In this book and its prequels/sequels, we see humanity guided by the
work of fictional "mathematician, Hari Seldon, who works out the rules
of psychohistory and makes a secret chart that the humankind spreads
across the galaxy will follow in order to shorten the thousands of
years of misery after the (impending) doom of the Empire. You may
think the guy never heard of "sensitive dependence on initial
conditions", but hey, there are mathematicians who are nudging people
in the right direction whenever a deviation occurs. FANTASTIC reading.
[The Foundation series] has merged with his "Robot" series, at the
beginning of which one of the directors of US Robotics is a
mathematician named Peter Bogert, who is vain and always makes wrong
decisions (to be put in his place by Susan Calvin, the legendary
For me, the Foundation series (just the three volumes published in the 1950s, not the four extra volumes published in the 1980s) is absolutely the best Science Fiction there is. The amazing story is told in very simple language and very short sentences. It is a synopsis of the various stages of human history, with the ascendence of military, religious and economic powers. The central character, who died in the very first chapter, was a mathematician. His philosophy (Hari Seldon's, and dare I say Isaac Asimov's) epitomizes the role of the universities, as the sole guardian of the long-term interest of human beings (Mac Kay). Right now, I see many education practices which are detrimental to real learning, and yet they are driven from so high up in the political and academic hierarchy that they are irrestible. So all I can do is to preserve and construct as much good material as I can manage, and hope that this will form a small part of the nucleus from which a new phoenix will arise after the current system has crumbled to ashes. Along with his short story
"The Feeling of Power", Asimov's Foundation series has profound influence on my career.
One of the problems with the Foundation trilogy, like some other comments I count only the three original books, is that it tries to put calculation as a defining factor in human action. I've been studying economics, rather than mathematics. The insights of Ludwig von Mises into the "socialist calculation problem" predicted not only the failure of any tightly regulated economy, but also why Long Term Capital Management, employing epic mathematical talent, failed and failed big time! The application of mathematics to human interaction cannot predict, because human preferences change. While Harry Seldon's calculations make for good fiction, the idea itself is a Utopian a dead end.
Like the concept of a ray gun, or the shot to the Moon, Issac Asimov showed the same mathimatical 'genius' that scientists use to predict Black Holes. There is a method to this madness and only a few geniuses can even comprehend the idea of it, although it would probably take a double genius to figure the need to accomplish it. I read the Foundation and Empire trilogy in the 1960's and it has become a basic frame over the years with which has helped me understand that a trip to chaos and back is predictible. Any movement is predicitble, static is not. Theory is not conclusive proof.
As of September 2021, there is also a TV adaptation of Foundation. It is a very well-made TV series with beautiful effects and compelling plots. The mathematicians Hari Seldon and Ga'al Dornick are major characters, and math is frequently discussed in a very positive light. The show also has attempted to add diversity, which is appreciated. For example, Ga'al is a woman of color. But, I am very unhappy with another change that was made which (IMHO) completely cancels out the benefit of the "modernization" which includes the increased diversity.
When Hari Seldon does math, he often does so by manipulating graphics floating in the air. This, I understand, is how film makers and television producers have decided to portray mathematical thought. It is, I would argue, misleading. However, the audience is still expected to believe that Hari is able to do what he does because he understands the math and because he thinks logically. In other words, he's a very smart person.
One of the horrible stereotypes in the science fiction novels and short stories written during the 20th century was that of the intuitive female. Men, the readers of those science fiction classics were led to believe, could think and figure things out, but women just had feelings. When the authors were generous, they might have suggested that this female intuition was sometimes more accurate than masculine thinking...but in any case it was something outside of the woman, some external nearly magical source, which imbued them with this knowledge, and therefore denied them any credit or authority.
Unfortunately, the people who adapted Foundation as a TV series (including many women who have worked on it) seem to have fully endorsed this viewpoint and incorporated it into the show. Ga'al (and her daughter) have visions, they "just know" things, and they have inexplicable "feelings" which leads them to show up at the right place at the right time. Although these certainly make them important characters whom the audience is rooting for, it suggests that they don't actually understand what they are doing. Unlike Hari Seldon, they are not figuring out the future and cleverly figuring out how to make things work out for the best. Instead, they seem to be merely the vessel for some spirit acting through them. (Ugh!)