# Difference between revisions of "Talk:Majoring in Mathematics"

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The purported proof of [[Fermat's Last Theorem]] would be an example of liberal math.--[[User:Aschlafly|Andy Schlafly]] 16:48, 26 February 2012 (EST) | The purported proof of [[Fermat's Last Theorem]] would be an example of liberal math.--[[User:Aschlafly|Andy Schlafly]] 16:48, 26 February 2012 (EST) | ||

+ | :This may quickly move outside my area of understanding, but could you clarify this at all? Is the concern the use of the [[axiom of choice]] and/or non-[[ZF]] axioms? I've read our article and vaguely remember a book I read in high school, but other than the use of some non-standard techniques, I wasn't aware there was any serious doubt as to the validity of the proof. --[[User:JustinD|JustinD]] 17:10, 26 February 2012 (EST) |

## Revision as of 17:10, 26 February 2012

This is an extremely rough outline for this new article. I will continue to expand it over the next few weeks based on feedback about the appropriateness of the problems and other suggestions for improvements. Please let me know what you think! --MarkGall 23:12, 4 October 2009 (EDT)

- well I was a math major in college many years ago (before Rubic's cube!) Suggest adding statistics.
- Ah, good idea. At my undergrad school mathematics and statistics were separate programs, but I guess this isn't typical. I'll throw in a new section. I'm not much for statistics -- can anyone suggest some good problems? --MarkGall 23:20, 4 October 2009 (EDT)

- well I was a math major in college many years ago (before Rubic's cube!) Suggest adding statistics.

Tremendous work, Mark. I'll try to add something for probability or statistics, which I studied.--Andy Schlafly 23:22, 4 October 2009 (EDT)

- Great, thanks. These are subjects in which I'm inexpert. Now I'm inclined to move Probability/Statistics to a "field" along with algebra, analysis, etc. Please add a nice problem or theorem if you have any in mind! --MarkGall 23:24, 4 October 2009 (EDT)

Terrific analysis on what college mathematics is not. That should be required reading for many seeking to major in math!--Andy Schlafly 22:30, 15 October 2009 (EDT)

Why is there no mention of the bible or theology in this article? It should be mentioned, as it is in Axiom_of_Infinity, that the notion of an infinite set is somewhat blasphemous. Tomkup32 10:58, 9 December 2009 (EST)

For Bezout's theorem, you have some inaccurate claims: the line x+y=0 and x+y=1 never interset. We need to move to projective space for the degree of the intersection to be exactly mn.

## Liberal bias

How can there be liberal bias in math? Does saying 1+1 = 2 have a motive?SusanP 23:29, 9 February 2012 (EST)

- College math is not completely immune to liberal influences that have destroyed other subjects like physics.--Andy Schlafly 23:37, 9 February 2012 (EST)

- Can you give an example of liberal bias in math? --Bogart12
- Possible liberal bias--the study of so-called "homomorphisms" in modern liberal algebra could be part of the gay agenda?--Bogart12
- No, sorry, that's absurd and I think you know it. "Homo" simply means same and is used in a wide variety of contexts that have nothing to do with liberal bias. Is homogenized milk liberal bias? Or homonyms? Homophones? I've already reverted your addition to the article once, so I won't do it again just yet, but please consider removing or modifying it yourself.--JustinD 19:32, 24 February 2012 (EST)
- There is a crucial difference between your examples and my claim. A homophone describes two words sounding the same but being different. Bat is not a homophone with bat, that doesn't make sense. Saying wind and wind are homophones acknowledges that they sound the same but are different words. A homomorphism allows groups that are different, like Z_2xZ_2 and the Klein four group, to be treated as equal. Additionally the global warming obsession is prolific. I didn't mean my writing to sound flippant, and perhaps its tone can be improved, but it was certainly not meant as a joke.
- I'm not sure I see the "crucial difference" you're seeing. I don't know what you mean by saying that homomorphisms "allow[] groups that are different . . . to be treated as equal." What do you mean by "treated as equal"? Obviously, if a homomorphism exists between two groups it shows that there are certain structural similarities between the two groups, but this hardly means that they are equal. The fact that 124 and 490 are both even shows that there are certain similarities between them (namely that each includes 2 in its prime factorization), but that doesn't mean we treat them as equal and it certainly isn't evidence that evenness is the result of some sort of liberal bias. Also, I think you have your examples backwards. Bat (animal) is a homophone with bat (sports) because both are pronounced the same but have different meanings. Wind (air flow) is not a homophone with wind (watches) because the pronunciation differs. They are, however, homographs. --JustinD 01:23, 26 February 2012 (EST)
- Haha you are absolutely right, my apologies. I thought I had picked a word specifically with no homophones. Allow me to elaborate: saying that 124 and 490 are both even emphasizes similarities which is fine. But consider a statement like "there is only one group of order 3." There are clearly many, because you can define one on any set with 3 elements. Nevertheless, you will never hear discussion of the many different groups of order 3, they are all lumped together because of homomorphisms. Compare this with the professor value of refusing to distinguish between men and women. To say men and women are both children of God is to discuss similarities while acknowledging differences, as in saying 124 and 490 are both even. To say men and women are basically the same, as universities today do, is consistent with saying that groups are essentially the same. I hope that clarifies what I was struggling to say before. --Bogart12
- They key point you are missing, however, is that in many, many subjects, such as in mathematical aptitude, there is no functional difference between male and female. So yes, in many situations, women and men are essentially the same.KenShomer 15:15, 26 February 2012 (EST)

- Haha you are absolutely right, my apologies. I thought I had picked a word specifically with no homophones. Allow me to elaborate: saying that 124 and 490 are both even emphasizes similarities which is fine. But consider a statement like "there is only one group of order 3." There are clearly many, because you can define one on any set with 3 elements. Nevertheless, you will never hear discussion of the many different groups of order 3, they are all lumped together because of homomorphisms. Compare this with the professor value of refusing to distinguish between men and women. To say men and women are both children of God is to discuss similarities while acknowledging differences, as in saying 124 and 490 are both even. To say men and women are basically the same, as universities today do, is consistent with saying that groups are essentially the same. I hope that clarifies what I was struggling to say before. --Bogart12

- I'm not sure I see the "crucial difference" you're seeing. I don't know what you mean by saying that homomorphisms "allow[] groups that are different . . . to be treated as equal." What do you mean by "treated as equal"? Obviously, if a homomorphism exists between two groups it shows that there are certain structural similarities between the two groups, but this hardly means that they are equal. The fact that 124 and 490 are both even shows that there are certain similarities between them (namely that each includes 2 in its prime factorization), but that doesn't mean we treat them as equal and it certainly isn't evidence that evenness is the result of some sort of liberal bias. Also, I think you have your examples backwards. Bat (animal) is a homophone with bat (sports) because both are pronounced the same but have different meanings. Wind (air flow) is not a homophone with wind (watches) because the pronunciation differs. They are, however, homographs. --JustinD 01:23, 26 February 2012 (EST)

- If that statement were true, then why are the top achievers on difficult math contests (such as the Putnam exam) more than 90% male, and less than 10% female?--Andy Schlafly 16:32, 26 February 2012 (EST)\

- I think the problem is a lack of imprecision when using words like "same" or "equal". In mathematics such terms have very precisely defined meanings and so to say that all groups of order three are the same or are equal (or, equivalently, to say that "there is only one group of order 3") is not to say that all such groups are the same in all respects (obviously, this isn't true or they would all have the same name/description and we wouldn't even doubt there were more than one such group), but instead only says that all such groups behave similarly in all the ways that are (currently) important to mathematicians. When dealing with real world situations like mathematical aptitude and gender, it's much easier to speak imprecisely (either mistakenly or maliciously) and thus much more plausible that some suggested equivalences are the result of liberal bias and not some underlying similarities. I just don't see how that is possible, however, in the realm of mathematics, at least with respect to homomorphisms.
- This is getting a bit off topic, but if Andy and you are right and (liberal?) universities improperly equate the aptitude of men and women (by analogy, posit a homomorphism between men and women), we shouldn't conclude that the positing of all equivalences is liberal bias (by analogy, that homomorphisms are the result of liberal bias), but instead should conclude that universities are mistaken and that no such equivalence exists in this case (by analogy, there is no homomorphism between a group of order 3 and a group of order 4, say).--JustinD 17:01, 26 February 2012 (EST)

## Examples of Liberal Math

The purported proof of Fermat's Last Theorem would be an example of liberal math.--Andy Schlafly 16:48, 26 February 2012 (EST)

- This may quickly move outside my area of understanding, but could you clarify this at all? Is the concern the use of the axiom of choice and/or non-ZF axioms? I've read our article and vaguely remember a book I read in high school, but other than the use of some non-standard techniques, I wasn't aware there was any serious doubt as to the validity of the proof. --JustinD 17:10, 26 February 2012 (EST)