[FOM] Great Achievements of F.O.M. 1

[Sam Sanders]

Being part of a European Math department, I have similar experiences to Harvey's: one usually encounters indifference or a version of the following:

> "Since mathematics is done on an informal level, formalization is pointless, meaningless, useless, misleading, countercultural, and backward. Therefore any results in f.o.m. based on any formal system is pointless, meaningless, useless, misleading, countercultural, worthless, and naive. In fact, formalization is constraining of mathematical activity, and in that sense, very dangerous. It is a preoccupation that has no place in any self respecting Math Department, because it is a preoccupation of third rate minds, attracted to rigidity for its own sake. People who work with formal systems and formalization know no mathematics, are devoid of any understanding of mathematics, and have no talent for real mathematics. Consequently, they hide in their inbred formal systems. This activity and the people pursuing it must be purged from Mathematics Departments in this age of limited resources. Given these truths, these people properly belong only in Philosophy Departments. If they can at least program a computer, then they might have some place in a Computer Science department."

However, there are some important caveats, which stem from my limited experience.

1) There is a number of mathematicians who *do* have an interest in f.o.m.; This interest is kept (semi)private because of the current climate.  
Nonetheless, some of these people even actively support f.o.m projects in grant committees (usually without explicitly showing support/interest for f.o.m.).    

2)  Most mathematicians are impressed by (even show interested in) f.o.m. after the presentation of an informal talk about Reverse Mathematics, stressing the Main Theme rather than technical detail.  
The reason for their interest is that they learned something new and surprising (the Main Theme of RM) about a subject they are supposed to know everything/a lot about.

3) I have witnessed other people deliver much-appreciated talks about f.o.m. to non-specialist audiences, including mathematics departments.


Given 1) to 3), it seems possible to (partially) reverse the trend described by Harvey.

Obviously, it is crucial (for any first introduction) to keep the level of technical detail to a minimum.  

This might sound trivial, but many people loose themselves in technical detail during talks, as this is where they feel safe.


Sam