Yesterday would have been Bertrand Russell’s 144^{th} birthday and numerous people on the Internet took notice of the occasion. Unfortunately several of them, including some who should know better, included in their brief descriptions of his life and work the fact that he was the author of *Principia Mathematica*, he wasn’t. At this point some readers will probably be thinking that I have gone mad. Anybody who has an interest in the history of modern mathematics and logic knows that Bertrand Russell wrote *Principia Mathematica*. Sorry, he didn’t! The three volumes of *Principia Mathematica* were co-authored by Alfred North Whitehead and Bertrand Russell.

Now you might think that I’m just splitting hairs but I’m not. If you note the order in which the authors are named you will observe that they are not listed alphabetically but that Whitehead is listed first, ahead of Russell. This is because Whitehead being senior to Russell, in both years and status within the Cambridge academic hierarchy, was considered to be the lead author. In fact Whitehead had been both Russell’s teacher, as an undergraduate, and his examiner in his viva voce, where he in his own account gave Russell a hard time because he knew that it was the last time that he would be his mathematical superior.

Both of them were interested in metamathematics and had published books on the subject: Whitehead’s *A Treatise on Universal Algebra* (1898) and Russell’s *The Principles of Mathematics *(1903). Both of them were working on second volumes of their respective works when they decided to combine forces on a joint work the result of the decision being the monumental three volumes of *Principia Mathematica* (Vol. I, 1910, Vol. II, 1912, Vol. III, 1913). According to Russell’s own account the first two volumes where a true collaborative effort, whilst volume three was almost entirely written by Whitehead.

People referring to Russell’s *Principia Mathematica* instead of Whitehead’s and Russell’s *Principia Mathematica* is not new but I have the feeling that it is becoming more common as the years progress. This is not a good thing because it is a gradual blending out, at least on a semi-popular level, of Alfred Whitehead’s important contributions to the history of logic and metamathematics. I think this is partially due to the paths that their lives took after the publication of *Principia Mathematica*.

Whilst Russell, amongst his many other activities, remained very active at the centre of the European logic and metamathematics community, Whitehead turned, after the First World War, comparatively late in life, to philosophy and in particular metaphysics going on to found what has become known as process philosophy and which became particularly influential in the USA.

In history, as in academia in general, getting your facts right is one of the basics, so if you have occasion to refer to *Principia Mathematica* then please remember that it was written by Whitehead and Russell and not just by Russell and if you are talking about Bertrand Russell then he was co-author of *Principia Mathematica* and not its author.

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Whitehead authored of one of my favorite quotes. Unfortunately, I have lately been unable to find the exact wording, so I paraphrase: One often hears it said that progress consists of thinking hard on the things we reason about. But in the mathematical sciences, the contrary often obtains: progress consists in the number of things we can reason about without thinking, because our notation does the thinking for us, thus freeing the mind for other things.

When I was a major/graduate student Russell and Whitehead were always named together for the Principia Mathematica although it was like that, Russell first. I’ll try to be aware of the problem in future references.

It’s from Whitehead’s An Introduction to Mathematics, ch. V:

“The interesting point to notice is the admirable illustration which this numeral system affords of the enormous importance of a good notation. By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race”

[…]

“This example shows that, by the aid of symbolism, we can make transitions in reasoning almost mechanically by the eye, which otherwise would call into play the higher faculties of the brain.

“It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.”

A lovely book although it is decades since I last read it

Ah, thanks!

As a side note, PM has not worn well as a foundation for math. For decades, Zermelo-Fraenkel set theory (ZF) (or Gödel-Bernays (GB), essentially the same thing) almost always provides the starting point.

Gödel’s famous paper was titled “On Formally Undecidable Propositions of Principia Mathematica and Related Systems”, but even a casual reading of the proof shows that the details of PM don’t matter.

On the other hand, the concept of impredicative definitions, associated with Russell (and also with Poincaré), may have lead Gödel to his definition of the constructive universe, the key to his relative consistency proof for the Axiom of Choice and the Continuum Hypothesis.

“Constructive” should be “constructible”.

In 1919, Russell sent in a short note to ‘Mind’ in which he took exception to C.D. Broad’s recent attribution – “for what reason I cannot guess” – of PM’s notational novelties (over Peano) to himself instead of their actual inventor, Whitehead. And in a 1922 book review Russell took “the opportunity to protest against Mr Keynes’s practice of alluding to Principia as though I were the sole author”. So, referring to the ‘Principia Mathematica’ as (if it were) the work of Russell alone (and by those who should know better) is seemingly nothing new no…

Thank you for this wonderful information ;))

Russell’s political activism, and his books and lectures for an educated, non-specialist audience, made him a fairly well-known intellectual in the English-speaking world during the first half of the 20th. century.

Fairly well-known is a massive understatement

I appreciate this post. I had heard Whitehead referenced a few times, mostly while reading RG Collingwood’s Idea of History; and came across his Process and Reality at a used bookstore. I admit that although I’ve read through Process and Reality, it was far above me-the kind of book I expect to read years from now and with greater understanding. It did, however, make me want to sit down and read Locke with more care. Somewhere in Process, Whitehead says that Locke is to English philosophy what Plato was to Greek. High praise indeed!

Poor Whitehead! His later work has appealed to second-raters, so he ends up being associated with the intellectual backwaters of American philosophy. This is a pity, because much of his work is first rate. His two books from the 1920s, “Enquiry into the Principles of Natural Knowledge” and “Concept of Nature,” are significant (and well-written: “Process and Reality” is famously difficult, but he wasn’t in general an obscure writer) contributions to the philosophy of science.

There was originally supposed to be a fourth volume of PM, devoted to Geometry, and written by Whitehead alone. It never came out, but some of the work on the foundations of geometry that would have gone (with more symbols!) into it is expounded in the books mentioned above. It influenced, among others, Tarski.

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