A Scientist's Comfort Zone
Scientists usually have better things to talk about than how hard it is doing research; and popular accounts of science, even more, concentrate on the glamour of achievement and dismiss the months of self-doubt and confusion: "suddenly she made another stunning and serendipitous discovery." Occasionally, though, even really top-class scientists confess to spending some time on the same level as the rest of us; and I find this comforting and somehow even inspiring.
Please email me with more quotes!
John Wallis
Quamquam enim hanc spes non exigua visa est affulsisse, lubricus tamen
quem prae manibus
habemus Proteus tam hic quam superius non raro elapsus, spem fefellit.
"Although no small hope seemed to shine, what we have in hand is slippery,
like Proteus, who
in the same way, often escaped, and disappointed hope."
On squaring the circle. The translation is in the first of two lovely articles by Jacqueline A. Stedall here.
Piet Hein
Problems worthy of attack,
Prove their worth by fighting back!
I saw this on J.D. Phillips' research page at homepage.
Nathaniel Bowditch
I never come across one of Laplace's "Thus it plainly appears" without feeling sure that I have many hours of hard work before me.
This appeared on the home page of the Missouri Club at Princeton University.
Cornelius J. Everett
Unusually for a mathematician of the very top rank, the technical side of mathematics was not Ulam's forté. He had, too, an aversion to writing, preferring to communicate his ideas orally. Paul Stein once asked Everett how he and Ulam had worked together on their three branching processes papers. Everett's laconic reply, "Ulam told me what to do, and I did it", is certainly revealing. But the abiding characteristics of Ulam's genius and humanity are his courage to explore new domains, his ability to inspire others and, above all, his depth of thought.Quoted from G. T. Q. Hoare "Stanisław Ulam 1909–1984", Mathematical
Gazette, 83, no. 496, 1999, 10–24.
Stanisław Ulam
Ulam never concealed his dependence on Everett: "I had some general, sometimes only vague, ideas. Everett supplied the rigor, the ingenuities and the details of the proof, and final constructions."
From p. 343 of Norman Macrea's John von Neumann, American Mathematical Society, 1999.
From an H.E. Robbins' review
of Ulam's autobiography.
Carol Robinson
When I look at where I've got to I think I'm just an ordinary person in the street. I've been very lucky, I've not given up, I'm quite determined and competitive, but I'm not a genius or anything! I don't think people should think that they can't do something because they haven't got an enormous IQ. It's how you apply yourself.
From an interview on www.moretolifethanshoes.com.
Stephen Smale
At least in my own case, understanding mathematics doesn’t come from reading or even listening. It comes from rethinking what I see or hear. I must redo the mathematics in the context of my particular background. And that background consists of many threads, some strong, some weak. My background is stronger in geometric analysis, but following a sequence of formulae gives me trouble. I tend to be slower than most mathematians to understand an argument. The mathematical literature is useful in that it provides clues, and one can often use these clues to put together a cogent picture. When I have reorganized the mathematics in my own terms, then I feel an understanding, not before.
I read this at math.berkeley.edu/~smale/biblio/chaos.ps (page 5).
David Hilbert
That I have been able to accomplish anything in mathematics is really due to the fact that I have always found it so difficult. When I read, or when I am told about something, it nearly always seems so difficult, and practically impossible to understand, and then I cannot help wondering if it might not be simpler. And on several occasions it has turned that it really was more simple!
Found in The Honours Class: Hilbert's Problems and their Solvers by Benjamin Yandell, AK Peters, Natick, MA, 2002.
Claude Bernard
On the life sciences: "je dirais que c'est un salon superbe tout resplendissant de lumière, dans lequel on ne peut parvenir qu'en passant par une lonque et affreuse cuisine"
From Introduction à l'étude de la médecine expérimentale. Source: Claude Bernard, " Introduction à l'étude ..." (click 'read online'; the above sentence is on page 12, para. 2)
Max Born
I believe there is no philosophical high-road in science, with epistemological signposts. No, we are in a jungle and find our way by trial and error, building our road behind us as we proceed.
Found on Donald Simanek's quotations page
Frank Plumpton Ramsay
We are in the ordinary position of scientists of having to be content with piecemeal improvements: we can make several things clearer, but we cannot make anything clear.
Found on Donald Simanek's quotations page
Charles Franklin Kettering
Every honest researcher I know admits he's just a professional amateur. He's doing whatever he's doing for the first time. That makes him an amateur. He has sense enough to know that he's going to have a lot of trouble, so that makes him a professional.
Found on Donald Simanek's quotations page
Frederick Weisskopf
It was absolutely marvelous working for Pauli. You could ask him anything. There was no worry that he would think a particular question was stupid, since he thought all questions were stupid.
Found on Donald Simanek's quotations page
Wolfgang Pauli
Physics is very muddled again at the moment; it is much too hard for me anyway, and I wish I were a movie comedian or something like that and had never heard anything about physics!
Quoted from a letter to R. Kronig, 25 May 1925, in Donald Simanek's quotations page
Paul Halmos
Mathematics is not a deductive science — that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.
From I Want to be a Mathematician, Washington: MAA Spectrum, 1985 (Carrie Rutherford told me about it.)
Julia Robinson's Job Description:
| Monday: | Try to prove theorem | |
| Tuesday | Try to prove theorem | |
| Wednesday | Try to prove theorem | |
| Thursday | Try to prove theorem | |
| Friday | Theorem false |
Eizabeth Scott in a tribute to Robinson, as quoted in the Association for Women in Mathematics article on Robinson.
Dorothy Hodgkin
I seem to have spent much more of my life not finding structures than finding them
Quoted in Georgina Ferry's Dorothy Hodgkin: A Life, Granta Books, 1999
Roger Penrose
Do not be afraid to skip equations (I do this frequently myself).
From the Preface to The Road to Reality, Vintage Books, London, 2005 (p. xix)
The subject of quantum gravity came up and Penrose and Feynman got into a heated argument. Penrose said, Feynman was so quick, he was usually about five steps ahead of me at any given point. Sometimes he didn't listen to what I was saying. The whole thing was mentally exhausting. I was completely drained at the end of the session. I have never encountered anyone so quick before. What Penrose and many other physicists didn't realize was the reason that accounted for Feynman's quickness on many matters in physics. Feynman thought about some of these areas in great depth and for long periods of time. A topic like quantum gravity would be one that Feynman had spent countless hours thinking about. It wasn't all off the cuff.
From Al Seckel on Feynman
Richard Feynman
In any thinking process there are moments when everything is going good and you've got wonderful ideas. Teaching is an interruption, and so it's the greatest pain in the neck in the world. And then there are the longer periods of time when not much is coming to you. You're not getting any ideas, and if you're doing nothing at all, it drives you nuts! You can't even say "I'm teaching my class."
From Feynman's "Surely You're Joking Mr. Feynman!" Adventures of a Curious Character, Bantam Books, New York, 1986. A slightly longer version can be read here.
James Joseph Sylvester
Writing to his old friend Arthur Caley, Sylvester confessed, "I expect Poincarre [sic] tomorrow and he will have rooms in College. I rather dread the encounter as there is so little in the way of Mathematics upon which I can hope to talk to him!"
From J. Fauvel, R. Flood and R. Wilson, eds, Oxford Figures. Eight Hundred Years of the Mathematical Sciences, OUP, 2000
John Sulston
Being a great ditherer, I would frequently start an experiment far too late in the afternoon simply because I'd spent the whole day pondering exactly how to set it up.
In "Why won't the public put their faith in scientists?", Times Higher Education Supplement, 10/6/05
Robert Browning
(he doesn't really belong here but I like this quote)
Ah, but a man's reach should exceed his grasp, Or what's a Heaven for?
From Andrea del Sarto, 1855
This page is part of Robin Whitty's MathSci site.
Robin Whitty, September 2008