Talk:Mathematician

From Wikipedia, the free encyclopedia

WikiProject Mathematics
Mathematics Portal
This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating: B Class High Priority  Field: General
One of the 500 most frequently viewed mathematics articles.
Archive
Archives
* Archive 1


Contents

[edit] Proofs by computer

I removed the phrase about proofs being verified by computers in the future because it's nonsense. This might only apply to very specific areas in mathematics, if at all. Also I changed the phrase about the source of mathematical problems. Most of them come from within mathematics, only a small part comes from economics and the sciences, and those problems would be concerned applied mathematics. —Preceding unsigned comment added by Alterationx10 (talk • contribs) 02:53, 27 February 2008 (UTC)

[edit] Worthless Quotation from St. Augustine

If the article acknowledges that Augustine's famously hostile saying about mathematicians was in fact directed at astrologers, then why is the son of a bitch even in the mathematician article? Wouldn't it create less confusion to simply omit the quotation which has created some measure of confusion over the years?

Agreed, it is irrelevant to the article, especially without context. Woudl anyone object to its removal?--&m@ 21:00, 26 June 2006 (UTC)
Dump it I say!  :-) capitalist 03:17, 27 June 2006 (UTC)
Done.--Konstable 03:47, 27 June 2006 (UTC)

[edit] This article requires cleanup!

I find the article rather confused: it does not know whether it is talking about mathematicians or mathematics. Some parts really should be moved or dropped. The Overview section is not about mathematicians! The Problems in mathematics section is not either. As it is now, the Differences section is only halfway about mathematicians.

We must set up a proper outline for what should be and what should not be in the article, and how it should be organized. PhS 08:14, 3 July 2006 (UTC)

[edit] More Interesting Demographic Analysis of Mathematicians

As always, an interesting point would concern the racial and ethnic composition of mathematicians (I see below that the Jews have nice mathematical heritage). I think that a link to the Race and Intelligence article would be good here. People with low IQs tend not to make good mathematicians. Perhaps also some reference to common moral attributes of mathematicians (mathematics has been held in high esteem in one form or other by almost all historic civilisations - perhaps that statement is true by definition).

I see on wikipedia that most mathematicians in history have been held to be white - some comments on the nationality of these white mathematicians would be interesting. Perhaps it is also fair to comment upon how it is that racial and ethnic differences between mathematicians have often resulted in different 'types' and 'flavours' of mathematics - there would be some interesting issues concerning the foundations of mathematics here. How do mathematicians know whether or not what they are doing is actually *real* mathematics (the answer here is usually ZFC - though it has been a long time since I say the following comment in a journal : "And here we have computationally, apolitically and non-racially verified the authenticity and accuracy of our theorems via the use of a colour-blind ZFC diagnostic routine to make sure that it was not complete b******s....". Well, you get the point. I found the following website interesting (though it probably wasn't programmed in by a black guy : ) : http://metamath.org/ (the last comment was given when observing that all the countries associated with meta-math are white, but I'm not complaining, merely stating colour-blond fact. )

Nukemason2 21:47, 22 November 2006 (UTC)

[edit] Erdos/Renyi coffee quote

I always heard this quote was from P.Erdos. Wikiquote agrees here. Where does the information about the author being A.Renyi come from? --Kajetan Wandowicz 17:12, 14 December 2006 (UTC)

I asked about the origin of this quote on Talk:Paul Erdős some years ago. See the response there (though it doesn't say much). It's probably impossible to determine who really said it first. It's always more likely to be attributed to Erdős rather than Rényi, as he is the more famous of the two. --Zundark 17:49, 14 December 2006 (UTC)
In that case shouldn't that be clarified in the article? As we cannot determine who said that, there are three possibilities:
1. Sign the quote with Renyi's name.
2. Sign it with Erdos' name.
3. Say (in the article) that there exists a controversy.
Out of which, given that Wikiquote attributes it to Erdos, second option shlould be chosen. Considering what you just said, the third option is the best. Either way, the worst option is 1 - but this one is used. --Kajetan Wandowicz 20:06, 16 December 2006 (UTC)
No objections here from anyone, so changed. --Kajetan Wandowicz 11:17, 18 December 2006 (UTC)

[edit] Doctoral degree statistics in the US

Can I just remove this section? While mildly interestig from a trivial point of view, it's not particularly encyclopedic or relevant to the notion of mathematician.--Boffob 16:26, 16 March 2007 (UTC)

  • I originally added the statistics section to complement the demographic information in the section above it and also as an attempt to give a rounded picture as mathematicians as a whole. Admittedly it doesn't fit in too smoothly and could be rewritten, but I believe that most of the information is of sufficient value to keep in the article. Perhaps it could be merged with the demographics section. TooMuchMath 04:15, 5 April 2007 (UTC)

[edit] Demographics section reeks of POV

How about a demographics section that tells us what proportion of mathematicians are male vs. female, a breakdown by age, a breakdown by race/ethnicity (if we must...) and so forth? Why do I have to be told that some group or another is "underrepresented?" Can't I take the basic facts from the encyclopedia article and decide that for myself? Who determines the "proper" representation of each group anyway? I'm proposing that we either radically rewrite or eliminate this section entirely. Other comments? capitalist 03:00, 17 April 2007 (UTC)

Whoops, I had forgotten that I had this rant here. I see an IP came in and rewrote the section to eliminate the POV at least. It reads much better now!  :) capitalist 03:14, 11 July 2007 (UTC)
Under-represented comes from the social sciences and is typically taken to mean representation within the subgroup compared with the population as a whole. --lquilter 18:39, 5 November 2007 (UTC)

[edit] Age

It would be useful, I think, to address in the demographics section about the popular belief that mathematicians are most productive in their 20s and that by their 30s and certainly 40s their most "brilliant" years are over. Sources on this topic? --lquilter 18:39, 5 November 2007 (UTC)

[edit] Inaccurate distinction

The article states:

"Mathematics differs from natural sciences in that physical theories in the sciences are tested by experiments, while mathematical statements are supported by proofs which may be verified objectively by mathematicians."

While it is true that outside of mathematics, proofs are not applicable, it is a mistake to imply that experiments do not apply to mathematics. A very large number of areas of mathematics are subject to experiment. Not infrequently, experiment will reveal a pattern that can then be proved. In some finite cases, the experimental results will themselves constitute a proof. (There are even a respected journal, "Experimental Mathematics" (A.K. Peters), and several books discussing the role of experiment in mathematics.)Daqu (talk) 01:36, 31 May 2008 (UTC)

We also have an article Experimental mathematics, and more on the issue is said in the section Mathematics#Mathematics as a science. There is also Philosophy of mathematics#Empiricism. In my opinion, there is an essential difference though between the role of experimentation in formal sciences like mathematics and in the natural sciences. No amount of experimental "testing" will avail to establish the validity of, e.g., Goldbach's conjecture or the Riemann hypothesis. In mathematical experiments there is no null hypothesis, no tests of significance, because there is no chance factor and no experimental error. Every "experiment" done by computer is in a sense the production of a formally provable theorem, and not a test in the sense of the scientific method. "Exploration" captures the nature of the activity much better than "experimentation".  --Lambiam 17:06, 31 May 2008 (UTC)
I think I agree with almost everything you write, Lambiam, but none of it affects the truth of what I wrote. The word "exploration" perfectly captures the nature of the activity known as "exploration". But I was speaking about "experimentation", which is best captured by the word "experimentation".
There are differences in the nature of experimentation for any two sciences, but that does not invalidate the fact that experimentation is experimentation.Daqu (talk) —Preceding comment was added at 03:07, 2 June 2008 (UTC)
Can you give an example then of a mathematical statement, held by a mathematician of repute, that has been tested by experiment but is not supported by (mathematical) proof?  --Lambiam 17:04, 2 June 2008 (UTC)
I'm not sure what "held by" means here.Daqu (talk) 01:23, 3 June 2008 (UTC)
It means that the mathematician accepts the statement as being true, on an equal footing with (proved) theorems.  --Lambiam 12:07, 3 June 2008 (UTC)
Sorry, I don't see the relevance.Daqu (talk) 17:13, 3 June 2008 (UTC)
The relevance is as follows. The contested sentence in the article states: "Mathematics differs from natural sciences in that physical theories in the sciences are tested by experiments, while mathematical statements are supported by proofs which may be verified objectively by mathematicians." For this contrast to make sense, the physical theories referred to have to be theories that are embraced by physicists: they have been tested and withstood the tests (which typically at the same time falsified a rival theory). Likewise, the mathematical statements are not just any statements, but statements embraced by mathematicians: they have attained theoremhood. You say that this distinction is inaccurate (but concede that proofs are not applicable outside of mathematics). To invalidate the contested sentence, we then need examples where a mathematical statement is embraced by mathematicians, not by dint of theoremhood, but because it has withstood the tests.  --Lambiam 23:48, 3 June 2008 (UTC)
Probably the Riemann hypothesis is an example; but it depends on what you mean by "held by." Experiments have led most (or all?) mathematicians to believe it is true, but they don't "hold" it to be true, because they can't prove it. So they hold it to be an open question. Dicklyon (talk) 19:11, 3 June 2008 (UTC)
Another example is Goldbach's conjecture. The difference is indeed the status conferred on a statement that does not immediately succumb to experiment. Although the general theory of relativity is a theory, it is taught as part of the canon of physics, as being confirmed by stringent tests – although physicists realize that sooner or later it may fail a test and need to be replaced. Mathematical statements that appear to be true for a few cases that have been examined (few, because they are negligeable compared to the infinity of all cases), but whose truth is not supported by a deductive argument, never attain a similar status in mathematics. Errors in proofs aside, a theorem will not fail a test, so it is pointless to attempt to test a statement that you accept as a theorem.  --Lambiam 23:49, 3 June 2008 (UTC)
Sounds like a mathematician speaking! It's not at all pointless to test the validity of a proved theorem on a finite number of test cases. Just because you have accepted it as a theorem doesn't mean it's true! "Errors in proofs aside" is sort of like "no offense, but..." Dicklyon (talk) 00:02, 4 June 2008 (UTC)
Further, Sheepyouare, if you really want to discuss the philosophy of experiment, then it should be noted that no amount of experiment in the "experimental sciences" like physics, chemistry and biology can conclusively show any fact other than what happened in the experiment. (And even then, as you mention, just as with any experiment, there is the possibility of experimental error.)
I will say it one last time, and not again: Just because mathematics is subject to proof (and as you may know, not all propositions are subject to proof, as Gödel showed; the twin prime conjecture, for example, may be impossible to ever prove or disprove, regardless of whether it is true or false) does not mean that it is not subject to experiment as well. I do numerical experiments to test various mathematical propositions All The Time, and so do many other mathematicians. That's all I have to say on the matter.Daqu (talk) 05:54, 4 June 2008 (UTC)