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About 20 years later, a German mathematician named Kurt Godel used what Russell and Whitehead had done in the Principia to show that it actually couldn't do what it aimed to do, that it couldn't contain all of math, that there would be true mathematical statements that were not logical consequences of the axioms that it set out.Īnd that really, it was completely shocking, and it completely transformed our understanding of what math fundamentally is. The book kind of laid the seeds for its own undoing. But the interesting thing is it's been influential in a kind of unexpected and, in some ways, sort of tragic way. REHMEYER: Well, it certainly has not been forgotten. SIEGEL: Now, how influential was this work, or was it simply a big deal for 1910 and subsequent years but forgotten long after? And when they proved it, they have this wonderful little note after it that says: The above proposition is occasionally useful.

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SIEGEL: That is a measure of their rigor that Ive read, which is how long it took them in this work to prove that one plus one equals two.

REHMEYER: Well, one version is where two parallel lines might in fact meet, and another version is where there are lots of different parallel lines through one point. SIEGEL: Where two parallel lines might in fact meet at some point. And in particular, what mathematicians had found that they were responding to was that they had discovered non-Euclidean geometries, which are kind of whole different universes of geometry that are mathematically consistent but utterly non-intuitive and not at all what we experienced in the everyday world. SIEGEL: Even if the math they were describing involved things that we didn't see in everyday life and that seemed to.

So, Russell and Whitehead set out to show that math really boiled down to logic and to define at the very most basic level what mathematics was, and to show then that all of math was logical consequences from some very, very simple principles. Mathematicians had found some surprising results that led them to realize they needed to be a whole lot more careful than they had been previously. REHMEYER: They were really trying to rescue math from a deep crisis of foundations. SIEGEL: And first, describe for us what Bertrand Russell and Alfred North Whitehead were trying to show in this book that in 1910. JULIE REHMEYER (Science Writer, and 'Wired' Magazine): Thank you, delighted to be here. And she joins us now from Berkeley, California. She writes about math for Science News and for Wired. I am deeply in over my head in these mathematical and philosophical waters, but Im hoping that Julie Rehmeyer can swim through them a bit. It was volume one of Bertrand Russell and Alfred North Whitehead's 'Principia Mathematica.' Two more volumes of the work would follow.

#Alfred north whitehead intrest in math full#

It is the failure of reform curricula to demand that children learn to work automatically-as Whitehead advocates, without thinking about what they are doing- that threatens the mission of university math and science departments.One hundred years ago this month, Cambridge University Press in England published a book that lost money, that according to one of its two co-authors was probably read in full by only six people, but that influenced the thinking of people who influenced the thinking of other people, who influenced the thinking of still others, and so on and so forth.

In contrast, students who don’t master the formal algebraic skills that should be acquired in grades K-12 are virtually impossible to remediate. If young students don’t completely understand the whys and wherefores of what they are doing, they can gain that knowledge when they are older and better able to think abstractly.

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Some mathematics educators focus only on the message of Whitehead’s first statement, but persistently and dangerously ignore the relevant warning of the second: Skills must be mastered to the point of automaticity in order to free the mind for the task at hand. Only by conflating Whitehead’s statements can one arrive at a holistic perspective, one that has been achieved by every working mathematician. Civilization advances by extending the number of important operations which we can perform without thinking about them.” “It is a profoundly erroneous truism, repeated by all copybooks and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing.