Terence Tao on Nostr: But also, by mathematically identifying the precise hypotheses and axioms needed to ...

But also, by mathematically identifying the precise hypotheses and axioms needed to establish a negative result, one can gain valuable clues as to how to find a substitute positive result. For instance, by identifying the role of conservation of money axiom in preventing the global profitability a pyramid scheme, one can see how it is possible, in economies where wealth can be created over time via long-term investment, to create social insurance schemes (such as Social Security in the US) that can generate broad social benefits despite having some superficial resemblance to a pyramid scheme. (This is not to say that such schemes are guaranteed to be sustainable over the long term, especially if mismanaged or designed badly; but it is not mathematically impossible for this to be the case.) Or: mathematical compression of all data is impossible; however, this reveals the possibility that compression of specific types of data, such as text, is still feasible, but must somehow utilize the structural properties of that data. (5/7)