[FOM] informal poll special terms in logic

[tchow]

Harvey Friedman wrote:

> In the legitimate and important movement to replace the term "pure
> mathematics" with "theoretical mathematics", perhaps the use of
> "theoretical physics" should be cited? Note that the physicists were
> not so stupid as to fall into the trap of adopting the term "pure
> physics".

There was a famous article in 1993 by Jaffe and Quinn with the term 
"theoretical mathematics" in the title.

http://www.ams.org/journals/bull/1993-29-01/S0273-0979-1993-00413-0/S0273-0979-1993-00413-0.pdf

Roughly speaking, they were suggesting the use of the term to refer to 
non-rigorous mathematics in the style of theoretical physics.  They 
claimed that some well-known people were making mathematical assertions 
that were not exactly conjectures (because they were backed up with 
arguments) but were not exactly theorems either (because the level of 
rigor of the arguments was similar to the level of rigor used in 
theoretical physics, not the level of rigor used in traditional 
mathematics).  They felt that this practice was harming the field by 
discouraging others from pursuing rigorous proofs because all the 
"credit" for the result had already been pre-empted.  They felt that 
introducing the term "theoretical mathematics" might help address this 
(alleged) problem by clarifying the status of such results.

This is not to say that the term "theoretical mathematics" can't be 
co-opted for other purposes; it's just a warning that the term has 
already been used to mean something different from what Friedman is 
suggesting.

Tim