We give a number of quotes by Luis Santaló taken from various sources. Some of the translations are taken from A Reventós, Professor Lluis Santaló (1911-2001), Contributions to Science 2 (3) (2003), 413-426.
- Luis Santaló was awarded an Honorary Doctorate by the Polytechnic University of Catalonia on 14 July 1977. This quote is from his reply:
This is the first academic function in which I am able to express myself in the language in which my understanding first knew things, named them and in which my spirit first showed its feelings and emotions, the language in which, when I was small, my mother told me stories and sang at the foot of my cradle. Clearly, this is Catalan.
- The following quote on Art is also from his reply at the Polytechnic University of Catalonia on 14 July 1977:
Mathematics is art, as it is creation and it uses fantasy; it is science, because through it better understanding of the principles and causes of things is acquired; and it is technique because it provides methods and means for resolving problems and acting on Nature and its phenomena.
- Lui Santaló was awarded an Honorary Doctorate by the Autonomous University of Barcelona on 13 June 1986. This quote is from his reply:
Sometimes, fear is expressed that, with the necessary predominance in education of science and technology, based on mathematical reasoning, men are steadily losing their emotional faculties and becoming cold and rigid in their temperaments, refractory to emotional feeling and passion. Not at all. The fact of having one's mind prepared for clear logical and mathematical reasoning does not mean that this is to the detriment of feelings. One can think and believe, and one can reason and love.
- The following quote by Santaló is taken from X Duran, Lluis Santaló, Collecció de Biografies de la Fundació Catalana per a la Recerca No. 7 (1999):
I think this is one of a teacher's main obligations. When you see someone who is intelligent, who is capable, he/she must be helped as much as possible to reach the maximum of his/her possibilities. The worst outcome is that someone who could achieve a lot does not do so because he/she has not found the right teacher or has not been guided. There must be a lot of people in that situation. It is the main thing that teaching, at any level of education, must avoid.
- In 'La matemàtica: una filosofia i una tècnica, Vic: Eumo editorial, 1993. Versión castellana, Barcelona: Ariel, 1994', Santaló writes of Mathematics and Art:
A lot of Mathematics is Art, in its creativity and also because it includes beauty, even though only initiates can admire this beauty, as also occurs with works of art and literature.
- In 'La matemàtica: una filosofia i una tècnica, Vic: Eumo editorial, 1993. Versión castellana, Barcelona: Ariel, 1994', Santaló writes about Mathematics and Philosophy:
If by science a systematised combination of knowledge is meant, which constitutes a branch of human knowledge, then Mathematics is the science par excellence.
- in L'educació matemàtica avui (Teide, Barcelona, 1975), Santaló writes of education:
One teaches for good, for truth and to know and understand the universe.
- In a 1982 interview 'El lenguaje universal de la Matemática', published in La Nación, Santaló spoke about the importance of mathematics and mathematical education:
When speaking of the resources of a country there is one, usually scarce, that it is not customary to mention: mathematical talents. Every child captures the essence of our science, but only some, naturally gifted, will come to stand out or attempt creative work. We know that they bloom at a very early age and if they are not educated then they fail; it is the duty of the school to discover and guide them; it is society's obligation to offer them an opportunity for their development. The rest of the citizens, without that special capacity or vocation, must, however, learn all the mathematics necessary to understand the world we live in. To ignore the language to which the sciences aspire and use its techniques, is to be locked away in illiteracy that a civilized country can not tolerate. Here the price of mismanagement is dependence, the loss of sovereignty.
- This quote explaining why he became a geometer, comes from C Barcelo i Vidal (ed.), Homenatge al professor Lluis Santaló i Sors (Catalan), Universidad De Girona (1 Oct 2002):
I was inclined to geometry which is more intuitive than the pure abstract reasoning of arithmetic. Here it tells what you see and then everything becomes simpler. When we speak of a geometric body, we are seeing it.
- On 9 June 1943, at the invitation of the Student Centre, Santaló delivered a lecture in Rosario with the title 'Brief History and Current State of Some Chimeras and Fantasies of Man'. We reproduce his conclusions on Astrology, because they seem to reflect a characteristic aspect of his personality:
By statistical methods, some astrologers have come to confirm relations and enact laws. They speak, for example, of a 'law of astral inheritance' ... ... In this way, compiling horoscopes and facts and submitting them to the calculation of probabilities, it is possible that one day we will come to resolve on a scientific basis if astrology has or has not some foundation. However, even assuming that this analysis led to negative results, which is most likely, the astrologers would not disappear: there would always be a means of attributing the disagreement to new data or elements not taken into account. And we do not believe that this is an evil. Removing those who make a lucrative deception out of astrology, there will always be dreamers of good faith, who studying the stars and looking for impossible chimeras, maybe they will discover certain relationships or, what is already much more likely, to open with their imagination and fantasy new ways to poetry and to hope.
- The following paragraph from Santaló's Historia de la Aeronáutica (History of Aeronautics) written in 1946, when the jet engines were still at the experimental stage, shows his ability to imagine the future:
For the moment, jet aircraft will not completely displace ordinary propeller-driven airplanes, because at very low speeds (below 700 km/h), the consumption of the former is much higher than that of the latter. The true performance of jet aircraft is for high speeds and also for high altitudes, since their "ceiling" or maximum flight height is much higher than that of propeller airplanes. Unless some kind of mixed-propeller and jet-powered aircraft are put into practice at the same time, to take advantage of both methods, it seems at the moment that propellers will continue to be used for airplanes intended for speeds of less than 600 or 700 km/h and heights below 8000 or 9000 metres, and jet engines for higher speeds or heights.
- Let us see how he refers to it in a memorable paragraph from his Historia de la Aeronáutica:
There are inventions, among the many that science has given to men through the ages, that appeared suddenly and unexpectedly, as a coincidence or accident in the midst of the speculations or experiences of certain theories that were unfolding without the aim of having a concrete practical purpose ... . Such inventions were not, before their discovery, either desired or predicted, and man found himself in possession of them without ever having thought of the possibility of them. As a modern example of this type we have radiotelephony. From the discovery of the airwaves, in which it began to be glimpsed its possible use to transmit signals, until the complete development of radio, very few years passed ... Radio is an invention with very little history: from its conception to its realization there is no more than a very short interval of time. Other inventions, on the contrary, were the obsession of generations and more generations, each with the means and the points of view that were their own, trying to carry them out. The most typical example of this kind of invention is that of aerial machines. The eagerness to be able to fly, to have wings or any apparatus that allowed man, like birds, to rise and move into the air, was certainly felt and desired by all men since the earliest times. The ease with which flying birds overcome the natural or artificial obstacles, such as rivers, precipices, mountain ranges, walls, etc., was necessarily appreciated by our most primitive ancestors in all things they valued .... Evident proof of these desires is that in all ancient mythologies and religions there appear gods or higher beings possessing the power to fly, a natural consequence of men attributing to their gods the qualities of perfection most desired that they could not obtain for themselves. In this sense aviation may be considered as the most desired invention, as the invention which most all generations have longed for.
- From Santaló's article 'La Enseñanza de las ciencias en la escuela media' (The Teaching of Sciences in Middle School), written in 1986, which contains his ideas about the importance of scientific education, we have extracted the following paragraph:
The world today needs men with a creative mind who can keep the advances made by science and technology and be able to use them successfully for the sake of general well-being while making them progress in possibilities and effectiveness. We must also educate people for work and effort. The pleasure of rest is fully enjoyed only after exertion, and a tendency to 'easiness', about delaying the general performance, contributes nothing to a happier life. Students have a lot of energy, physical and intellectual, that they need to spend continuously. The school must channel this energy into useful and profitable ways. If the school is 'easy' the student will pour his energies towards extracurricular activities, not always recommended.
- The following quote is from Santaló's article 'Aplicaciones y problemas actuales de algunas teorías matemáticas which was published in the Anales de la Sociedad Cientâifica Argentina (1950):
It has often been tried to mathematize theories without greater success. This is because they are too complex theories, with too many imponderables to be able to fit them into the too rigid norms of mathematical thinking. Of course, when this is possible, a sudden flourishing of the theory is immediately evident, since all the tools of mathematics are placed at its service, besides giving it elegance and logical security, helping it to deepen into otherwise unaffordable regions.
- The following quote by Santaló is given, without reference to the original source, in La Ménsula 5 (15) (April 2012):
Many attempts to subject certain disciplines to mathematical calculations, such as ethics, aesthetics, or even ambitious projects of cybernetics, may seem fantastic and unrealizable. Too many factors and too complex - it is said - are involved in them, to allow them to be schematized in a mathematical model. There may be some degree of reason in this scepticism, but it must not be forgotten that the same difficulty must have arisen at the beginnings of the mathematical treatment of any theory. Tycho Brahe could scarcely suspect that all his tables of observations could be condensed into the simple mathematical formula of Newton's universal law of attraction.