9 ms·

Working mathematician here -- 1. Langlands is indeed a great mathematician, whose work has been enormously influential. 2. Most of us aren't all that eccentri

Working mathematician here -- 1. Langlands is indeed a great mathematician, whose work has been enormously influential. 2. Most of us aren't all that eccentric. He wrote his paper in Russian, a language which he (presumably) does not natively speak, apparently just for the heck of it? That's just weird. Most of the mathematicians I know, including the most influential ones, are relatively normal people. And they want as many people to read their work as possible, and don't throw up artificial roadblocks. (Most working mathematicians cannot read or write Russian.) 3. There is not that big of a conflict between pure and applied mathematicians. (Except when they're competing for money, or trying to decide whom to hire in their departments.) The most common attitude among pure mathematicians is: we work on mathematical questions for their own sake, and don't think too much about applications to the "real world" -- but we are happy if it is brought to our attention that such applications exist.

thanatropism 8y ago
In the library here they have a book called "Russian for Mathematicians".
- Double_a_92 8y ago
  Maybe if you need to look up some soviet era literature?
  - thanatropism 8y ago
    The weird thing is that while modern-style mathematics with lots of display maths is supposedly to be less dependent on subtleties of text (as opposed to the arguments of old-style topology books like Munkres, which use display equations a lot less and pack a lot of oomph into dense paragraphs with inlined symbols). But mathematical terminology actually changes a lot -- it's enough to open a page in Wikipedia and switch languages to see. A "field" in the algebraic sense (the real numbers are a "complete ordered field") in portuguese is corpo, but vector fields are campos. And both in Portuguese and French, manifolds and algebraic varieties are the same word (variedades/varietés). Maybe if one starts graphing these separations and collisions across many languages some structure emerges -- obviously no one mixes up algebraic fields with physics fields, but the manifold/variety collision hints at some historical commonality that matters for expressive power at the level of a Grothendieck trying to say something sweeping about the entire landscape of mathematics.
    - Koshkin 8y ago
      To be fair, a ‘campo’ is also a ‘corpo’ that is commutative.
      - thanatropism 8y ago
        An observation that illustrates my point.
        deleted 8y ago
        [deleted]
        deleted 8y ago
        [deleted]
      - metalsteady 8y ago
        Can you elaborate? Vector spaces and fields differ in how they define multiplication. In the former, we multiply vectors with scalars while in the latter we multiply two scalars. Also, vector fields are functions from points to vectors whereas field is an algebraic structure.
        thanatropism 8y ago
        I'm not entirely sure what he meant, but the flow maps of vector fields are semigroups. If irreversible, they're groups. And a field is like a group and a ring over the same set, right?
        metalsteady 8y ago
        A group is a set with a single operation defined on it that abides by certain axioms. A field is a set with two operations defined on it. But the field operations must abide by more axioms than a group operation. While vector spaces and fields are very similar (two operations, similar number of axioms), vector spaces are defined over fields (for example, an element cv is defined where v is a vector and c is a scalar) while fields are not defined over anything -- they are just a structure with two operations and a number of axioms (there's no element cv in a field, but it does have an element c_1 * c_2 where c_i is a scalar). That said, vector field is a different object. It's a function. Likely named so by physics people while the structures like group/ring/field/etc were named by math folk. I have no idea what flow maps of vector fields are, but if you give me their definition, it'd be trivial to check if they form a semigroup under a certain operation: we'll just check it for associativity. To get a hang of this stuff I recommend the following books: Book of Proof by Richard Hammack (tools of the trade) Linear Algebra by Kuldeep Singh (rigorous tutorial: combines the rigor of a textbook and the ease of use of tutorial) Abstract Algebra by the Dos Reis (rigorous tutorial) Real Analysis by Lara Alcock (this books makes the rigorous definition of sequences trivial) Real Analysis by Jay Cummings (contains much more info than the one above and is very similar in spirit) Real Analysis by Rafi Grinberg (takes you from reals to Euclidean Spaces and Metric Spaces) After that you ccan start reading intro level mathematical physics books to get an easy intro to differential geometry, manifolds and analysis in abstract spaces. Once you get an intuitive hang of this stuff, you can come back to the more brutal pure math setting. Here, I like Modern Math Physics by Peter Szekeres. It's gentle and more about geometry and less about analysis.
aquadrop 8y ago
According to Wikipedia: " Langlands likes to learn foreign languages, both for better understanding of foreign publications on his topic and just as a hobby. He speaks French, Turkish, German and Russian". I'd say it's not _that_ weird, if he likes foreign languages, to combine both his passions and write one paper in Russian :) Also considering there are actually a lot of mathematicians who can read and write Russian.
- impendia 8y ago
  A half-remembered, and possibly apocryphal, story which another mathematician once told me: Langlands was once invited to lecture in France, and he chose to give his talk in French. Evidently his accent was not all that good, and the audience found it a bit painful. Jean-Pierre Serre, one of the leading mathematicians of the 20th century, and a Frenchman, was attending the lecture that day. He interrupted to ask a question, in English. Declining to take the hint, Langlands answered in French and carried on with his lecture.
  - thanatropism 8y ago
    Frenchmen are legendarily intolerant of badly-spoken French. This was a recurring theme in my couple of years as a student at Alliance Française - when in France (most people hoped to go to college or grad school there) if you're not solid don't even try. In Brazil people will be glad you're trying and try to speak slowly in return.
    - huhtenberg 8y ago
      Speaking bad French to French people helps them to suddenly remember that they also speak English.
      - hprotagonist 8y ago
        German has a similar effect, too.
    - celticninja 8y ago
huhtenberg 8y ago
Presumably that's the paper in Russian - https://publications.ias.edu/sites/default/files/iztvestiya_3.pdf https://publications.ias.edu/sites/default/files/iztvestiya_... It's understandable, but with lots of grammatical, spelling and stylistic mistakes. Basically it reads like something Google Translate would produce.
- schoen 8y ago
  He has a discussion at the very end (on the last two pages) about his decision to write in Russian, in which he acknowledges that he may not have done very well. Google Translate's version of the final paragraph: > This article is a consequence of two pushes, first of all, an attempt to understand the nature of the geometric theory, to form a clear idea about the difference between it and the arithmetic theory and their similarity. Here I think I was successful, although I do not argue a little. Secondly, I wanted to significantly improve my knowledge of Russian. Here I had only limited success. For me, Russian is on a completely different level than the two foreign languages with which I am familiar, French and German. As I noted above, Russian is much more difficult than I appreciated, even more than Turkish, another language in which I have a limited but hard-to-work ability. Therefore, my efforts and the efforts of friends and acquaintances who encouraged me as I wrote this article had limited success. I am still pleased that, despite my age, I do not regret either the time or the effort that I have given her.

thanatropism 8y ago

In the library here they have a book called "Russian for Mathematicians".

Double_a_92 8y ago
Maybe if you need to look up some soviet era literature?
- thanatropism 8y ago
  The weird thing is that while modern-style mathematics with lots of display maths is supposedly to be less dependent on subtleties of text (as opposed to the arguments of old-style topology books like Munkres, which use display equations a lot less and pack a lot of oomph into dense paragraphs with inlined symbols). But mathematical terminology actually changes a lot -- it's enough to open a page in Wikipedia and switch languages to see. A "field" in the algebraic sense (the real numbers are a "complete ordered field") in portuguese is corpo, but vector fields are campos. And both in Portuguese and French, manifolds and algebraic varieties are the same word (variedades/varietés). Maybe if one starts graphing these separations and collisions across many languages some structure emerges -- obviously no one mixes up algebraic fields with physics fields, but the manifold/variety collision hints at some historical commonality that matters for expressive power at the level of a Grothendieck trying to say something sweeping about the entire landscape of mathematics.
  - Koshkin 8y ago
    To be fair, a ‘campo’ is also a ‘corpo’ that is commutative.
    - thanatropism 8y ago
      An observation that illustrates my point.
      - deleted 8y ago
        [deleted]
      - deleted 8y ago
        [deleted]
    - metalsteady 8y ago
      Can you elaborate? Vector spaces and fields differ in how they define multiplication. In the former, we multiply vectors with scalars while in the latter we multiply two scalars. Also, vector fields are functions from points to vectors whereas field is an algebraic structure.
      - thanatropism 8y ago
        I'm not entirely sure what he meant, but the flow maps of vector fields are semigroups. If irreversible, they're groups. And a field is like a group and a ring over the same set, right?
        metalsteady 8y ago
        A group is a set with a single operation defined on it that abides by certain axioms. A field is a set with two operations defined on it. But the field operations must abide by more axioms than a group operation. While vector spaces and fields are very similar (two operations, similar number of axioms), vector spaces are defined over fields (for example, an element cv is defined where v is a vector and c is a scalar) while fields are not defined over anything -- they are just a structure with two operations and a number of axioms (there's no element cv in a field, but it does have an element c_1 * c_2 where c_i is a scalar). That said, vector field is a different object. It's a function. Likely named so by physics people while the structures like group/ring/field/etc were named by math folk. I have no idea what flow maps of vector fields are, but if you give me their definition, it'd be trivial to check if they form a semigroup under a certain operation: we'll just check it for associativity. To get a hang of this stuff I recommend the following books: Book of Proof by Richard Hammack (tools of the trade) Linear Algebra by Kuldeep Singh (rigorous tutorial: combines the rigor of a textbook and the ease of use of tutorial) Abstract Algebra by the Dos Reis (rigorous tutorial) Real Analysis by Lara Alcock (this books makes the rigorous definition of sequences trivial) Real Analysis by Jay Cummings (contains much more info than the one above and is very similar in spirit) Real Analysis by Rafi Grinberg (takes you from reals to Euclidean Spaces and Metric Spaces) After that you ccan start reading intro level mathematical physics books to get an easy intro to differential geometry, manifolds and analysis in abstract spaces. Once you get an intuitive hang of this stuff, you can come back to the more brutal pure math setting. Here, I like Modern Math Physics by Peter Szekeres. It's gentle and more about geometry and less about analysis.

aquadrop 8y ago

According to Wikipedia: " Langlands likes to learn foreign languages, both for better understanding of foreign publications on his topic and just as a hobby. He speaks French, Turkish, German and Russian". I'd say it's not _that_ weird, if he likes foreign languages, to combine both his passions and write one paper in Russian :) Also considering there are actually a lot of mathematicians who can read and write Russian.

impendia 8y ago
A half-remembered, and possibly apocryphal, story which another mathematician once told me: Langlands was once invited to lecture in France, and he chose to give his talk in French. Evidently his accent was not all that good, and the audience found it a bit painful. Jean-Pierre Serre, one of the leading mathematicians of the 20th century, and a Frenchman, was attending the lecture that day. He interrupted to ask a question, in English. Declining to take the hint, Langlands answered in French and carried on with his lecture.
- thanatropism 8y ago
  Frenchmen are legendarily intolerant of badly-spoken French. This was a recurring theme in my couple of years as a student at Alliance Française - when in France (most people hoped to go to college or grad school there) if you're not solid don't even try. In Brazil people will be glad you're trying and try to speak slowly in return.
  - huhtenberg 8y ago
    Speaking bad French to French people helps them to suddenly remember that they also speak English.
    - hprotagonist 8y ago
      German has a similar effect, too.
  - celticninja 8y ago

huhtenberg 8y ago

Presumably that's the paper in Russian - https://publications.ias.edu/sites/default/files/iztvestiya_3.pdf https://publications.ias.edu/sites/default/files/iztvestiya_... It's understandable, but with lots of grammatical, spelling and stylistic mistakes. Basically it reads like something Google Translate would produce.

schoen 8y ago
He has a discussion at the very end (on the last two pages) about his decision to write in Russian, in which he acknowledges that he may not have done very well. Google Translate's version of the final paragraph: > This article is a consequence of two pushes, first of all, an attempt to understand the nature of the geometric theory, to form a clear idea about the difference between it and the arithmetic theory and their similarity. Here I think I was successful, although I do not argue a little. Secondly, I wanted to significantly improve my knowledge of Russian. Here I had only limited success. For me, Russian is on a completely different level than the two foreign languages with which I am familiar, French and German. As I noted above, Russian is much more difficult than I appreciated, even more than Turkish, another language in which I have a limited but hard-to-work ability. Therefore, my efforts and the efforts of friends and acquaintances who encouraged me as I wrote this article had limited success. I am still pleased that, despite my age, I do not regret either the time or the effort that I have given her.