On Scientists and Science
...the concept of polite mathematics emerged, the underlying idea of
which is that, even if you have only 60 readers, it pays to spend an
hour if by doing so you can save your average reader a minute. By
inventing an idealized "average reader," we could translate most of
the lofty human goal of politeness into more or less formal criteria
we could apply to our texts.
(Edsger Dijkstra, 2002)
Mr Goulburn, Chancellor of the Exchequer, asked my opinion on the utility
of Mr Babagge's calculating machine, and the propriety of spending further
sums of money on it. I replied, entering fully into the matter, and giving
my opinion that it was worthless.
(Sir George Airy, Astronomer Royal, 1842)
Darwin's theory was presented to the Linnaean Society of London in 1858.
It had rather little impact. The president (a dentist interested in reptiles)
claimed that the year had not "been marked by any of those striking
discoveries which at once revolutionize, so to speak, the department of
science on which they bear; it is only at remote intervals that we can
reasonably expect any sound and brilliant innovation that shall produce a
marked and permanent impression on the character of any brand of knowledge."
(Steve Jones in the New York Review of Books, July 17, 1997)
Thinking is the great enemy of perfection.
...the thing of greatest importance to mathematics in Europe was the
discovery by Tartaglia that you can solve a cubic equation--which, although
it is very little used, must have been psychologically wonderful because it
showed a modern man could do something no ancient Greek could do, and
therefore helped in the renaissance which was the freeing of man from the
intimidation of the ancients...
You say you are a nameless man. You are not to your wife and to your child.
You will not long remain so to your immediate colleagues if you can answer
their simple questions when they come into your office. You are not nameless
to me. Do not remain nameless to yourself--it is too sad a way to be. Know
your place in the world and evaluate yourself fairly, not in terms of the naive
ideals of your youth, nor in terms of what you erroneously imagine your
teacher's ideals are.
Best of luck and happiness.
Richard P. Feynman
(To a former student who was unhappy with his life as a
scientist because he was not working on fundamental problems.)
During the period of the mid-1940s and following, S. Chandrasekar
used to drive some hundred miles between Yerkes Observatory in Williams Bay
and the University of Chicago, week after week, to meet with a class
of two students... When the Nobel Prize in physics was awarded in
1957, it went to the whole class, Messrs. Lee and Yang.
The most exciting phrase to hear in science, the one that heralds new
discoveries, is not "Eureka!", but "That's funny..."
When feeling burdened or downcast,... the human mind will gladly turn to the
realms of Mathematics, where a lucid and precise grasp of objectivities is
obtained and insight is gained so pleasantly through appropriate concept
formation. Here the human spirit feels at home.
I believe there exists, and I feel within me, an instinct for truth, or
knowledge or discovery, of something of the same nature as the instinct of
virtue, and that our having such an instinct is reason enough for scientific
researches without any practical results ever ensuing from them.
Philosophy is written in that great book which is ever before our eyes
-- I mean the universe -- but we can never understand it if we do not
first learn the language and grasp the symbols in which it is written.
The book is written in mathematical language and the symbols are triangles,
circles, and other geometrical figures, without whose help it is
impossible to comprehend a single word of it; without which one
wanders hopelessly through a dark labyrinth.
It seems to be one of the fundamental features of nature that fundamental
physical laws are described in terms of mathematical theory of great beauty
and power, needing quite a high standard of mathematics for one to
understand it. You may wonder: Why is nature constructed along these lines?
One can only answer that our present knowledge seems to show that it is so
constructed. We simply have to accept it. One could perhaps describe the
situation by saying that God is a mathematician of a very high order, and
He used very advanced mathematics in constructing the universe. Our feeble
attempts at mathematics enable us to understand a bit of the universe, and
as we proceed to develop higher and higher mathematics we can hope to
understand the universe better.
From long experience, all working mathematicians know that there is a
preliminary period of rapid advancement in ideas without worrying about
exact definitions and proofs, after which there is very hard work to go
from that level of accuracy to finished mathematics, where the bugs in
definitions and proofs are gone, and concepts are quite clear. A lot of
things change in the process. This is the essence of finishing
I do not know what I may appear to the world; but to myself
I seem to have been only like a boy playing on the seashore, and diverting
myself in now and then finding a smoother pebble or a prettier shell than
ordinary, whilst the great ocean of truth lay all undiscovered before me.
Giuseppe Peano was one of the first to use what we now call symbolic logic,
and he habitually wrote out all of his lecture notes in his new symbolism.
He taught at a military academy, and his students were so
incensed by his formalistic approach to mathematics that they rebelled
(despite his promise to pass them all) and got him fired. Subsequently
he found a more congenial setting at the University of Turin.
Michael Faraday, after a public demonstration of an electrical experiment,
was asked what was the use of electricity? He replied, "What use, madam,
is a new-born baby?"
Being a mathematician (as well as a logician, and perhaps a philosopher of
a sort), I have had the opportunity to attend many discussions between
specialists in mathematics, where the problem of applications is
especially acute, and I have noticed on several occasions the following
phenomenon: If a mathematician wishes to disparage the work of one of his
colleagues, say, A, the most effective method he finds for doing this is
to ask where the results can be applied. The hard-pressed man, with his
back against the wall, finally unearths the researches of another
mathematician B as the locus of the application of his own results. If
next B is plagued with a similar question, he will refer to another
mathematician C. After a few steps of this kind we find ourselves
referred back to the researches of A, and in this way the chain closes.
Speaking more seriously,
I do not wish to deny that the value of a man's work may be increased
by its implications for the research of others and for practice. But I
believe, nevertheless, that it is inimical to the progress of science to
measure the importance of any research exclusively or chiefly in terms of
its usefulness and applicability. We know from the history of science
that many important results and discoveries have had to wait centuries
before they were applied in any field. And, in my opinion, there are also
other important factors that cannot be disregarded in determining the
value of a scientific work. It seems to me that there is a special domain
of very profound and strong human needs related to scientific research,
which are similar in many ways to aesthetic and perhaps religious needs.
And it also seems to me that the satisfaction of these needs should be
considered an important task of research. Hence, I believe, the question
of the value of any research cannot be adequately answered without taking
into account the intellectual satisfaction which the results of that
research bring to those who understand it and care for it. It may be
unpopular and out-of-date to say it -- but I do not think that a scientific
result which gives us a better understanding of the world and makes it
more harmonious in our eyes should be held in lower esteem than, say, an
invention which reduces the cost of paving roads, or improves household
(Alfred Tarski, "The Semantic Conception of Truth and the Foundations of
Some years ago, someone wrote a book called "The Seven Laws of Money." One
of the "laws" went something like this: "Do good work and don't worry about
money; it will come along as a side effect." Whether or not that's true of
money, I don't know, but in my experience, it's true of credit for scientific
work. Just make sure you keep working at important problems, enjoying a life
of science, and don't worry so much about credit. You will probably get what
you deserve -- as a side effect.
Lifschitz's web page