Math Mystery: Shinichi Mochizuki and the Impenetrable Proof

Scientific American ^ | 10/8/15 | Davide Castelvecchi

[Heart-Rest]

             

So that's it!  I was soooooooooooooooooo close!

[Rome2000]

Ok, but can you keep score by hand when bowling?

[Fai Mao]

“can you sum up this article in a paragraph that makes sense to someone without a 180 IQ?”

Generally I wait for a real math guy to summarize it for me. I am very much an interloper in their club.

I am not familiar with the problem this man claims to have solved so I can can’t really provide a lot of detail but it is interesting to see the arguments over his work. I enjoy reading this type of stuff and struggling with the concepts. Math is weird in that when you go from basic arithmetic into algebra it gets harder but the higher types sort of get easier - at least in concepts.

That said try these for an introduction to the interesting history of the problems dealt with in higher math

“Fermat’s Last Theorem”
http://tinyurl.com/pzploae

The Professor and the Housekeeper
http://tinyurl.com/ot26jdc

The second book, despite its rather risque sounding title is especially suitable for kids that are struggling with mathematical concepts. It has no sex, violence or foul language.

[rabidralph]

Maybe Big Bird can help.

[spokeshave]

Ha,,....maybe Mochizuki, can solve us a few common core maths problems.

[kevao]

I can work out actual calculus problems, but lose it when I think about their explanations (numbers approaching infinity in whatever context, especially).

If infinity messes you up, then you haven't even approached the limit of the power of the Calculus ;)

[opbuzz]

When the worlds top math folks are trying to figure it out...got my respect.

[opbuzz]

When the worlds top math folks are trying to figure it out...got my respect.

[aquila48]

Bookmark

[dr_lew]

You can get the gist of it by experiment. I have cygwin with bc, which will spit out calculations involving millions of digits without choking.

The fact is, exceptions to the rule of "c < d" are hard to find, so while one can appreciate that the theorem is hard to PROVE, as a matter of experiment, one would suppose that the exceptions "peter out" pretty quickly.

Wikipedia gives the example of 2^7 = 3 + 5^3, with 128 > 30, as one of these exceptions. Of course, these are very small numbers. The next example in this pattern that I found was 2^14 = 759 + 5^6, with 16384 > 7590 ... hmmm. Well, and then 2^28 = 24294831 + 5^13, with 268435456 > 242948310 .

It takes a little work, because bc doesn't do factors, although the bash shell will take you pretty high. So we've got real power at our fingertips these days.

[dr_lew]

Well, they don’t peter out all that fast! Note this:

for( i=7 ; i<1000 ; i++ ){
for( j=1 ; 5^j < 2^i ; j++ ){}
if((2^i-5^(j-1))*10 < 2^i ) i
}
7
14
21
28
72
79
86
93
137
144
151
158
165
209
216
223
230
274
281
288
295
302
346
353
360
367
411
418
425
432
476
483
490
497
504
548
555
562
569
613
620
627
634
641
685
692
699
706
750
757
764
771
815
822
829
836
843
887
894
901
908
952
959
966
973
980

So these are the values of i such that (2^i - 5^j) *10 < 2^i, for some j. The last example has:

2^980-5^422
98572376703202965492169752825178002041673673337303057739076283487555\
46960879767539742261910099240198190716485086873048815196627230093618\
84287626693787764142921903239868072489333147534493860489512377512967\
02300928414227090926298660480965721138994950586311160850663090058942\
8048219799410664754551
2^980
10218702384817765435680628290748613458265350453429542612493041881278\
52488636909601681898478332229478957743332784226557564913888250057519\
95429845596072183368720384290455095586637697931337951384943751851865\
32064890845853749530218856391110938974453986086436459043203870933208\
875495579361330830770176

So recall that the theorem has that epsilon. It only says the “exceptions” succeed by less than an arbitrarily small exponential margin, after a certain limit.

[Talisker]

Haha.

[Talisker]

Yep.