The thematic term 2003 consists of four events. The first event is devoted to mathematics and informatics engineering and focuses on soft computing and complex systems. The second event deals with modelling and simulation in chemical engineering. The third event is related to modelling and numerical simulation in continuum mechanics. The fourth event is concerned with mathematics and telecommunications.
Each one of these events is an Advanced School and Workshop, where short courses, lectures and invited talks will be given by well-known invited scientists. So it is expected that the thematic term 2003 will attract a large number of postgraduate students, mathematicians and engineers, interested in contributing to the development of mathematics and its applications to engineering.
The programme of events is the following:
Harnessing complexity is an important aspect of today problem solving. Complexity may be due to the presence of uncertain information or because the regularities of a system, we are trying to understand, cannot be briefly described. We will discuss recent developments in dealing with complexity, by means of introducing the methods and their sound mathematical foundations, as well as through the work of some difficult problems.
The workshop will be held at the Mathematics Department - University of Coimbra.
This event comes in the follow-up of rather successful, even if less ambitious event, ``Matemática em Telecomunicações: Que Problemas?" with similar objectives organized by IT in 1997.
The CIM Scientific Committee, in a meeting held in Coimbra on February 8, approved the CIM scientific program for 2004.
The Thematic Term for 2004 will be dedicated to Mathematics and the Environment. The Organizers-Coordinators are Juha Videman (IST, Lisbon, Portugal) and José Miguel Urbano (University of Coimbra, Portugal).
The list of events is the following:
Applicants should fill in the electronic application form
This is mirrored at http://at.yorku.ca/cim.www/
Departmento de Matematica, Universidade de Porto
The main tool underlying our approach is found in profinite constructions, be it semigroups, groups, graphs or categories. Generally speaking, profinite structures are a way of encoding, with the help of an additional topological structure, common properties of a class of finite structures of the same type. This idea can be found in various areas, from Galois theory to finite semigroup theory.
Results which are given without reference are announced here for the first time and will be proved elsewhere.
The piece includes a sample problem, labeled "An Easy One." "A right circular cone has a base of radius 1 and a height of 3. A cube is inscribed on the cone so that one face of the cube is contained in the base of the cone. What is the length of an edge of the cube?" Check Time for the answer.
The best way to lace depends on your criteria, but in all allowable lacings each eyelet is connected to at least one eyelet on the opposite side. The strongest lacings with n pairs of eyelets are the "crisscross" (when the ratio h of vertical eyelet spacing to horizontal is below a certain value hn) and the "straight" (when h is greater than hn). The shortest lacings are the "bowties". There is only one minimal bowtie lacing when n is even, but there are (n+1)/2 when n is odd. The shortest "dense" lacing (no vertical segments) is the crisscross.
Time series of a random wave train showing the appearance of a large
rogue wave with height 20m occurring at 140 seconds.
r(j) = f(j)(|A cos M|p + |B sin M|q)-1/nwhich, for various values of the parameters A, B, M, p, q, n and various choices of the function f(j) does in fact give a wide variety of interesting shapes. Whether this mathematical unity is of any botanical significance is harder to see. Whitfield quotes Ian Stewart (Warwick): "I'm not convinced ... , but it might turn out to be profound if it could be related to how things grow" as is the case, for example, with D'Arcy Thompson's explanation of the logarithmic spiral in mollusk shells. Gielis' position, as quoted by Whitfield: "Description always precedes ideas about the real connection between maths and nature." A botanical Kepler awaiting his Newton. Meanwhile, Gielis has applied for a patent on his discovery: Methods and devices for synthesizing and analyzing patterns using a novel mathematical operator, USPTO patent application No. 60/133,279 (1999).
P(|rt| > x) ~ x-3where rt is the change of the logarithm of stock price in a given time interval Dt (for a given stock), V is trading volume and N is the number of trades. The model "is based on the hypothesis that large movements in stock market activity arise from the trades of large participants." (Authors: X. Gabaix, P. Gopihrishnan, V. Plerou, H. E. Stanley).
P(V > x) ~ x-1.5
P(N > x) ~ x-3.4
Originally published by the American Mathematical Society in What's New in Mathematics, a section of e-MATH, in
http://www.ams.org/new-in-math/note-archive.htmlReprinted with permission.
When I studied mathematics at school, nearly all of my efforts were applied to solving problems in text books, instead of reading the texts. Then my teachers marked and discussed my solutions instead of instructing me in a formal way. I enjoyed this kind of work greatly, especially when I was able to find answers to difficult questions myself. Thus I gained a good understanding of some fields of mathematics, but I became unwilling to learn about new subjects at a general introductory level, because I do not have a good memory, and to me it was without fun. I also disliked the breadth of the range of courses that one had to take at Cambridge University as an undergraduate in mathematics. Fortunately, I was able to complete that work adequately in two years, which allowed me to study for the Diploma in Numerical Analysis and Computation during my third year. It was a relief to be able to solve problems again most of the time, and the availability of the Edsac 2 computer was a bonus. I welcomed the use of analysis and the satisfaction of obtaining answers. I wished to continue this kind of work after graduating, but the possibility of remaining in Cambridge for a higher degree was not suggested to me. Contributing to academic research and publishing papers in journals were not suggested either, although I developed a successful algorithm for adaptive quadrature in a third year project. Therefore in 1959 I applied for three jobs at government research establishments, where I would assist scientists with numerical computer calculations. I liked the location of Harwell and the people who interviewed me there, so it was easy for me to accept their offer of employment.
You obtained your doctor of science only in 1979, twenty years after your bachelors degree and three years after being hired as a professor in Cambridge. Why was that the case?
After graduating from Cambridge in 1959 with a BA degree, I had no intention of obtaining a doctorate. All honours graduates from Cambridge are eligible for an MA degree after about 3 further years, without taking any more courses or examinations, but from my point of view that opportunity was not advantageous, partly because one had to pay a fee. When I became the Professor of Applied Numerical Analysis at Cambridge in 1976, I was granted all the privileges of an MA automatically, and my official degree became BA with MA status. Two years later, I was fortunate to be elected as a Professorial Fellow at Pembroke College, and the Master of Pembroke suggested that I should follow the procedure for becoming a Master of Arts. Rather than expressing my reservations about it, I offered to seek an ScD degree instead, which required an examination of much of my published work. Thus I became an academic doctor in 1979.
M. J. D. Powell
Was it hard to adapt to the academic life after so many years in Harwell?
After about five years at Harwell, most of my time was spent on research, which included the development of Fortran software for general computer calculations, the theoretical analysis of algorithms, and of course the publication of papers. The purpose of the administrative staff there was to make it easier for scientists to carry out their work. On the other hand, I found at Cambridge that one had to create one's own opportunities for research, which required some stubbornness and lack of cooperation, because of the demands of teaching, examining and admitting students, and also because administrative duties at universities can consume the time that remains, especially during terms. This change was particularly unwelcome, and is very different from the view that most of my relatives and friends have of university life. Indeed, when I was at Harwell they did not doubt that I had a full time job, but they assume that at Cambridge the vacations provide a life of leisure.
In your work in optimization we find several interesting and meaningful examples and counter-examples. Where did you get this training (assuming that not all is natural talent)? From your exposure to approximation theory? From the hand calculations of the old computing times?
The construction of examples and counter-examples is a natural part of my strong interest in problem solving, and of the development of software that I have mentioned. Specifically, numerical results during the testing of an algorithm often suggest the convergence and accuracy properties that are achieved, so conjectures arise that may be true or false. Answers to such questions are either proofs or counter-examples, and often I have tried to discover which of these alternatives applies. Perhaps my training started with my enjoyment of geometry at school, but then the solutions were available. I am pleased that you mention hand calculations, because I still find occasionally that they are very useful.
Was exemplification a relevant tool for you when you taught numerical analysis classes? Did your years as a staff member at Harwell influence your teaching?
My main aim when teaching numerical analysis to students at Cambridge was to try to convey some of the delightful theory that exists in the subject, especially in the approximation of functions. Only 36 lectures are available for numerical analysis during the three undergraduate years, however, except that there are also courses on computer projects in the second and third years, where attention is given to the use of software packages and to the numerical results that they provide. Moreover, in most years I also presented a graduate course of 24 lectures, in order to attract research students. The main contribution to my teaching from my years at Harwell was that I became familiar with much of the relevant theory there, because it was developed after I graduated in 1959, but I hardly ever mentioned numerical examples in my lectures, because of the existence of the Cambridge computer projects, and because the mathematical analysis was more important to my teaching objectives. Therefore my classes were small. Fortunately, some of the strongest mathematicians who attended them became my research students. I am delighted by their achievements.
Could you tell us how computing resources evolved at Harwell in the sixties and seventies and how that impacted on the numerical calculations of those times?
Beginning in 1958, I have always found that the speed of computers and the amount of storage are excellent, because of the huge advances that occur about every three years. On the other hand, the turnaround time for the running of computer programs did not improve steadily while I was at Harwell. Indeed, for about four years after I started to use Fortran in 1962, those programs were run on the IBM Stretch computer at Aldermaston, the punched cards being transported by car. Therefore one could run each numerical calculation only once or twice in 24 hours. Of course it was annoying to have to wait so long to be told that one had written dimesnion instead of dimension, but ever since I have been grateful for the careful attention to detail that one had to learn in that environment. Moreover, it was easier then to develop new algorithms that extend the range of calculations that can be solved. Conveying such advances to Harwell scientists was not straightforward, however, mainly because they wrote their own computer programs, using techniques that were familiar to them. The Harwell Subroutine Library, which I started, was intended to help them, and to reduce duplication in Fortran software. Often it was highly successful, but many computer users, both then and now, prefer not to learn new tricks, because they are satisfied by the huge gains they receive from increases in the power of computers.
You once wrote: ``Usually I produced a Fortran program for the Harwell subroutine library whenever I proposed a new algorithm,...'' [A View of Nonlinear Optimization, History of Mathematical Programming: A Collection of Personal Reminiscences (J.K. Lenstra, A.H.G. Rinnooy Kan, and A. Schrijver eds), North-Holland (Amsterdam), 119-125 (1991)]. In fact, writing numerical software has always been a concern of yours. Could you have been the same numerical analyst without your numerical experience?
My principal duty at Harwell was to produce Fortran programs that were useful for general calculations, which justified my salary. My work on the theoretical side of numerical analysis was also encouraged greatly, and its purpose was always to advance the understanding of practical computation. Indeed, without numerical experience, I would be cut off from my main source of ideas. It is unusual for me to make progress in research by studying papers that other people have written. Instead I seek fields that may benefit from a new algorithm that I have in mind. I also try to explain and to take advantage of the information that is provided by both good and bad features of numerical results.
Roger Fletcher wrote once that ``your style of programming is not what one might call structured''. Some people think that a piece of software should be well structured and documented. Others that it should be primarily efficient and reliable. What are your views on this?
I never study the details of software that is written by other people, and I do not expect them to look at my computer programs. My writing of software always depends on the discipline of subroutines in Fortran, where the lines of code inside a subroutine can be treated as a black box, provided that the function of each subroutine is specified clearly. Finding bugs in programs becomes very painful, however, if there are any doubts about the correctness of the routines that are used. Therefore I believe that the reliability and accuracy of individual subroutines is of prime importance. If one fulfils this aim, then in my opinion there is no need for programs to be structured in a formal way, and conventional structures are disadvantageous if they do not suit the style of the programmer who must avoid mistakes. Those people who write reliable software usually achieve good efficiency too. Of course it is necessary for the documentation to state what the programs can do, but otherwise I do not favour the inclusion of lots of internal comments.
And by the way, how do you regard the recent advances in software packages for nonlinear optimization?
Most of my knowledge of recent advances in software packages has been gained from talks at conferences. I am a strong supporter of such activities, as they make advances in numerical analysis available for applications. My enthusiasm diminishes, however, when a speaker claims that his or her software has solved successfully about 90% of the test problems that have been tried, because I could not tolerate a failure rate of 10%. Another reservation, which applies to my programs too, is that many computer users prefer software that has not been developed by numerical analysts. I have in mind the popularity of simulated annealing and genetic algorithms for optimization calculations, although they are very extravagant in their use of function evaluations.
Many people working in numerical mathematics undervalue the paramount importance of numerical linear algebra (matrix calculations). Would you like to comment on this issue? How often was research in numerical linear algebra essential to your work in approximation and optimization?
An optimization algorithm is no good if its matrix calculations do not provide enough accuracy, but, whenever I try to invent a new method, I assume initially that the computer arithmetic is exact. This point of view is reasonable for the minimization of general smooth functions, because techniques that prevent serious damage from nonlinear and nonquadratic terms in exact arithmetic can usually cope with the effects of computer rounding errors, as in both cases one has to restrict the effects of perturbations. Therefore I expect my algorithms to include stability properties that allow the details of the matrix operations to be addressed after the principal features of the algorithm have been chosen. Further, I prefer to find ways of performing the matrix calculations myself, instead of studying relevant research by other people.
I read in one of your articles that ``a referee suggested rejection because he did not like the bracket notation''. What is your view about the importance of refereeing? How do you classify yourself as a referee?...
The story about the bracket notation is remarkable, because the paper that was nearly rejected is the one by Roger Fletcher and myself on the Davidon-Fletcher-Powell (DFP) algorithm. As a referee, I ask whether submitted work makes a substantial contribution to its subject, whether it is correct, and whether the amount of detail is about right. I believe strongly that we can rely on the accuracy of published papers only if someone, different from the author(s), checks every line that is written, and in my opinion that task is the responsibility of referees. When it is done carefully, then refereeing becomes highly important. I try to act in this way myself, but, because my general knowledge of achievements in my fields is not comprehensive, I often consider submissions in isolation, although I should relate them to published work.
Actually, in my previous question I had in mind the difficulty that others might face to meet your high standards. This brings me to your activity as a Ph.D adviser. What difficulties and what rewards do you encounter when advising Ph.D. students?
Of course I take the view that my requirements for the quality of the work of my PhD students are reasonable. I require their mathematics to be correct, I require relevance to numerical computation, and I require some careful investigations of new ideas, instead of a review of a subject with some superficial originality. Further, I prefer my students to work on topics that are not receiving much attention from other researchers, in order that they can become leading experts in their fields. Some of them have succeeded in this way, which is a great reward, but two of them switched to less demanding supervisors, and another one switched to a well paid job instead of completing his studies. I also had a student that I never saw after his first four terms. Eventually he submitted a miserable thesis, that was revised after his first oral examination, and then the new version was passed by the examiners, but the outcome would have been different if university regulations had allowed me to influence the result. On the other hand, all my other students have done excellent work and have thoroughly deserved their PhDs. One difficulty has occurred in several cases, namely that, because each student has to gain experience and to make advances independently, one may have to allow his or her rate of progress to be much slower than one could achieve oneself. Another difficulty is that my knowledge of pure mathematics has been inadequate for easy communication between myself and most of my students who have studied approximation theory. Usually they were very tolerant about my ignorance of distributions and properties of Fourier transforms, for example, but my heart sinks when I am asked to referee papers that depend on these subjects.
Most of your publications are single-authored. Why do you prefer to work on your own?
I believe I have explained already why I enjoy working on my own. Therefore, when I begin some new research, I do not seek a co-author. Moreover, as indicated in the last paragraph, I prefer my students to make their own discoveries, so usually I am not a co-author of their papers.
I have been trying to avoid technical questions but there is one I would like to ask. What is your view on interior-point methods (a topic where you made only a couple - but as always relevant and significant - contributions)?
My view of interior point methods for optimization calculations with linear constraints is that it seems silly to introduce nonlinearities and iterative procedures for following central paths, because these complications are not present in the original problem. On the other hand, when the number of constraints is huge, then algorithms that treat constraints individually are also unattractive, especially if the attention to detail causes the number of iterations to be about the number of constraints. It is possible, however, to retain linear constraints explicitly, and to take advantage of the situation where the boundary of the feasible region has so many linear facets that it seems to be smooth. This is done by the TOLMIN software that I developed in 1989, for example, but the number of variables is restricted to a few hundred, because quadratic models with full second derivative matrices are employed. Therefore eventually I expect interior point methods to be best only if the number of variables is large. Another reservation about this field is that it seems to be taking far more than its share of research activity.
My book on Approximation Theory and Methods was published in 1981. Two years later, my son died in an accident, and then I wished to write a book on Nonlinear Optimization that I would dedicate to him. I have not given up this idea, but other duties, especially the preparation of work for conferences and their proceedings, have caused me to postpone the plan. Of course, because of the circumstances, I would try particularly hard to produce a book of high quality.
Let me end this interview with the very same questions I asked T.R. Rockafellar (who, by the way, shared with you the first Dantzig Prize in 1982). Have you ever felt that a result of yours was unfairly neglected? Which? Why? What would you like to prove or see proven that is still open (both in approximation theory and in nonlinear optimization)? What was the most gratifying paper you ever wrote? Why?
I was taught the FFT (Fast Fourier Transform) method by J.C.P. Miller in 1959, and then it made Cooley and Tukey famous a few years later. Moreover, my 1963 paper with Roger Fletcher on the DFP method is mainly a description of work by Davidon in 1959, and it has helped my career greatly. Therefore, by comparison, none of my results has been unfairly neglected. My main theoretical interest at present is trying to establish the orders of convergence that occur at edges, when values of a smooth function are interpolated by the radial basis function method on a regular grid, which is frustrating, because the orders are shown clearly by numerical experiments. In nonlinear optimization, however, most of my attention is being given to the development of algorithms. Since you ask me to mention a gratifying paper, let me pick ``A method for nonlinear constraints in minimization problems'', because it is regarded as one of the sources of the ``augmented Lagrangian method'', which is now of fundamental importance in mathematical programming. I have been very fortunate to have played a part in discoveries of this kind.
He made many seminal contributions in approximation theory, nonlinear optimization, and other topics in numerical analysis. He has written a book in approximation theory and more than one hundred and fifty papers. A View of Nonlinear Optimization, History of Mathematical Programming: A Collection of Personal Reminiscences (J.K. Lenstra, A.H.G. Rinnooy Kan, and A. Schrijver eds), North-Holland (Amsterdam), 119-125 (1991).
José Tiago da Fonseca Oliveira was an eminent statistician and university professor. His name is already registered in the history of the 20th century Statistics due to his important contributions to the development of the theory of extreme values. As a Portuguese scientist his name will remain forever associated to the recognition of Statistics as a science in Portugal.
Tiago de Oliveira
Tiago de Oliveira was born in Lourenço Marques, Mozambique, on the 22th of December 1928. A very interesting account of his times in Mozambique, where he lived until 1945, is given by Eugénio Lisboa, one of his friends from childhood, in Tiago de Oliveira, O Homem e a Obra, 1993, eds. Colibri.
Tiago de Oliveira finished his high school education in 1945. Because of his outstanding performance he was awarded, that year, the prize for the best student of Liceu Lourenço Marques. He also received a grant from Caixa Económica Postal which helped him to leave Mozambique and pursue his studies in Porto. His intention was to study Naval Engineering at the University of Porto. However, during his trip back to the Continent he stopped in Lobito, Angola. A visit to a local bookshop led him to buy a book on Statistics, written in Spanish. It was then, according to his son José Carlos Tiago de Oliveira (in Tiago de Oliveira, O Homem e a Obra, 1993, eds. Colibri), that he found is vocation. Instead of Naval Engineering he studied Mathematics and finished his degree in 1949. In 1950 he got a degree in Geographic Engineering, and in 1951 he received the Rotary Club Prize for the best student of the Faculty of Sciences.
Tiago de Oliveira's political views against Salazar's regime were well known. As a consequence it was not easy for him to get a job despite his achievements as a student. Twice he was invited for the place of assistant at the Faculty of Sciences in Porto, but twice he saw his appointment denied for political reasons. He moved to Lisbon in 1951 and got a job at the Institute of Marine Biology as a research assistant in biometry and biostatistics. By the time he left the Institute in 1953 to become an assistant lecturer at the Faculty of Sciences at the University of Lisbon, he had already published seven papers in Statistics. This was only the beginning of an extraordinary career in the area of probability and statistics.
He entered the Faculty of Sciences as an assistant, thanks to the influence of Prof. António Almeida e Costa, a true scientist and a person with vision, who knew how to separate science from politics. Tiago de Oliveira studied under his supervision and in 1957 he finished his doctoral thesis in the area of Algebra with a dissertation entitled ``Residuais de Sistemas e Radicais de Anéis". However, his interest in Statistics had not died out and it was with a thesis on ``Estatística de Densidades; resultados Assintóticos" that he applied in 1965 for the position of Professor Extraordinário. He studied probability and statistics as an autodidact. His ``bible", as he used to call it, was the work of Kendall and Stuart. In 1967, when he became a full professor, he had already 63 publications, some of them in well-known periodicals such as Annals of Mathematical Statistics and Bulletin of the International Statistical Institute, among others.
It is not clear how Tiago de Oliveira got interested in the theory of extreme values, his main area of research. His first publication in this area, ``Extremal Distributions", dates back to 1959. In 1960 he went for the first time to Columbia University, as Senior Research Assistant, and there he had the opportunity to work with the most prominent scientist in the area, E. J. Gumbel. This collaboration marked the beginning of a very fruitful research career for Tiago de Oliveira. In 1961 he published some extensions of Gumbel's results in the theory of univariate extremes, to the bivariate and multivariate cases. His pioneer work was followed by many other important contributions and new developments in the area of multivariate extremes. He also developed several methods for the estimation of the parameters of Gumbel, Fréchet and Weibull models and for the estimation of high quantiles. Together with S. B. Littauer he worked on prediction of extremal models. He also had important contributions in statistical decision problems related to the Weibull distribution, and in the study of univariate extremes in dependent sequences. Another pioneer work of Tiago de Oliveira was on the statistical choice of univariate extremal models. In a paper published in Statistical Distributions in Scientific Work, vol. 6, in 1981, he developed locally most powerful (LMP) tests for discrimination between extremal models. This problem was approached from a computational point of view in a joint paper with A. Frasen, and with M. I. Gomes he studied exact and asymptotic behaviour of alternative statistical tests to the same problem.
Although Tiago de Oliveira is well known due to his work in Extreme Value Theory, his research went well beyond this particular area. He had important contributions in many other themes such as Demography, Quality Control, Outliers, Mixtures, Non-parametric Statistics, Risk Theory, Actuarial Mathematics, just to mention a few.
Tiago de Oliveira was also a man of broad interests, both scientific and cultural. He had a deep understanding of history and Portuguese political culture. He wrote several historical, philosophical and didactical articles. Particularly interesting are his views on the development of mathematics in Portugal from the XVI to the XIX centuries (in Collected Works of J. Tiago de Oliveira, vol. II). Overall, he published around 160 scientific papers, 9 books, 22 historical and philosophical papers, 18 didactic and expository articles, and 21 other papers on miscellaneous subjects. At the time of his death, on the 23th of June 1992, he had six papers and four more books in preparation. His book Statistical Analysis of Extremes was posthumously published due to the efforts of his son, José Carlos Tiago de Oliveira, who also compiled all his works in a six-volume series entitled Collected Works of J. Tiago de Oliveira and published by Pendor.
Tiago de Oliveira was not just a great scientist. He was a man with strong views and strong convictions who would fight for his own ideals. He fought for the autonomy of the area of Applied Mathematics in the Faculty of Sciences at the University of Lisbon, and later for the autonomy of Statistics and Operations Research, founding in 1981 a Department of Statistics, Operations Research and Computation, today the Department of Statistics and Operations Research of the FCUL. He was also a founder of the Center of Statistics and Applications of the University of Lisbon and the Portuguese Statistical Society. Due to his trust in the younger generations and constant encouragement he brought, in the late seventies and early eighties, many people to the areas of Statistics, Operations Research and Computation. The ``Portuguese Statistical School of Extremes", which today is internationally respected, owes its existence to him. Later, when in 1987 he left the University of Lisbon and went to the Faculty of Sciences and Technology of the New University of Lisbon, he again put all his efforts in bringing up a new group of people working in his areas of choice. In that Faculty he founded the Laboratory of Statistics and Actuarial Mathematics. He also served the scientific community as Secretary of State for scientific research from 1976 to 1978.
Tiago de Oliveira had been a Fellow of the Royal Statistical Society since 1952. However, in 1987, in recognition of his merit and important contributions to the area of Statistics, he was awarded the title of Honorary Fellow of the Royal Statistical Society. He was also a member of the International Statistical Institute, a member of the Bernoulli Society for Mathematical Statistics, a Fellow of the Institute of Mathematical Statistics, a full member of the Academia das Ciências de Lisboa, a corresponding member of the Real Academia de las Ciencias Exactas, Físicas y Naturales de Madrid, among many other scientific associations.
During his life he was awarded three prizes in recognition of his outstanding scientific work. The A. Malheiros Prize for Mathematical Sciences of the Academy of Sciences of Lisbon, in 1969; the Calouste Gulbenkian Foundation Prize for Sciences and Technology in 1984; the Science Prize of the Oriente Foundation in 1992.
The sphere of activity of Tiago de Oliveira was not limited to the academic level. He was deeply interested and involved in the problems of society in general and of the Portuguese society in particular. As such he was a founding member of the Socialist party, a member of the Union of Teachers of Greater Lisbon (Sindicato dos Professores da Grande Lisboa), a member of the Association of Statisticians for Human Rights, a member of the Portuguese Association of Human Rights, and a member of the Portuguese Section of the International Amnesty.
For the outstanding scientific legacy Tiago de Oliveira left behind, he deserves a very special place among the Great Portuguese Mathematicians of the 20th Century.
To write this short sketch I based myself on the following documents:
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