fredag 25 augusti 2023

Physics Collectivism vs Mathematics Individualism



It is sometimes claimed that physics is a collective effort, while mathematics is rather a collection of individual efforts. Let us test this hypothesis by analysing the use of the first person plural pronoun "we".  

Let us start with physics noting how Andrew Strominger as a modern physicist of reputation invited by Lex Fridman to an interview entitled Black Holes, Quantum Gravity, and Theoretical Physics responds the following question by Lex:
  • What is the effort of quantum gravity (to reconcile the standard model and general theory of relativity as the main open problem of modern physics)?
Andrew tells Lex:
  • The one fully consistent model we have is string theory.
  • We do not know if in any sense string theory describes the world.
We see that Andrew uses the pronoun "we" to send a message that modern physics is a collective effort, or more precisely a selective collective effort performed by an inner circle of leading modern physicists. For someone outside this group (which is not well defined) to say "we" in this context would be pretentious. By using an exclusive "we" Andrew signals that he belongs to the inner circle. 

There is another inclusive "we" often used in mathematical reasoning starting with a phrase like "We assume that x is a positive real number". Here "we" includes the reader or just anybody without asking for any qualification.

We know that the mathematics of Calculus was invented (in competition) by Leibniz and Newton, who both could say with confidence that "I invented Calculus", but never "We invented Calculus". 

More generally, a mathematician would rarely use "we" in the exclusive inner circle meaning, since the inner circle typically would have only one member. Mathematical theorems or theories mostly carry just one name like Brouwer's Fixed Point Theorem or Galois Theory. 

Maybe this indicates a difference between (modern) physics and mathematics, with physics being shared by physicists as some form of common reality or fiction, while mathematics is a human construct created by individuals like pieces of literature or art as individual efforts. 

But it may be tempting for both a physicist and mathematician to use "we" to signal membership in some group of prestige behind some theorem/theory. You can make your own observations...

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