A Japanese math professor has a major new proof. But no-one can understand it

[Sunny-side-up]

Posted by johnf (here)
I am curious if and how the mathematician in the OP is being funded. Also throughout this thread are demonstrations
of the principle that to teach, or find agreement on an idea, one must start where the student is. If you can find what step the student understands, then you can build a bridge to more advanced and obscure ideas. I have tried to do this with the subject of fractals, and I can grasp simple concepts such as order underlying apparently random patterns, but then there is a picture of the Mandelbrot set, and I try to grasp that and my brains fall out. I read a lot of posts on the Buddhabrot set thread, and I couldn't find a bridge to understand (with my intellect) how it represented anything in the real world. But that thread had pictures, and they looked beautiful. In this one though my brains just fell out, but enough remained to agree with most posts! Thank God there is more to life than intellect. Also I hope he is on to something that someone can use to enrich lives in the future.


John

Yes john, well said, BTW my 'brains just fell out' when I spent 3 years of day to day meditative life or was it the first (Many times) time I wen't over the handle bars of my motor bike and other such experiences.

That was partly my imaginary example about explaining Pythagoras' Theorem to a Homo Erectus.

In our frame of reference, it's a proven truth. (And it's quite a simple one, too.) In the Homo Erectus world, it'd be incomprehensible and of absolutely no meaning or relevance. They'd all be excited about making a fire that evening, which you'd just taught them how to do.

Re Inter-universal Teichmüller theory, some think (maybe wisely!) that we'll just have to wait a few generations until someone comes along who's bright enough to (a) understand it all, and (b) explain it all clearly to everyone else.

That may be so Bill,
but given the latest views and findings of the ancient world, and the fact that we couldn't make or understand how they did it even to day?
Those ancient ancestors of ours look like they where sitting around a plastic table with great minds from some other place's or time's, holding chins and nodding about the task at hand.
or did they just have great abilities over matter that we in our over complicated mathematical world have not.

Either way we were all made to forget?
Made to start again and to see what we can come up with next.

No new discoveries but re-found, remembered ones, or hidden from us ones.

I must confess I do find it amazing that some people can actually put the universe into numbers and actually now what they are doing 0.o

[Bill Ryan]

For anyone reading this who's been enjoying this unusual discussion, this extract from this article might raise a further smile.

If Mochizuki had carved his argument on slate in Linear A and then dropped it into the Mariana Trench, then there would be little doubt that asking about the veracity of the argument would be beside the point. The reality, however, is that this description is not so far from the truth.

[Kryztian]

So what can homo sapiens in the 21st century do with this math? Can we build a better mousetrap with it? Will there be a new method of propulsion or an anti-dote to COVID-19 that can be developed based on this math? If there aren't any practical applications now, might there be some day? And if not, shouldn't we just tell all the mathematicians in the world to stop showing up for work and go mushroom picking instead?

[Anka]

I think I understand the conjuncture from the depth of its simplicity of being, which is neither ignorance nor concealment of a secret, seems to be simply an ethics of individual natural human rigor in which Dr.Perelman said:
- "I have published all my calculations. This is what I can offer the public."
-"I'm not interested in money or fame; I don't want to be on display like an animal in a zoo."
…and
One journalist who managed to reach him on his cellphone was told: "You are disturbing me. I am picking mushrooms."
Another extract from that article that I like is:
“But the idea that several hundred hours at least would be required even to scratch the beginnings of the theory, is either utter rubbish, or so far beyond the usual experience of how things work that it would be unique not only in mathematics, but in all of science itself.

So where to from here?”

I like the diversity of the topic on this thread, it gives anyone the opportunity to be purely inspired to write from current ideas and from their own experiences.
Man is a rational being endowed with consciousness, which dramatically experiences the impossibility of total knowledge, and expresses live, the natural course of its development, which is not a pain but a normal expansion that can be magnificent to see over generations.

Its originality comes from the way in which an inventive, creative spirit transforms existence into a spectacle, can be a syntagma, in reflecting from the perspective of the inner world the objective world outside through mathematics, I do not know, but it is wonderful that it is a qualitative feature that is in the power of contemplative selection and production of the equations in the metaphorical beauty of the metaphysical "fragmentation"

[East Sun]

We know that often geniuses are " lacking in what we would call common sense, like Tesla for example but
we are blind to what they can give us. The exploiters and manipulators lways take advantage of them.
We should be aware of that and protect them at all costs.

[Bill Ryan]

This is mostly unrelated — but the link is that this guy, too, was a Good Will Hunting type genius. It's a great story.

George Dantzig was at college at Berkeley in 1939, and was late for a lecture. At the end of the class, he jotted down his homework assignment from a note he copied from the blackboard.

He thought it was a little harder than usual, but completed the assignment in a couple days.

A little while later, his college professor came to bang on the door of his house at 8 am. He excitedly told Dantzig that what he'd handed in wasn't the homework assignment, but two major famous problems the professor had written on the board as never having been solved.

Later, when he came to begin his PhD, he asked what he might work on. "Easy," came the reply. "Just put your two proofs in a binder, and there's your PhD right there."

His later mathematical work had a whole bunch of important real world applications. He enabled the airline industry to schedule crews and make fleet assignments. Shipping companies used his work to determine how many planes they need and where their delivery trucks should be deployed. The oil industry used his work in refinery planning, as it determines how much of its raw product should become different grades of gasoline and how much should be used for petroleum-based byproducts. His work is used in manufacturing, revenue management, telecommunications, advertising, architecture, circuit design and countless other areas.

Almost as valuable as picking mushrooms.

[araucaria]

Posted by Bill Ryan (here)

Almost as valuable as picking mushrooms.

And just as potentially lethal??

[Anka]

The level of each superficiality or ingenuity must compete not with the morality or reality of a perception, but on the contrary with "finding" the threshold of intelligence in perfect wisdom,
a threshold for which we must find viable solutions for survival in one's own thinking and especially in good conditions.
In any statistic or theory of technology itself there is a problem, the idea is that while we still wonder what the problem is, technology seems to live on us, sometimes even differently.
What is the strategy or the mismatch between our needs and the simple duty of living, contains a philosophy that is perhaps far too broad.
I do not think it is about any action, desire, or faith, it is an individual factual state that belongs to us in a funny way collectively.
We are all here in a classic scene that characterizes us, but we can always appreciate the authenticity throughout its understanding for genius people, so what remains to be done (?), because sometimes it seems flawless,I do not know.
There are simply rhetorical thoughts, along a search that will find us, I think ...

And because I may have been too serious, although things are vitally important, the video below demonstrates in a funny way that there is a riddle of life, but sometimes I am not so great as to discover it...

Source: https://youtube.com/watch?v=_j9qAhXfNAU

I'm sorry, I could not help but sometimes, genius does not lead us to the path of performance, although sometimes performance stands as the proof of genius within our reach.

[happyuk]

Posted by Bill Ryan (here)
This is mostly unrelated — but the link is that this guy, too, was a Good Will Hunting type genius. It's a great story.

George Dantzig was at college at Berkeley in 1939, and was late for a lecture. At the end of the class, he jotted down his homework assignment from a note he copied from the blackboard.

He thought it was a little harder than usual, but completed the assignment in a couple days.

A little while later, his college professor came to bang on the door of his house at 8 am. He excitedly told Dantzig that what he'd handed in wasn't the homework assignment, but two major famous problems the professor had written on the board as never having been solved.

Later, when he came to begin his PhD, he asked what he might work on. "Easy," came the reply. "Just put your two proofs in a binder, and there's your PhD right there."

His later mathematical work had a whole bunch of important real world applications. He enabled the airline industry to schedule crews and make fleet assignments. Shipping companies used his work to determine how many planes they need and where their delivery trucks should be deployed. The oil industry used his work in refinery planning, as it determines how much of its raw product should become different grades of gasoline and how much should be used for petroleum-based byproducts. His work is used in manufacturing, revenue management, telecommunications, advertising, architecture, circuit design and countless other areas.

Almost as valuable as picking mushrooms.

Ah I knew that name rang a bell. The simplex method. His work has become so important I can't even begin to express it, but you name any industrial problem requiring any kind of optimisation ("minimise f(x), subject to ... constraints) it's almost certain to have his stamp on it. Many companies operating in today's ultra-competitive environment, where profit margins are extremely tight, rely on these kinds of techniques to identify where the savings are to be made - and that saving they make is essentially their profit.