Proof involving bootstrapping?

Question

Sometimes I read in papers that a certain line was achieved by use of "bootstrapping". No one has really defined for me explicitly what this means and I am having trouble finding resources which explain this. Can someone explain to me what this means?

Answer 1

Truth be told, I was going to ask a similar question, but found this.

Since the term bootstrapping is general and can appear in many places, if you see it in a proof just interpret it as providing a hint/clue in understanding the subsequent argument.

If you read the bootstrapping wiki article it is interesting to note the different subject areas that have a professional use of the word, but you don't see mathematics as an application. I think this is due to the fact that compared to other areas, the mathematics discipline in very stable.

Two disciplines, theoretical physics and AI, will most likely get 'bootstrapping' to be adopted by some applied mathematicians; things will start moving even faster.

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I googled this topic and found these two articles:

QUANTUM FIELDS AND STRINGS
The Bootstrap: Building nature, from the bottom up

and

THEORETICAL PHYSICS
Physicists Uncover Geometric ‘Theory Space’
A decades-old method called the “bootstrap” is enabling new
discoveries about the geometry underlying all quantum theories.

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Since this is a 'soft question' and I provided a 'soft answer' I am marking it community wiki. Everyone is invited to edit this, add links or delete it.