I really appreciate your patient engagement with the doubters in this thread, but I think that your determination to make your point has led you astray here.
> Now 6 has a "smallest" factor of 2, and a "smallest" factor of (1 - sqrt(-5)).
As [nilkn](https://news.ycombinator.com/item?id=11955341) mentioned upthread, if you consider well ordering part of the intuition of the positive integers, then you have (depending on what else you consider obvious) practically pinned down the integers already. This reference to the 'smallest' factor is not just a throwaway, and it sinks this example (why is 1 - sqrt(-5) smaller than 1 + sqrt(-5), for example?).
> So you are claiming that the author of the linked article, Prof Sir Tim Gowers, winner of the Fields Medal, Fellow of the Royal Society, doesn't understand multiplication?
This gives the impression that math is subject to an appeal to authority, which I think is a shame. The newest student can find the error in the work of the Fields Medallist—though he or she probably won't, and the error he or she seems to have found is more likely to be a concealed subtlety—and to suggest avoiding dissenting on the grounds of eminence gives entirely the wrong idea of how mathematical argument should proceed.
> Now 6 has a "smallest" factor of 2, and a "smallest" factor of (1 - sqrt(-5)).
As [nilkn](https://news.ycombinator.com/item?id=11955341) mentioned upthread, if you consider well ordering part of the intuition of the positive integers, then you have (depending on what else you consider obvious) practically pinned down the integers already. This reference to the 'smallest' factor is not just a throwaway, and it sinks this example (why is 1 - sqrt(-5) smaller than 1 + sqrt(-5), for example?).
> So you are claiming that the author of the linked article, Prof Sir Tim Gowers, winner of the Fields Medal, Fellow of the Royal Society, doesn't understand multiplication?
This gives the impression that math is subject to an appeal to authority, which I think is a shame. The newest student can find the error in the work of the Fields Medallist—though he or she probably won't, and the error he or she seems to have found is more likely to be a concealed subtlety—and to suggest avoiding dissenting on the grounds of eminence gives entirely the wrong idea of how mathematical argument should proceed.