Donald Knuth
was born 80 years ago
10th January 1938
Donald Knuth is an American mathematician most famous for inventing the LATEX typesetting language.
@infinitymath
was born 80 years ago
10th January 1938
Donald Knuth is an American mathematician most famous for inventing the LATEX typesetting language.
@infinitymath
جدا از اینکه باوجود فیلترینگ کانال همواره فعال میباشد. ما تصمیم گرفتیم. تا صفحهای نیز در اینستاگرام داشته باشیم. باسپاس از همراهیتان. ما را در اینستاگرام نیز دریابید.
@infinitymath
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@infinitymath
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Abstract:
@infinitymath
The modern mathematical study of infinity began in the period 1879-84 with a series of papers by Cantor that defined the fundamental framework of the subject. Within 40 years the key ZFC axioms for Set Theory were in place and the stage was set for the detailed development of transfinite mathematics, or so it seemed. However, in a completely unexpected development, Cohen showed in 1963 that even the most basic problem of Set Theory, that of Cantor's Continuum Hypothesis, was not solvable on the basis of the ZFC axioms.
The 50 years since Cohen's announcement has seen a vast development of Cohen's method and the realization that the occurrence of unsolvable problems is ubiquitous in Set Theory. This arguably challenges the very conception of Cantor on which Set Theory is based.
However, during this same period, the detailed study of special cases of the Continuum Hypothesis led to a remarkable success. This was the discovery and validation of the determinacy axioms for Second Order Number Theory. The resulting theory is largely immune to Cohen’s method.
Almost 25 years before Cohen’s discovery of forcing, Gödel discovered the Constructible Universe of Sets and defined the axiom "V = L” which is the axiom that asserts that every set is constructible. This axiom implies the Continuum Hypothesis and more importantly, Cohen’s method of forcing cannot be used in the context of the axiom "V = L”. However the axiom "V = L" is false since it limits the fundamental nature of infinity. In particular the axiom refutes (most) strong axioms of infinity and it refutes the determinacy axioms of Second Order Number Theory.
A key question emerges. Is there an “ultimate” version of Gödel’s constructible universe yielding an axiom "V = Ultimate L" which retains the power of the axiom "V = L" for resolving questions like that of the Continuum Hypothesis, which is also immune against Cohen’s method of forcing, and yet which does not refute strong axioms of infinity? Such an axiom would necessarily provide the generalization of the determinacy axioms of Second Order Number Theory to the entire universe of sets.
Until recently there seemed to be a number of convincing arguments as to why no such ultimate L can possibly exist. But the situation is now changed.
Abstract:
@infinitymath
The modern mathematical study of infinity began in the period 1879-84 with a series of papers by Cantor that defined the fundamental framework of the subject. Within 40 years the key ZFC axioms for Set Theory were in place and the stage was set for the detailed development of transfinite mathematics, or so it seemed. However, in a completely unexpected development, Cohen showed in 1963 that even the most basic problem of Set Theory, that of Cantor's Continuum Hypothesis, was not solvable on the basis of the ZFC axioms.
The 50 years since Cohen's announcement has seen a vast development of Cohen's method and the realization that the occurrence of unsolvable problems is ubiquitous in Set Theory. This arguably challenges the very conception of Cantor on which Set Theory is based.
However, during this same period, the detailed study of special cases of the Continuum Hypothesis led to a remarkable success. This was the discovery and validation of the determinacy axioms for Second Order Number Theory. The resulting theory is largely immune to Cohen’s method.
Almost 25 years before Cohen’s discovery of forcing, Gödel discovered the Constructible Universe of Sets and defined the axiom "V = L” which is the axiom that asserts that every set is constructible. This axiom implies the Continuum Hypothesis and more importantly, Cohen’s method of forcing cannot be used in the context of the axiom "V = L”. However the axiom "V = L" is false since it limits the fundamental nature of infinity. In particular the axiom refutes (most) strong axioms of infinity and it refutes the determinacy axioms of Second Order Number Theory.
A key question emerges. Is there an “ultimate” version of Gödel’s constructible universe yielding an axiom "V = Ultimate L" which retains the power of the axiom "V = L" for resolving questions like that of the Continuum Hypothesis, which is also immune against Cohen’s method of forcing, and yet which does not refute strong axioms of infinity? Such an axiom would necessarily provide the generalization of the determinacy axioms of Second Order Number Theory to the entire universe of sets.
Until recently there seemed to be a number of convincing arguments as to why no such ultimate L can possibly exist. But the situation is now changed.
@infinitymath
Prof. Schindler is a well-known set theorist working mostly on inner model theory, an important subject in set theory.
Prof. Schindler is a well-known set theorist working mostly on inner model theory, an important subject in set theory.
From IPM's homepage:
TWAS, The Word Academy of Sciences, has elected Professor Siamak Yassemi as a Fellow for the advancement of science in developing countries from January 1, 2018. TWAS, The Word Academy of Sciences, has elected Professor Siamak Yassemi as a Fellow for the advancement of science in developing countries from January 1, 2018. He is the first Iranian Mathematician nominated for this Fellowship.
Siamak Yassemi is currently the Professor of Mathematics at the University of Tehran. He has been a Senior Researcher at the School of Mathematics of IPM since 2000. He had also been the head of the School of Mathematics, IPM, for two years during 2007-2009.
The main criterion for election as a TWAS Member is scientific excellence. Only those scientists who have attained the highest international standards and have made significant contributions to the advancement of science can be nominated.
@infinitymath
TWAS, The Word Academy of Sciences, has elected Professor Siamak Yassemi as a Fellow for the advancement of science in developing countries from January 1, 2018. TWAS, The Word Academy of Sciences, has elected Professor Siamak Yassemi as a Fellow for the advancement of science in developing countries from January 1, 2018. He is the first Iranian Mathematician nominated for this Fellowship.
Siamak Yassemi is currently the Professor of Mathematics at the University of Tehran. He has been a Senior Researcher at the School of Mathematics of IPM since 2000. He had also been the head of the School of Mathematics, IPM, for two years during 2007-2009.
The main criterion for election as a TWAS Member is scientific excellence. Only those scientists who have attained the highest international standards and have made significant contributions to the advancement of science can be nominated.
@infinitymath
The international Doctoral Training in Mathematical Sciences in Paris - MathInParis - Cofunded by Marie Sklodowska-Curie Actions offers 40 PhD fellowships within the framework of the European Horizon 2020 program "Marie Sklodowska-Curie Co-funding of Regional, National and International Programmes".
This project has received funding from the European Uninion's Seventh Framework Programme for research, technological development and demonstration under grant agreement n°754362
The main features of the program is to enhance the potential and future career perspective of young researchers by offering :
1- an extremely attractive place in FSMP network for international brilliant students planning to prepare a PhD in mathematics
2- a strengthened advising
3- a broadened support for career development
1. Paris is indeed the city with the highest concentration of professional researchers and one of the main nodes of international research with tremendous scientific opportunities both in academic and industrial framework. FSMP is the largest network of mathematical institutions in the world, gathering all thematics in applied and fundamental mathematics as well as theoretical computer science in interaction with other sciences. In this very stimulating inter-disciplinary environment FSMP has a strong partnership with industries and support joint PhD fellows.
2. MathsinParis students follow the doctoral training research, participate to laboratory and thematic seminars following the PhD thesis topic decided with their advisor*, they are followed by a tutor who has an external vision of the thesis progress and a external advisor* who organize a mandatory 2/3 months abroad internship. In addition FSMP support various activities as presentation of scientific progress in a « Restitution day» or the participation at least one research school for year.
3. MathInParis Doctoral program structures also a wide range of non research oriented activities as training session for professional insertion with help of Adoc Talent Management and attending specific day as MathInParis Conference (Journée carrière des mathématiques) or Maths Jobs Forum.
The FSMP team guarantees a dedicated assistance for visa issues, housing, health, banking, etc. Furthermore, fellows will be affiliated to the French Social Security during the stay.
@infinitymath
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This project has received funding from the European Uninion's Seventh Framework Programme for research, technological development and demonstration under grant agreement n°754362
The main features of the program is to enhance the potential and future career perspective of young researchers by offering :
1- an extremely attractive place in FSMP network for international brilliant students planning to prepare a PhD in mathematics
2- a strengthened advising
3- a broadened support for career development
1. Paris is indeed the city with the highest concentration of professional researchers and one of the main nodes of international research with tremendous scientific opportunities both in academic and industrial framework. FSMP is the largest network of mathematical institutions in the world, gathering all thematics in applied and fundamental mathematics as well as theoretical computer science in interaction with other sciences. In this very stimulating inter-disciplinary environment FSMP has a strong partnership with industries and support joint PhD fellows.
2. MathsinParis students follow the doctoral training research, participate to laboratory and thematic seminars following the PhD thesis topic decided with their advisor*, they are followed by a tutor who has an external vision of the thesis progress and a external advisor* who organize a mandatory 2/3 months abroad internship. In addition FSMP support various activities as presentation of scientific progress in a « Restitution day» or the participation at least one research school for year.
3. MathInParis Doctoral program structures also a wide range of non research oriented activities as training session for professional insertion with help of Adoc Talent Management and attending specific day as MathInParis Conference (Journée carrière des mathématiques) or Maths Jobs Forum.
The FSMP team guarantees a dedicated assistance for visa issues, housing, health, banking, etc. Furthermore, fellows will be affiliated to the French Social Security during the stay.
@infinitymath
👇👇👇👇👇👇
Forwarded from انجمن ریاضی ایران (IMS)