More recently have been looking more to what I call number authority, with demonstrations of number theory with actual numbers where is primarily sums of squares because that's easy for me with some of my research. Like:
349672 + 7522 + 11282 + 18802 + 26322 + 41362 + 48882 = 357212
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Maybe was TOO easy for me. As didn't think much of my ability to do such things, until I did some searches to find how world's number theorists summed an arbitrary number of squares to get a square. And could not find evidence they knew how. Was so depressing for me, and disappointing too, will admit.
Disillusionment is not fun. And yes, have had plenty of reasons to realize before, but kept rationalizing. Finally realized there was no more room for benefit of the doubt.
Shifted my thinking and my approach to posts, such things. Is just one example. Maybe they do have a way. Web search used: sum squares to square
Checked again for this post. Maybe someone knows another? (Found something!!! I do keep searching and saw a paper from 1953, for a sum of 7 squares to a square.) For over a decade and before, wanted to think one way, and grudgingly have shifted to another as recent posts reflect. But like check this out.
Forgot I had this list:
1) 12 + 22 = 5
2) 32 + 42 = 25 = 52
3) 112 + 22 = 125 = 53
4) 72 + 242 = 625 = 54
5) 412 + 382 = 3125 = 55
6) 1172 + 442 = 15625 = 56
Which comes from a post from December 2014, when thought could do something clever to drum up interest.
People have to be interested in such things though. You cannot make them. And for a long time I rationalized that modern number theorists think such things trivial, and that they hearken back to older number theory which is well-worked and boring. But I've proven it is neither.
Recently came up with another list:
42 + 32 = 52
132 + 92 = 2(53)
72 + 242 = 54
792 + 32 = 2(55)
442 + 1172 = 56
3072 + 2492 = 2(57)
Why? Why not? I find numbers interesting and like to play with them. Also at times prefer that number authority that stands alone when I know there can't be a mistake, once I've checked enough to eliminate silly errors. The results are just perfect. They are absolute truths.
I find them comforting.
The social problem is not that big of a deal in the history of working mathematics. Science and technology were protected for the most part. Still, guess my job protecting the discipline of mathematics is slightly related. Have been more concerned with HUGE timeframes. Human beings come and go, but the numbers do not.
People who found a way to gain a success by pretending to be something that demonstrably does not interest them are also a problem I have to resolve, but so easily their work will be dismissed from human history. Just exclude anything presented with ring of algebraic integers as the ring should clear most of it, maybe all.
Even if I consider it dismissively, a social problem must I guess be handled.
Other mathematicians are apparently simply weak. Not smart enough to do the right thing either.
To me even the idea that it's even slightly worth it, shows how little they know of the value of perfect knowledge, or of the thrill of discovery.
The best? Accept nothing less than truth.
The best discoverers make history. Because truth works better. Duh.
Is WAY more fun too! Like, get to make cool pronouncements read all over the world.
Is SO cool.
Maybe I should take my responsibilities more seriously.
Thinking about it. Working on it.
James Harris
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