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I read two comments of Lang that basically places algebra over other math subjects. One of this comments is on his calculus book preface (see Remark 1 below); I am not finding his other comment, but it was an interaction he had with someone at Yale´s math department coffee break and is written somewhere. It basically says that algebra is superior to any other math subject, if I recall it correctly. My problem with his comments is that I have no idea what he is talking about. They baffle me. I suppose I stand in the exact opposite from his viewpoints. For me, you can´t compare the applicability and importance of analysis and differential equations to that of modern algebra. Hence:

1) Is there an article of Lang explaining in detail his viewpoints? 2) or, do you know what is his point?

Remark 1) On the preface of his Calculus book, Serge Lang basically says that he thinks bright students may benefit more in studying abstract algebra before or at the same time they learn calculus. My book is in portuguese, so I give a rough translation: " when I was a student I didn´t like calculus nor analysis. I probably woundn´t like this book either... [today I think] that calculus and analysis are overestimated, with a loss to algebra, mainly because of historical accidents." He goes on to say that a beginner course in algebra should consist in a study of vector spaces and groups, that this is independent of calculus and has important applications to other fields, and that some people prefer this material over calculus. He also says that there is no reason someone should be forced to study calculus before algebra. This being true specially for the most talented students.

Remrak 2) "I remember one time when I was a grad student, I was standing next to him at tea while he was explaining to a first-year that analysis is just “number theory at infinity”. I said Come on, that’s not true. He immediately turned up the volume, challenging me to stop bullshitting and give an example. I said OK, p-adic analysis, and then walked away. But I’ve always wished I had stayed to see what his reaction would have been. We need more trouble makers like him. ", from the site Not Even Wrong.

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    It's an interesting question. But nothing you have quoted by Lang gets anywhere near claiming the **superiority** of algebra. Rather, he is questioning the primacy of analysis in the mathematical curriculum and the fact that one must wade through it to get to other branches of mathematics. From my pure mathematician's perspective, I agree that this seems to be largely due to historical inertia: one could equally well learn algebra first, or some topology, or number theory, or... (Like many other people, I did learn some number theory before I studied university-level mathematics.)2012-03-09
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    What I wrote is perhaps very long and you missed that the "superiority" part was expressed in his Yale common room exchange. Unfortunately, I did not find it.2012-03-09
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    $@$Espinho: I am responding to what you directly quoted. If you are going to ask a question about what someone (especially no someone no longer living) said, it seems only reasonable to supply a direct reference. Otherwise we're just trafficking in rumors and hearsay.2012-03-09
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    I would advise extreme caution about "philosophical" comments by celebrated mathematicians. Some of them, like Lang and Arnold, delight in controversies and provocative statements. I've heard both make outrageous claims that didn't strike me as particularly convincing, to put it mildly. Fortunately other mathematicians show remarkable restraint and totally abstain from pontificating, Deligne being the ultimate example of such wise behaviour.2012-03-09
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    @Pete, I am not traficking on anything. My question is quite to the point: is there an article **of Lang** explaning his viewpoint on algebra, or anyone that **actually knows** about his viewpoint on algebra. I gave the general direction of what I want to know more - and then asked for a reference or source to go further. Altough I welcome any side remark and personal impression, what I asked for is some insight into **Lang´s** mental math map. In particular, I doubt that he would think that topology could came before analysis.2012-03-13
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    @Espinho: Your title is **Serge Lang's remarks on the superiority of algebra**. But you haven't given any documentation of this whatsoever. You've only alluded to a coffee break conversation at which you were not present: that's pretty much the definition of hearsay. Further, it is not really clear to me that insight into a deceased mathematician's mental math map is on topic for this site: how are the rest of us to judge the correctness of such an answer? Finally, as to what Lang thought...he had (and documented) a lot stranger thoughts than topology before analysis, to be sure.2012-03-13
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    @Pete: if you have problems with this question, bring it to meta. Else, provide the references I asked for (the point of this question, read (1) on the question), or abstein from expressing your personal opinions. This is not what I am asking for, and it just derails the question to bickering.2012-03-13
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    Besides, you misquoted the title of my question. It is Serge Lang´s remarks on the superiority of algebra. **What it actually means?**2012-03-13
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    @Espinho da Flor: I *quoted* the part of your title which was relevant to my point. I don't see where I have expressed any "personal opinions". Recently I voted to close your question; you can take the above comments as an explanation of why. In any case, you may have noticed that your question has not received the kind of answer you are looking for. If you are still interested, you might want to modify it somehow...2012-03-13

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