Academics From Poland

"For most of my life, one of the persons most baffled by my own work was myself."

"I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit."

"Science would be ruined if (like sports) it were to put competition above everything else, and if it were to clarify the rules of competition by withdrawing entirely into narrowly defined specialties. The rare scholars who are nomads by choice are essential to the intellectual welfare of the subtle disciplines"

"I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid — a term used in this work to denote all of standard geometry — Nature exhibits not simply a higher degree but an altogether different level of complexity … The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous.""

"A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales..."

"Being a language, mathematics may be used not only to inform but also, among other things, to seduce."

"How Long Is the Coast of Britain?"

"When you seek some unspecified and hidden property, you don't want extraneous complexity to interfere. In order to achieve homogeneity, I decided to make the motion end where it had started. The resulting motion biting its own tail created a distinctive new shape I call Brownian cluster. … Today, after the fact, the boundary of Brownian motion might be billed as a "natural" concept. But yesterday this concept had not occurred to anyone. And even if it had been reached by pure thought, how could anyone have proceeded to the dimension 4/3? To bring this topic to life it was necessary for the Antaeus of Mathematics to be compelled to touch his Mother Earth, if only for one fleeting moment."

"I always saw a close kinship between the needs of "pure" mathematics and a certain hero of Greek mythology, Antaeus. The son of Earth, he had to touch the ground every so often in order to reestablish contact with his Mother; otherwise his strength waned. To strangle him, Hercules simply held him off the ground. Back to mathematics. Separation from any down-to-earth input could safely be complete for long periods — but not forever. In particular, the mathematical study of Brownian motion deserved a fresh contact with reality."

"One of my conjectures was solved in six months, a second in five years, a third in ten. But the basic conjecture, despite heroic efforts rewarded by two Fields Medals, remains a conjecture, now called MLC: the Mandelbrot Set is locally connected. The notion that these conjectures might have been reached by pure thought — with no picture — is simply inconceivable."

"For many years I had been hearing the comment that fractals make beautiful pictures, but are pretty useless. I was irritated because important applications always take some time to be revealed. For fractals, it turned out that we didn't have to wait very long. In pure science, fads come and go. To influence basic big-budget industry takes longer, but hopefully also lasts longer."

"My efforts over the years had been successful to the extent, to take an example, that fractals made many mathematicians learn a lot about physics, biology, and economics. Unfortunately, most were beginning to feel they had learned enough to last for the rest of their lives. They remained mathematicians, had been changed by considering the new problems I raised, but largely went their own way."

"My ambition was not to create a new field, but I would have welcomed a permanent group of people having interests close to mine and therefore breaking the disastrous tendency towards increasingly well-defined fields. Unfortunately, I failed on this essential point, very badly. Order doesn't come by itself."

"There is a saying that every nice piece of work needs the right person in the right place at the right time. For much of my life, however, there was no place where the things I wanted to investigate were of interest to anyone. So I spent much of my life as an outsider, moving from field to field, and back again, according to circumstances. Now that I near 80, write my memoirs, and look back, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years "ahead of my time."

"The Mandelbrot set covers a small space yet carries a large number of different implications. Is it a fitting epitaph? Absolutely."

"My work is more varied than at any other point in my life. I am still carrying out research in pure mathematics. And I am working on an idea that I had several years ago on negative dimensions. … Negative dimensions are a way of measuring how empty something is. In mathematics, only one set is called empty. It contains nothing whatsoever. But I argued that some sets are emptier than others in a certain useful way. It is an idea that almost everyone greets with great suspicion, thinking I've gone soft in the brain in my old age. Then I explain it and people realise it is obvious. Now I'm developing the idea fully with a colleague. I have high hopes that once we write it down properly and give a few lectures about it at suitable places that negative dimensions will become standard in mathematics."

"In a different era, I would have called myself a natural philosopher. All my life, I have enjoyed the reputation of being someone who disrupted prevailing ideas. Now that I'm in my 80th year, I can play on my age and provoke people even more."

"There is a problem that is specific to financial markets. In most fields of research, when someone makes an important finding, they publish it. In the case of prices, they set up a firm and sell advice about their discovery. If they can make money from it, they will. So the research into market dynamics is a closed field."

"The most important thing I have done is to combine something esoteric with a practical issue that affects many people. In this spirit, the stock market is one of the most attractive things imaginable. Stock-market data is abundant so I can check everything. Financial markets are very influential and I want to be part of this field now that it is maturing."

"You cannot hope to build a better world without improving the individuals. To that end each of us must work for his own improvement, and at the same time share a general responsibility for all humanity, our particular duty being to aid those to whom we think we can be most useful."

"The chief difficulty lay in the fact that pitchblende is a very complex mineral and contains in varying quantities nearly all the known metals. ...The analysis of pitchblende by chemical methods, using the procedure sketched above, led to the discovery of two very active bodies, polonium and radium. The name polonium was given to the first substance discovered by Mme Curie in honor of the country of her birth. The name radium was a very happy inspiration of the discoverers, for this substance in the pure state possesses the property of radio-activity to an astonishing degree."

"It seemed probable that the large activity of some of these minerals, compared with uranium and thorium, was due to the presence of small quantities of some very active substance, which was different from the known bodies thorium and uranium. This supposition was completely verified by the work of M. and Mme Curie, who were able to separate from pitchblende by purely chemical methods two active bodies, one of which in the pure state is over a million times more active than the metal uranium. This important discovery was due entirely to the property of radio-activity possessed by the new bodies. The only guide in their separation was the activity of the products obtained. ...The activity of the specimens thus served as a basis of rough qualitative and quantitative analysis, analogous in some respects to the indication of the spectroscope."

"Marie Curie made a detailed examination by the electrical method of the great majority of known substances, including the very rare elements, to see if they possessed any activity. In cases when it was possible, several compounds of the elements were examined. With the exception of and , none of the other substances possessed an activity even of the order of 1/100 of ."

"Although born in a strongly Catholic country, at the age of 17 Marie Curie rejected all forms of religion, professing atheism and placing her trust solely in Enlightenment rationality and progress. She therefore adhered to Positivism, which became her mindset and guided her every action. Feminism found in her an icon of redemption and emancipation. Suffice it to say that in 1885, she went to the employment office to look for work, due to the financial difficulties her family was experiencing at the time, and found a job as a governess."

"In the 1970s we were rediscovering women whose lives had been dropped out of history or distorted, like Susan B. Anthony, Harriet Tubman, Emily Dickinson, Marie Curie, Ida B. Wells-Barnett, Hannah Senesch, Ethel Rosenberg."

"One never notices what has been done; one can only see what remains to be done."

"Marie Curie was at heart a Baconian, boiling tons of crude uranium ore to demolish the dogma of the indestructibility of atoms."

"I am one of those who think like Nobel, that humanity will draw more good than evil from new discoveries."

"There are sadistic scientists who hurry to hunt down errors instead of establishing the truth."

"I was taught that the way of progress was neither swift nor easy."

"I have no dress except the one I wear every day. If you are going to be kind enough to give me one, please let it be practical and dark so that I can put it on afterwards to go to the laboratory."

"Be less curious about people and more curious about ideas."

"Life is not easy for any of us. But what of that? We must have perseverance and above all confidence in ourselves. We must believe that we are gifted for something, and that this thing, at whatever cost, must be attained."

"We must not forget that when radium was discovered no one knew that it would prove useful in hospitals. The work was one of pure science. And this is a proof that scientific work must not be considered from the point of view of the direct usefulness of it. It must be done for itself, for the beauty of science, and then there is always the chance that a scientific discovery may become like the radium a benefit for humanity."

"All my life through, the new sights of Nature made me rejoice like a child."

"Humanity needs practical men, who get the most out of their work, and, without forgetting the general good, safeguard their own interests. But humanity also needs dreamers, for whom the disinterested development of an enterprise is so captivating that it becomes impossible for them to devote their care to their own material profit. Without doubt, these dreamers do not deserve wealth, because they do not desire it. Even so, a well-organized society should assure to such workers the efficient means of accomplishing their task, in a life freed from material care and freely consecrated to research."

"I am among those who think that science has great beauty. A scientist in his laboratory is not only a technician: he is also a child placed before natural phenomena which impress him like a fairy tale. We should not allow it to be believed that all scientific progress can be reduced to mechanisms, machines, gearings, even though such machinery also has its beauty. Neither do I believe that the spirit of adventure runs any risk of disappearing in our world. If I see anything vital around me, it is precisely that spirit of adventure, which seems indestructible and is akin to curiosity."

"I believe international work is a heavy task, but that it is nevertheless indispensable to go through an apprenticeship in it, at the cost of many efforts and also of a real spirit of sacrifice: however imperfect it may be, the work of Geneva has a grandeur that deserves our support."