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I have a differential equations student who said the following (I'm paraphrasing of course):

A long time ago, my math teacher told me that when I finished differential equations, I would be able to read Einstein's paper on relativity. I'm really excited for that.

I went and looked at a paper of Einstein's, but the one I found didn't seem like a good idea. I'd like to provide a suitable substitute, and I really like this form of motivation: just finish this series of classes, and you will understand [famous paper or idea].

Have you ever taken an undergraduate through a famous text in this way? Can differential equations students really look forward to anything like this? I'm not really asking specifically about Einstein.

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  • $\begingroup$ How about changing the title to "can we motivate undergraduates by saying they will be able to read certain famous papers?" $\endgroup$ – Mark Fantini Sep 4 '14 at 18:08
  • $\begingroup$ @MarkFantini A good point; fixed. $\endgroup$ – Chris Cunningham Sep 4 '14 at 21:01
  • $\begingroup$ I have definitely motivated myself in this way. In fact, my knowledge of differential geometry would not be half as good as it is today if I didn't learn about the Riemann Curvature tensor just so I could understand general relativity. It is quite far from my research interests, but I was motivated just by the need to increase my general awareness of how our universe operates. $\endgroup$ – Steven Gubkin Sep 4 '14 at 21:24
  • $\begingroup$ Spivak's sequence of books on differential geometry does exactly this as one of the books (book II, I think) contains papers by Gauss (and Riemann?). $\endgroup$ – Loop Space Sep 4 '14 at 21:30
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    $\begingroup$ The paraphrased student indicates that the answer to your title question is yes. I suppose ideal answers would detail how such a process was undertaken (and be more practice-based than theory-based)? I can say that I did this as the student with Dwork's proof of the rationality of the Weil Conjectures; this led me to read Koblitz's graduate text on p-adic analysis and, at a more accessible level, Gouvea's undergraduate text on p-adic numbers. To me, that suggests not only the approach of "finish this then read X," but rather to try to read X directly and, when confused, read simpler works. $\endgroup$ – Benjamin Dickman Sep 5 '14 at 1:27
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Surely some undergraduates will respond to the motivation of reading famous papers, but I'd usually recommend motivating them with ideas or applications instead.

1) What they expect in the paper may not be in the paper. Your student probably wants to see $E=mc^2$ from the time Einstein understood this. They may be disappointed to learn that Einstein's closest paper from 1905 said only "Gibt ein Korper die Energie L in Form von Strahlung ab, so verkleinert such seine Masse um $L\,/\,V^2$", or "if a body gives off the energy $L$ in the form of radiation, its mass diminishes by $L\,/\,V^2$."

2) Many famous papers are hard to read. Often the first presentation of an idea is messy. Often after an idea is recognized as noteworthy, people start talking about the idea in a different context, so that the original context seems odd and difficult to understand. What was common knowledge at the time the paper was written may not be common knowledge now, or may not be known to the student.

3) Even if they succeed in reading the paper, they may not be able to answer basic questions like: What was new in this paper? What similar things were known beforehand? Answering those questions requires studying the historical context, which is hard. Most profs would have difficulty providing accurate historical context for most famous mathematical papers.

However: if they want to read some historical papers in an area (rather than one particularly famous paper), there are lots of sourcebooks with accessible selections and helpful introductions. I recommend those sourcebooks for studying the history of math, rather than fixating on one famous paper.

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  • $\begingroup$ +1: Nice answer! $\endgroup$ – Mark Fantini Sep 5 '14 at 10:03

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