The feedback by several of the mathematicians of “bird” type told me that this summary of some exchanges fits their mentality quite good. Actually, some of the remarks on poetry I made a few days ago in some other discussion here come directly from those feedbacks.
However, the distinction you draw between “birds” and procedure- or algorithm-mindedness is not so strict: You see this in the way they deal with QFT, leading to (among others) Kontsevich’s, Manin’s and Voevodsky’s previously posted thoughts comes directly from their acceptance that e.g. Feynman integrals are nice ideas, justifyed by their computational power, and that their deficient consistency a topic of minor importance (i.e. you don’t need a logical consistent th. physics, because your point of reference is the nature itself, whose consistency is not a reasonable issue; similar with the platonic world of mathematics). A close look to e.g. Manin’s and Kontsevich’s work shows that they are largely determined by computational issues.
Grothendieck is among those “giants of 20th century mathematics” a very special case, as one sees from the astounded admiration which one senses among those “giants” who met him personally. It is not surprising that Grothendieck thought of himself as “mutant” (after analysing his work and comparing it with that of others). And, as others around him with medical expertise observed, he was different, strangely similar to the novel figure Odd John. There is a very good talk by Yves Andre online and here an other great article by Herreman. A video of Scharlau’s talk (in english) at the IHES is here. It may be of interest that acc. to those who knew her, Grothendieck’s sister was a genius of comparable power.
And: Somehow my upvote of your post didn’t work, some of my links do not too in my QFT-AI post.
However, the distinction you draw between “birds” and procedure- or algorithm-mindedness is not so strict: You see this in the way they deal with QFT, leading to (among others) Kontsevich’s, Manin’s and Voevodsky’s previously posted thoughts comes directly from their acceptance that e.g. Feynman integrals are nice ideas, justifyed by their computational power, and that their deficient consistency a topic of minor importance (i.e. you don’t need a logical consistent th. physics, because your point of reference is the nature itself, whose consistency is not a reasonable issue; similar with the platonic world of mathematics). A close look to e.g. Manin’s and Kontsevich’s work shows that they are largely determined by computational issues.
I’ll have to think about this. Certainly there are examples both of bird/beaver hybrids and frog/beaver hybrids.
Grothendieck is among those “giants of 20th century mathematics” a very special case, as one sees from the astounded admiration which one senses among those “giants” who met him personally. It is not surprising that Grothendieck thought of himself as “mutant” (after analysing his work and comparing it with that of others). And, as others around him with medical expertise observed, he was different, strangely similar to the novel figure Odd John. There is a very good talk by Yves Andre online and here an other great article by Herreman. A video of Scharlau’s talk (in english) at the IHES is here. It may be of interest that acc. to those who knew her, Grothendieck’s sister was a genius of comparable power.
Thanks for the references which I had not seen before.
The feedback by several of the mathematicians of “bird” type told me that this summary of some exchanges fits their mentality quite good. Actually, some of the remarks on poetry I made a few days ago in some other discussion here come directly from those feedbacks.
However, the distinction you draw between “birds” and procedure- or algorithm-mindedness is not so strict: You see this in the way they deal with QFT, leading to (among others) Kontsevich’s, Manin’s and Voevodsky’s previously posted thoughts comes directly from their acceptance that e.g. Feynman integrals are nice ideas, justifyed by their computational power, and that their deficient consistency a topic of minor importance (i.e. you don’t need a logical consistent th. physics, because your point of reference is the nature itself, whose consistency is not a reasonable issue; similar with the platonic world of mathematics). A close look to e.g. Manin’s and Kontsevich’s work shows that they are largely determined by computational issues.
Grothendieck is among those “giants of 20th century mathematics” a very special case, as one sees from the astounded admiration which one senses among those “giants” who met him personally. It is not surprising that Grothendieck thought of himself as “mutant” (after analysing his work and comparing it with that of others). And, as others around him with medical expertise observed, he was different, strangely similar to the novel figure Odd John. There is a very good talk by Yves Andre online and here an other great article by Herreman. A video of Scharlau’s talk (in english) at the IHES is here. It may be of interest that acc. to those who knew her, Grothendieck’s sister was a genius of comparable power.
And: Somehow my upvote of your post didn’t work, some of my links do not too in my QFT-AI post.
I’ll have to think about this. Certainly there are examples both of bird/beaver hybrids and frog/beaver hybrids.
Thanks for the references which I had not seen before.