doesn't that suggest somehow that this was a system waiting to be discovered, rather than invented?

My only hesitation is due to this question: could there be another logic system, totally different from what mathematicians employ, that could just as reliably explain/predict/prove what our mathematics do? If a culture on some alien planet employed mathematics, could their system differ completely, with no resemblance whatsoever, to ours, and yet remain just as effective as ours? If the answer is "no," to that last question, then why doesn't that suggest somehow that this was a system waiting to be discovered, rather than invented?---Vox

Your point is well taken.

To say there could not be 'another system' does implicitly say it was there, as a system, to be discovered...I think.

Clearly, another system in a on another planet by another species can be created, and...

If that species is only incrementally different from us, it will be as different from ours as ours 'counting system' is different from that of the chimpanzee.

I got that rationale from Neil the astrophysicist.

PEACE

Jim Chester

I suck at math. So, I'm amazed at how scientists can use math to answer difficult questions.

For example, I was watching Neil deGrasse Tyson discuss his new book on black holes. He thinks that Sir Isaac Newton was the greatest mind ever! Anyway, Tyson talks about how someone posed the question to Newton about how/why planets move in ellipses with the Sun. Newton didn't know the answer but said, "I'll get back to you." (At least that's how Tyson put it.)

So Newton goes off and invents some kind of new calculus to answer the question about how bodies move in elliptical paths with the Sun.

Again, I suck at math. So, I don't get how one can create a new kind of math to answer previously unexplanable questions. (Like, if I had a brilliant mind, could I invent a new math to solve my procrastination problem, or explain why I love chocolate so much? Okay, j/k)

The question is simple, I will ask it again. How fast does thought travel? How do you measure thought? We are talking about Math right , created or discovered?

quote:

Originally posted by ZAKAR:
The question is simple, I will ask it again. How fast does thought travel? How do you measure thought? We are talking about Math right , created or discovered?

Wrong!!!!

I don't have a quantitative answer.

However, qualitatitvely, thought travels at precisely the speed of the brain's processing speed.

Well????????????

I'm no mathematician either.

PEACE

Jim Chester

what am i wrong about ? So thought travels according to the processing speed of a persons brain? How do you measure that? Does it vary depending on the person?

The reason I ask the question is because I havent seen or heard of anyone who has measured thought, or calculated how fast it traveled?

If I see something happen I know ive seen it happen exactly the same way before , what does that mean?