Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don't look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.
Interpretation
This quote emphasizes that mathematics, like science, seeks to find similarities and connections between seemingly different concepts.
Gian-Carlo Rota highlights that mathematics is essentially about discovering relationships, drawing parallels between different analogies, much like the broader scientific endeavor. This pursuit reflects a deep-seated psychological drive to find unity in diversity, suggesting that true understanding comes from recognizing that disparate elements can share fundamental principles.
In practice
During a lecture on mathematical theories, a professor could use this quote to illustrate the nature of scientific exploration.
The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.
Every lecture should state one main point and repeat it over and over, like a theme with variations. An audience is like a herd of cows, moving slowly in the direction they are being driven towards. If we make one point, we have a good chance that the audience will take the right direction; if we make several points, then the cows will scatter all over the field. The audience will lose interest and everyone will go back to the thoughts they interrupted in order to come to our lecture.
A mathematician's work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more often than not a way of making sure that our minds are not playing tricks.
God created infinity, and man, unable to understand infinity, had to invent finite sets.
[In mathematics] There are two kinds of mistakes. There are fatal mistakes that destroy a theory, but there are also contingent ones, which are useful in testing the stability of a theory.
I think physicists are the Peter Pans of the human race. They never grow up and they keep their curiosity.
I take no pleasure in the fact that the scientific predictions I’ve relayed to popular audiences turn out to be true.
Ideas which have been developed simultaneously or in immediate succession in the same mind mutually reproduce each other, and do this with greater ease in the direction of the original succession and with a certainty proportional to the frequency with which they were together
Every great advance in natural knowledge has involved the absolute rejection of authority.
In less than eight years "The Origin of Species" has produced conviction in the minds of a majority of the most eminent living men of science. New facts, new problems, new difficulties as they arise are accepted, solved, or removed by this theory; and its principles are illustrated by the progress and conclusions of every well established branch of human knowledge.
The Three Laws of Robotics: 1: A robot may not injure a human being or, through inaction, allow a human being to come to harm; 2: A robot must obey the orders given it by human beings except where such orders would conflict with the First Law; 3: A robot must protect its own existence as long as such protection does not conflict with the First or Second Law; The Zeroth Law: A robot may not harm humanity, or, by inaction, allow humanity to come to harm.
Subscribe for the occasional hand-picked quote. No noise.