Profession: mathematician.
Born 1768, Auxerre, France.
Died 1830, Paris, France.
Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics. (Source: Analytical Theory of Heat)
The differential equations of the propagation of heat
express the most general conditions, and reduce
the physical questions to problems of pure analysis,
and this is the proper object of theory. (Source: Analytical Theory of Heat)
The profound study of nature is the most fertile source of mathematical discoveries. (Source: Morris Kline, Mathematical Thought from Ancient to Modern Times, New York, 1972)
Profession: mathematician.
Born 1811, Paris, France.
Died 1832, Paris, France.
Unfortunately what is little recognized is that the most
worthwhile scientific books
are those in which the author clearly indicates
what he does not know;
for an author most hurts his readers
by concealing difficulties.
In most sciences one generation tears down what another has built
and what one has established another undoes. In mathematics alone
each generation adds a new story to the old structure.
Paul Erdos has a theory that God has a book containing all the theorems of mathematics with their absolutely most beautiful proofs, and when he wants to express particular appreciation of a proof he exclaims, “This is from the book!”
Profession: mathematician. Born 1877, Surrey, England. Died 1947, Cambridge, England.
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
"In these days of conflict between ancient and modern studies,
there must surely be something to be said for a study
which did not begin with Pythagoras and
will not end with Einstein,
but is the oldest and
youngest of all."
The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.
Profession: scientist. Born 1901, Wurzburg, Germany. Died 1976, Munich, Germany.
I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.
Born 1923, Lublin, Poland.
Died 1988, Chicago, Illinois.
Very often in mathematics the crucial problem is to recognize and
discover what are the relevant concepts; once this is accomplished
the job may be more than half done.