Open thread, June. 19 - June. 25, 2017

Elo

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If it's worth saying, but not worth its own post, then it goes here.

Notes for future OT posters:

1. Please add the 'open_thread' tag.

2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)

3. Open Threads should start on Monday, and end on Sunday.

4. Unflag the two options "Notify me of new top level comments on this article" and "Make this post available under..." before submitting

People have attacked the consistency of ZF with much more powerful tools and failed. Your attack wouldn't sound promising to these people, because it already sounds unpromising to me. Each further minute of your time spent on this problem would be a failure of rationality.

If you want another problem that's really fun, prove or disprove that every division of the square into triangles of equal area will have an even number of triangles :-)

0gjm9y

Strongly agree. This problem [EDITED to add: I mean Thomas's, not cousin_it's] sounds about as much worth working on as one that says: "Can you find positive integers x,y,z such that x^3+y^3=z^3? If so, ZF is broken!" No, you can't; the proof isn't all that difficult (though harder than the one for Thomas's cube-division question); the fact that the answer is no unless ZF is broken is just another way of saying "the answer can be proved to be no". I am not much interested in searching for solutions to problems that have been proved to have no solutions.