“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.”

—  Benoît Mandelbrot

New Scientist interview (2004)

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "My work is more varied than at any other point in my life. I am still carrying out research in pure mathematics. And I …" by Benoît Mandelbrot?
Benoît Mandelbrot photo
Benoît Mandelbrot 56
Polish-born, French and American mathematician 1924–2010

Related quotes

Carl Ludwig Siegel photo

“I am afraid that mathematics will perish by the end of this century if the present trend for senseless abstractin — as I call it: theory of the empty set — cannot be blocked up.”

Carl Ludwig Siegel (1896–1981) German mathematician

in a 1964 letter to L. J. Mordell as quoted by [C. S. Yogananda, The Life and Times of Bourbaki, June 2015, Resonance, 556–559, http://www.ias.ac.in/article/fulltext/reso/020/06/0556-0559] (quote from p. 558)

Paul Dirac photo

“A good deal of my research work in physics has consisted in not setting out to solve some particular problems, but simply examining mathematical quantities of a kind that physicists use and trying to get them together in an interesting way regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later that the work does have an application. Then one has had good luck.”

Paul Dirac (1902–1984) theoretical physicist

P.A.M. Dirac, "Pretty Mathematics," International Journal of Theoretical Physics, Vol. 21, Issue 8–9, August 1982, p. 603 http://link.springer.com/article/10.1007/BF02650229#page-1

Rajneesh photo

“If you really want to know who I am, you have to be as absolutely empty as I am. Then two mirrors will be facing each other, and only emptiness will be mirrored. Infinite emptiness will be mirrored: two mirrors facing each other. But if you have some idea, then you will see your own idea in me.”

Rajneesh (1931–1990) Godman and leader of the Rajneesh movement

Come Follow To You, Vol. 2, Chapter 4; in Autobiography of a Spiritually Incorrect Mystic (2000), Part 2.

Edward Frenkel photo

“I was proud of my work with Yakov Isaevich, and he of me. Despite our good relationship, however, I kept my “other” mathematical life – my work with Fuchs and Feigin and all of that – secret from him as I did from most other people. It was as though applied mathematics was my spouse, and pure mathematics was my secret lover.”

Edward Frenkel (1968) mathematician working in representation theory, algebraic geometry, and mathematical physics

Source: Love and Math, 2013, p. 139

David Levithan photo

“There's no way for them to take away my sadness, but they can make sure I am not empty of all the other feelings.”

David Levithan book Love Is the Higher Law

Source: Love Is the Higher Law

Alexander Stepanov photo

“I discovered the works of Euler and my perception of the nature of mathematics underwent a dramatic transformation. I was de-Bourbakized, stopped believing in sets, and was expelled from the Cantorian paradise. I still believe in abstraction, but now I know that one ends with abstraction, not starts with it. I learned that one has to adapt abstractions to reality and not the other way around. Mathematics stopped being a science of theories but reappeared to me as a science of numbers and shapes.”

Alexander Stepanov (1950) Russian programmer

Bjarne Stroustrup: Evolving a language in and for the real world: C++ 1991-2006. ACM HOPL-III. June 2007., 2008-04-25, http://web.archive.org/web/20071120015600/http://www.research.att.com/~bs/hopl-almost-final.pdf, 2007-11-20 http://www.research.att.com/~bs/hopl-almost-final.pdf,

Anish Kapoor photo

“I think I’ve had three or four moments in my work over the last twenty-five years that have been real discoveries. The pigment pieces felt to me as if they were a discovery about an object and what an object can be; how an object can be and not be. Then, of course, the void pieces. The idea that if I empty out all the content and just make something that is an empty form, I don’t empty out the content at all. The content is there in a way that’s more surprising than if I tried to make a content. So, therefore, the idea that subject matter is somehow not the same as content. Then, in a different sort of way, moving from matte surfaces to shiny surfaces. In terms of the fact that the traditional sublime is the matte surface, deep and absorbing, and that the shiny might be a modern sublime, which is fully reflective, absolutely present, and returns the gaze. This feels like a new way to think about the non-objective object.”

Anish Kapoor (1954) British contemporary artist of Indian birth

Anish kapoor in conversation with Heidi Reitmaier in July 2007 in "Anish Kapoor" by Royal Academy Organization.

Louise L. Hay photo

“I say “Out” to every negative thought that comes to my mind. No person, place, or thing has any power over me, for I am the only thinker in my mind. I create my own reality and everyone in it.”

Louise L. Hay (1926–2017) American writer
Denise Scott Brown photo

“I now receive inquiries of interest for deanships and departmental chairs several times a year. I find myself on committees where I am the only woman and there is one black man. We two tokens greet each other wryly. I am frequently invited to lecture at architecture schools, ‘to be a role model for our girls.’ I am happy to do this for their young women but I would rather be asked purely because my work is interesting.”

Denise Scott Brown (1931) American architect

"Sexism and the star system in architecture"

Vincent Van Gogh photo

“So please don't think that I am renouncing anything, I am reasonably faithful in my unfaithfulness and though I have changed, I am the same, and what preys on my mind is simply this one question: what am I good for, could I not be of service or use in some way, how can I become more knowledgeable and study some subject or other in depth?”

Vincent Van Gogh book The Letters of Vincent van Gogh

1880s, 1880, Letter to Theo (Cuesmes, July 1880)
Source: The Letters of Vincent van Gogh
Context: So please don't think that I am renouncing anything, I am reasonably faithful in my unfaithfulness and though I have changed, I am the same, and what preys on my mind is simply this one question: what am I good for, could I not be of service or use in some way, how can I become more knowledgeable and study some subject or other in depth? That is what keeps preying on my mind, you see, and then one feels imprisoned by poverty, barred from taking part in this or that project and all sorts of necessities are out of one's reach. As a result one cannot rid oneself of melancholy, one feels emptiness where there might have been friendship and sublime and genuine affection, and one feels dreadful disappointment gnawing at one's spiritual energy, fate seems to stand in the way of affection or one feels a wave of disgust welling up inside. And then one says “How long, my God!”

Related topics