A mathematician thinks aloud
In a previous post I discussed the topic of conjugacy of vector fields on , concentrating on the case where the vector field and the conjugation are smooth, i.e. . In what follows I will continue to consider smooth vector fields but allow the conjugations to have only finite differentiability. In the last post I [ ]
A vector field on the real line can be written in the form and in this sense it is equivalent to a function. From a geometrical point of view it is different from a function because it has a different transformation behaviour under diffeomorphisms. If a function is transformed using a diffeomorphism to get a [ ]
In mathematics definitions play a central role. Before starting a mathematical discussion it is necessary to fix necessary definitions. When mathematicians discuss other subjects they also often want to know the definitions of the terms being used and this is often difficult. It can already be difficult in physics and of course it is much [ ]
Here I consider a system of ODE or equivalently a vector field on an open subset of Euclidean space. The question is in what way it can be simplified by a coordinate transformation. This leads to the theory of normal forms. My main source for what follows is the book Qualitative Theory of Planar Differential [ ]
These days people often talk about how society is divided when it somes to various political issues. What is remarkable is a certain correlation. People who are on the same side in the case of one political issue often find themselves on the same side in the case of an apparently unrelated issue. This is [ ]
Yesterday I heard a personal account of the aftermath of a terrorist attack from Sarah Levy. This made me think of an experience of my own. In 1995 I was living in Bures-sur-Yvette near Paris and working at the Institut des Hautes Etudes Scientifiques. I used to frequently travel into Paris in the evenings to [ ]
I have just read the book The Parasitic Mind by Gad Saad. Its subject is political correctness and the decline of rationality and freedom of speech in the West. The author was born in Lebanon and escaped with his Jewish family to Canada as conditions in Lebanon became unacceptable for them. His parents made the [ ]
As I mentioned in a post I wrote a long time ago the writer I admire most is Marcel Proust. This is something which has remained constant for very many years. In fact a long time ago he was part of a trinity in my personal literary heaven together with Virginia Woolf and James Joyce. [ ]
I have just attended the conference mentioned in the title of this post. My general impression is that mathematics as I understand it is being more and more excluded by on the one hand masses of data and on the other hand by reliance on computers related to machine learning, AI etc. A cynical formulation [ ]
I was able to leave hospital on 28.2 (in my last post I wrongly wrote 28.4) and there is nothing spectacular to report there. There was another inaccuracy in what I wrote in the last post. The oral antibiotic I am taking now is amoxicillin, not penicillin I got all my penicillin intravenously. What [ ]