Upvoted That was strangely free of mathematics but heck of a sales pitch for the subject and the cutting edge of research. It feels like the front page of a road map that shows you which page the other maps are on. Now I know that there are these other pages and each page represents a place I haven't been and want to visit.
In non-technical jargon, one can think of the dimension of a manifold in the following way: if you were an ant lying on any point of the manifold you would feel like you live in a space of ten dimension, i.e., you would be able to move in 10 different directions, all perpendicular to each other. For example, if you are a tiny ant on a sphere (or a flat-Earther) you would feel like you live in a space of two dimensions.
@@raguram3030 Well it can't exist in our three-dimensional world, no, but on paper it can. Mathematicians work in dimensions higher than 3 all the time. There are actual applications of this to concrete real world problems, it's not just mathematicians being very abstract for the sake of it. For example, if you gather some data that has 4 independent parameters, then you can think of each parameter as one dimension, and your piece of data lives in a space of 4 dimensions.
7:26 Nicholas Bourbaki: was not a physical person but a group of influential mathematicians. 5 mathematicians (Henri Cartan, Claude Chevalley, Jean Delsarte, André Weil, and Jean Dieudonné) formed a group to not only repair the fractured community but to set the curriculum for the next 2 decades. However, they didn’t realize they were setting in motion a multi-generational endeavor to rethink the foundations of mathematics. They also delighted and annoyed the rest of the mathematical community along the way. They would soon comically name their group after Charles-Denis Bourbaki, a French general famous for his spectacular failures during the Franco-Prussian War. Nicolas is thought by some to refer to St. Nicolas, perhaps suggesting the group knew the gifts they were about to bring to the struggling mathematics community.
I left pure mathematics within five years of finishing my Ph.D in the early 70s. I consider those spending their entire careers in this math fantasy world to be with stunted life maturation. Some describe them as useless, I categorize them as chess players. There’s a lot of self gratification in that group.
As far as i can understand , nothing has been added to geometry . What bites me is the sentence " .... changed geometry forever " , from the mouth of Abel Committee representative ! Shame on you , that think , world is west , and Greco- waspish people were and are the only Noble ones !
@@goenzoy712 first thing first check your grammar ! Next , you sure know who i am ( institutionaly being watched ) , so i dont think , there is any need for i replying to your comment !
This was so enlightening
who are you ?
Upvoted
That was strangely free of mathematics but heck of a sales pitch for the subject and the cutting edge of research.
It feels like the front page of a road map that shows you which page the other maps are on. Now I know that there are these other pages and each page represents a place I haven't been and want to visit.
excellent!
Amazing
25:22 what does he ( what do you ) mean , dimension ? when he ( you ) say 10-dimension ?
In non-technical jargon, one can think of the dimension of a manifold in the following way: if you were an ant lying on any point of the manifold you would feel like you live in a space of ten dimension, i.e., you would be able to move in 10 different directions, all perpendicular to each other.
For example, if you are a tiny ant on a sphere (or a flat-Earther) you would feel like you live in a space of two dimensions.
@@danieltolosa6763 Does such a thing : 10 dimensions,directions each perpendicular to each other exist? It can't logically.
@@raguram3030 Well it can't exist in our three-dimensional world, no, but on paper it can. Mathematicians work in dimensions higher than 3 all the time. There are actual applications of this to concrete real world problems, it's not just mathematicians being very abstract for the sake of it.
For example, if you gather some data that has 4 independent parameters, then you can think of each parameter as one dimension, and your piece of data lives in a space of 4 dimensions.
7:26 Nicholas Bourbaki: was not a physical person but a group of influential mathematicians. 5 mathematicians (Henri Cartan, Claude Chevalley, Jean Delsarte, André Weil, and Jean Dieudonné) formed a group to not only repair the fractured community but to set the curriculum for the next 2 decades. However, they didn’t realize they were setting in motion a multi-generational endeavor to rethink the foundations of mathematics. They also delighted and annoyed the rest of the mathematical community along the way.
They would soon comically name their group after Charles-Denis Bourbaki, a French general famous for his spectacular failures during the Franco-Prussian War. Nicolas is thought by some to refer to St. Nicolas, perhaps suggesting the group knew the gifts they were about to bring to the struggling mathematics community.
And for a long while the names were kept secret!
I would guess that prof Hopkins would know that
I left pure mathematics within five years of finishing my Ph.D in the early 70s. I consider those spending their entire careers in this math fantasy world to be with stunted life maturation. Some describe them as useless, I categorize them as chess players. There’s a lot of self gratification in that group.
What do you mean by stunted life maturation? Did you leave or had to leave academia?
Could you explain more?
As far as i can understand , nothing has been added to geometry . What bites me is the sentence " .... changed geometry forever " , from the mouth of Abel Committee representative ! Shame on you , that think , world is west , and Greco- waspish people were and are the only Noble ones !
What exactly is the problem off course Dennis Sullivan did work on geometry
@@goenzoy712 first thing first check your grammar ! Next , you sure know who i am ( institutionaly being watched ) , so i dont think , there is any need for i replying to your comment !
@@amiraslkhalili5638 check your grammer