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Mathematicians that also were good teachers?

  1. Nov 3, 2016 #1
    I will try to explain what I mean.

    There are scientists that publish their professional work in a manner suitable only for the expert, and it is really difficult for a beginner to follow what they have published.

    But there are some of them that write their scientific work in a way that is very comprehensive. For example Leonard Euler, Lagrange, Klein all wrote in a nice way.

    Do you know other mathematicians that published like those I mentioned?

    I guess you understand what I mean.

    The oppositte to what I am talking about is Newton or Gauss, both are genious and discovered extremely difficult theorems but when they published something (when they did) they didn't make any effort to make thinks easy to understand for the begginer.
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  3. Nov 3, 2016 #2


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    Publications are always written for experts. Early work is more accessible today simply because there was not that much knowledge that could be necessary as prerequisite. There are publications easy to read for experts and publications harder to read for experts, but if you give a recent publication to someone with no background in the field they will be lost in either case.

    In addition to writing papers, scientists can write articles for different target audiences - those can be much easier to understand.
  4. Nov 3, 2016 #3


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    Do you have an example by chance? I haven't read anything from these gentlemen before.
  5. Nov 3, 2016 #4
    Yes, you are right.

    Maybe I should have said if they have written articles or books to teach math.

    Euler---> Algebra, Introduction analysis infinitorum, differential calculus, integral calculus

    Lagrange--> Analytical Mechanics, I know it is not an "easy read" but Lagrange makes the effort to talk about the entire history of every concept introduced, I like that and shows clearly he really wants you to understand what he is going to do.

    Felix Klein-- Development of Mathematics in the 19th century, Elementary Mathematics from advanced Standpoint: Arithmetic, ALgebra, Analysis.

  6. Nov 7, 2016 #5


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    in my experience different students have different opinions on who is or is not a good teacher. I think what that statement means is that the teacher spoke clearly to the student who is making the evaluation. So being a good teacher is a relative phenomenon involving both teacher and student. I for example do not care at all for Klein's famous volumes on Elementary mathematics from an advanced standpoint, finding them more opinionated than instructive, but find Gauss's Disquisitiones quite insightful. I also do not recommend Euler's famous and much praised book Analysis of Infinities as a learning source, although it is interesting, but I do like his outstanding algebra book, which really makes an attempt to explain thoroughly.

    Many fine mathematicians are also excellent teachers in person or in class, even if they never take time to write expository works. Raoul Bott for example was a wonderful lecturer, but to me his monographs and papers are not all that readable, with the exception of the fine book Differential forms in algebraic topology, perhaps for the excellent reason that it was actually written by his very lucid collaborator Loring Tu.
  7. Nov 7, 2016 #6
    Disquisitiones is a very difficult book, but very important, since it was used by Galois to found Group Theory (and many other things I know), I tried to follow this historical event but found it very difficult to understand.

    Why don't you recommend Euler's book on Infinities?

    I have read his algebra and I agree is a wonderful book.
  8. Dec 5, 2016 #7
    Cornelius Lanczos was a famous mathematician and also had a reputation as an excellent lecturer. He was one of Einstein's math assistants for some time. His most famous book is Applied Analysis.

    His book The Variational Principles of Mechanics is one of my personal favorites. It's beautiful.

    He wrote several other books, including one on Einstein. Lanczos said that even though he worked in applied mathematics his favorite subject was relativity theory.

    For something ancient, there is Euclid. I learned geometry in high school from a standard text. It was my favorite subject at the time. The textbook was adequate, but nothing to write home about. But when I studied Euclid on my own from Heath's edition, it was an awe inspiring experience. Although I admit I skipped most of Heath's notes. Personally I would require young students to study Euclid, just like they did in the old days. I would not use Heath however. I would use a good 19th or early 20th century version that is designed for use in schools. You can find them quite easily on archive.org. Anyway I suppose one could say that Euclid was the supreme math teacher of all time.

    Lectures on Elementary Mathematics by Lagrange is an 18th century gem.
    Last edited: Dec 5, 2016
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