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

[Bill Ryan]

I only learned about this yesterday, and I confess I found it VERY interesting.

I'll make this as concise and easy to understand as possible!

A brilliant Japanese mathematician called Shinichi Mochizuki (https://en.wikipedia.org/wiki/Shinichi_Mochizuki) spent more than 10 years of his life developing what he called Inter-universal Teichmüller theory (https://en.wikipedia.org/wiki/Shinichi_Mochizuki#Inter-universal_Teichmüller_theory). Among much else, it proves something very important called the abc conjecture (https://en.wikipedia.org/wiki/Abc_conjecture). (No, that's not simple!)

To accomplish this, he had to develop an entirely new set of mathematical concepts and a new system of notation.

But here's the problem. It's so impenetrable, no-one else can understand it. Not even the world's very, very best. An IQ of 200 doesn't help at all. One of his peers commented:
"It looks like it's from the future, or from outer space."
:)

And so an interesting discussion has ensued about what constitutes proof. In other words, how do you use logic to show if a statement is true or not, if on-one else understands what you're talking about?

Let's take Pythagoras' Theorem: that for a right-angled triangle, a2+b2=c2. My guess is that everyone reading this knows that one from school. And yes, you can easily prove it's always true.

But supposing you went back in time to meet a Homo Erectus. And let's assume he's friendly.

You could teach him how to make fire and cook meat. Or make better tools and clever traps. Or even maybe how to make a net and catch fish.

But you'd never be able to get him to understand the proof of Pythagoras' Theorem. And even if you're the only person in that prehistoric world who understands it, it's still true. It doesn't matter that Homo Erectus doesn't understand a lot about triangles.

But with Mochizuki's proof, the world of math has pretty much reached the consensus the proof can't be regarded as valid. Two world-class German mathematicians did work REALLY hard to try to wade through it all, and say they found a flaw. Mochizuki says they didn't understand it. No-one else has a clue.

This is just one of Mochizuki's four papers. The total runs to 500 pages, all full of notation, concepts and symbolism no-one has ever seen before.

http://kurims.kyoto-u.ac.jp/~motizuki/Alien%20Copies,%20Gaussians,%20and%20Inter-universal%20Teichmuller%20Theory.pdf (http://www.kurims.kyoto-u.ac.jp/~motizuki/Alien%20Copies,%20Gaussians,%20and%20Inter-universal%20Teichmuller%20Theory.pdf)

http://projectavalon.net/Inter-universal_Teichmuller_Theory.pdf

~~~

So now you know what it feels like to be a Homo Erectus.

:P

[EFO]

I'm not good at all at math,but when I say that 1+1 is not equal with 2,but with a bigger 1,no one believe me :),or when my wife "find" new words or phrase constructions combining 2,3 words in one and when we speak with other people in this new "language" nobody understand us not to mention that are untranslatable.:)

Yes,is intriguing what this professor found but we have to get ride of all dogmas,prejudices and constrains and only then we can be creative in understanding what he discovered.

Interesting for me at the moment is:
1.3. Introduction of identical but mutually alien copies

but I need to read the entire document.

[Karen (Geophyz)]

Well, I have been told I am good at math.....but I stopped at "These two mutually alien copies of conventional scheme theory are glued together" and my mind began to wander....and I was staring out the window wondering what my dog was digging up.......

[scanner]

42 I know, but it made you smile:bigsmile:

[Fellow Aspirant]

Years ago I spent a night helping a friend celebrate his having finally been awarded his doctorate in mathematics. A scary-smart dude with a high capacity for Chivas Regal. Far more than mine, anyway. But I digress.

He finally convinced me to read his thesis, expecting me to express my admiration for such a scholarly achievement. My intellectual forte is in the field of English study, so I have spent my life avoiding numbers, but curiosity got the better of me: I gave it a shot. And here's the thing: there were no numbers in his paper! None! Its content, which ran to thirty pages, had lots of concepts and arcane symbols, but it was all nonsensical to me, even without the confusion of numbers. I did express my admiration for his intellectual prowess and ability to focus on such fantastical concepts, but I had no idea what he had actually presented, let alone proven. Mathematics, I have concluded, is a realm outside of what non-mathematicians consider reality to be.

Thus, to learn of a mathematician who is working beyond the ken of high performance mathematicians, I can but shrug and hope that they are able to sort it out amongst themselves.

Brian

[East Sun]

Consider me totally stupid, if you like, but what difference does it make to anything of any relevance to anything really
important in this time? What will anything benefit from what they have said is of relevance?

I have always been considered as stupid by so called peers I think but maybe not.
I did not read most of the foregone data so really should shut up now.Sorry for wasting your time,

[DeDukshyn]

Ahhhh trying to wade into the weird world of attempting to make effable, the ineffable ... without sounding like a complete fool. I feel this guys pain ...

[Mashika]

Consider me totally stupid, if you like, but what difference does it make to anything of any relevance to anything really
important in this time? What will anything benefit from what they have said is of relevance?

Call me stupid if you want, I may be, I have always been considered as stupid by so called peers. Nothing new in that.
I did not read most of the foregone data so really should shut up, now Sorry for wasting your time,

Consider the Atom, no one had a use for that knowledge way back, what did it matter to know there's such a thing as an atom? It won't help anyone get their job done, or put food on the table, get a better job or keep everyone healthy in the family and so on back then

But without the understanding of how atoms work, we would not have any of the current technology today, so we would be stopped in time living a very different lifestyle, no planes, no rockets, no science as it exists today

Stuff like what's on that doc is not meant really to suddenly affect current life, it can't, it mean to set the base for future improvements, just like first generation that saw the power of the atom may not even be around anymore but we have all sorts of great stuff that came out of that

Someone has to figure things out and open new roads for future generations, right?

[Bill Ryan]

Someone has to figure things out and open new roads for future generations, right?For sure. The history of mathematics has often been that first things are figured out simply as theoretical intellectual exercises. Then generations later, it's realized that all that arcane theoretical stuff is really useful in engineering. Electronics, aerospace, car and airplane engines, power stations, radio waves, your phone and computer. Maybe even your toaster!

An example: Isaac Newton, and the apple that dropped from the tree (maybe! :) ), and his insights into gravity, and what are now known as Newton's Laws of Motion. Those same equations — and the calculus he also developed — are now used in spaceflight. But that's not why Newton worked all that out... he did it simply because he could.

[James]

The Force will be strong with the comments on this thread, but seriously, I want to find a Limitless pill just to understand what he’s even talking about.

:nerd:

[Satori]

If no one can understand his papers on the subject, how can anyone be sure he is correct or be sure that he is incorrect?

It seems to me that mathematics is too important to leave to faith

What value is added to our understanding of universe or practical aspects of day-to- day life if no one can grasp the veracity, or not, of his assertions? Are we to hand the topic over to him and rely on his genius alone? Does what he writes about and his calculations and such make any difference to us at a basic level, or is he simply displaying his genius? How would we know?

I have questions, not answers.

[Bill Ryan]

Well, I have been told I am good at math.....but I stopped at "These two mutually alien copies of conventional scheme theory are glued together" and my mind began to wander....and I was staring out the window wondering what my dog was digging up.......There's a short Numberphile video (https://www.youtube.com/watch?v=RkBl7WKzzRw) about the abc conjecture (https://en.wikipedia.org/wiki/Abc_conjecture) (which this entire thesis, together with 3 other long papers, is claimed to prove). The Numberphile subscribers are pretty bright people. Quite a few of the YouTube comments were about the wallpaper behind the presenter, which was inexplicably patterned with pigeons. :)

[Bill Ryan]

If no one can understand his papers on the subject, how can anyone be sure he is correct or be sure that he is incorrect?

It seems to me that mathematics is too important to leave to faith

What value is added to our understanding of universe or practical aspects of day-to- day life if no one can grasp the veracity, or not, of his assertions? Are we to hand the topic over to him and rely on his genius alone? Does what he writes about and his calculations and such make any difference to us at a basic level, or is he simply displaying his genius? How would we know?

I have questions, not answers.Exactly. :highfive: 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. :)

Shinichi Mochizuki (https://en.wikipedia.org/wiki/Shinichi_Mochizuki) is clearly an eccentric geeky supergenius oddball — to say the least. When he finished this magnum opus, he never even shouted from the rooftops. He just quietly posted a small note on his blog, and never said a word to anyone. Then one or two people started to notice and it gradually all spread on social media.

His response to most people who ask him to please, please explain and expand on things (maybe he could do a lecture program! He'd sell a lot of tickets) is that they should just work harder at understanding what he's written. Doesn't help much!

There's a similar example, actually. Such a fascinating human story.

Another very famous conjecture (a 'conjecture' is something mathematicians believe is true, but it's never actually been proved) was called The Poincaré Conjecture. The best of the very best in the world had tried and failed to make any progress at all for a whole century.

Then a brilliant, eccentric, reclusive Russian, Grigori Perelman (https://en.wikipedia.org/wiki/Grigori_Perelman), succeeded. When he mentioned that he'd proved it, at first no-one believed him. But then others checked, out of intense curiosity, and realized that he was 100% right. He'd really done it.

He was awarded the Fields Medal (this is like the Nobel Prize for Math), but he declined it. Then he was awarded a million dollars cash, which was a longstanding prize for whoever might possibly prove the Poincaré conjecture. And he turned down the million dollars, too, though he was living in his mother's apartment in genuine poverty.

He said: "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo."

This article describes Perelman quite well, after he'd refused the million dollar prize:


World's top maths genius jobless and living with mother
https://telegraph.co.uk/news/1526782/Worlds-top-maths-genius-jobless-and-living-with-mother.html

Homo Erectus would find all that hard to understand, too. :)

[eagle0027]

Well...im far from stupid....and care not what iq others think they are...especially if they cant explain their so called theroies in a manner that us appaeent less iq equivilents possess

[Mashika]

If no one can understand his papers on the subject, how can anyone be sure he is correct or be sure that he is incorrect?

It seems to me that mathematics is too important to leave to faith

What value is added to our understanding of universe or practical aspects of day-to- day life if no one can grasp the veracity, or not, of his assertions? Are we to hand the topic over to him and rely on his genius alone? Does what he writes about and his calculations and such make any difference to us at a basic level, or is he simply displaying his genius? How would we know?

I have questions, not answers.

I don't think it will be left to faith, at any time in history things looked impossible complex and then humanity went past that roadblock. Someone else will come up with an explanation and say true or false on this theory. Then later on, if true, someone may be good uses out of it.

Right now, we won't most likely figure out the entire thing because we look a it from an inadecuate point of view, maybe we are not smart enough yet to understand it but someone will eventually

I cannot build a rocket engine but i sure know why it can move in space without air, try explaining that to someone from 100 years ago (traveling on space without air), things just move forward and people get more knowledge aggregated so they can understand things better than previous generations (in my day, we had machine learning algorithms and google A.I. and stuff! Yes shut up grandma you're interrupting my virtual universe creation session, i got this planet orbit calculations wrong because of your yelling!)

Maybe this will end in nothing LOL, someone will completely prove it wrong and that's it, or prove it right?

[Anka]

The short history of humanity and the longest evolution path in full freedom of choice gives us in the most beautiful way the symptomatic emotion between the illusion, the attention and the memory of knowing in an overview of the human from billions of perspectives seen from sources of psychology, sociology, neurobiology, anthropology, neuroscience, a true literature developed to raise awareness of the way and environment in which we function, but also from the perspective that "Anything is possible":bigsmile:

"Anything can be possible?" ... we say yes, but how long will it take to find usefulness in this, individually or perhaps at the same time collectively (?)

Sometimes, in my mind, I become my own source of culture in which mathematical terms explain my individual sovereignty through a single degree of spiritual coherence that I cannot explain in words and if I tried, it would not be, what must be according to science.
But it's a little fun for me and maybe I'll learn some of it, who knows, in another way, another time:inlove:
Time ... a detail in the path or within reach of spirituality and science, who knows.
I just know, inexplicable, that now I have to drink my coffee...:p

[Bill Ryan]

[There's a similar example, actually. Such a fascinating human story.

Another very famous conjecture (a 'conjecture' is something mathematicians believe is true, but it's never actually been proved) was called The Poincaré Conjecture. The best of the very best in the world had tried and failed to make any progress at all for a whole century.

Then a brilliant, eccentric, reclusive Russian, Grigori Perelman (https://en.wikipedia.org/wiki/Grigori_Perelman), succeeded. When he mentioned that he'd proved it, at first no-one believed him. But then others checked, out of intense curiosity, and realized that he was 100% right. He'd really done it.

He was awarded the Fields Medal (this is like the Nobel Prize for Math), but he declined it. Then he was awarded a million dollars cash, which was a longstanding prize for whoever might possibly prove the Poincaré conjecture. And he turned down the million dollars, too, though he was living in his mother's apartment in genuine poverty.

He said: "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo."

This article describes Perelman quite well, after he'd refused the million dollar prize:



World's top maths genius jobless and living with mother
https://telegraph.co.uk/news/1526782/Worlds-top-maths-genius-jobless-and-living-with-mother.html


Homo Erectus would find all that hard to understand, too. :)

~~~

A little more about Perelman, who has fastidiously avoided journalists and any form of publicity. Even the author of the book about him, Perfect Rigour: A Genius and the Mathematical Breakthrough of the Century, was unable to meet him.

One journalist who managed to reach him on his cellphone was told: "You are disturbing me. I am picking mushrooms."

Now that, Homo Erectus would understand. :)

[Mashika]

[There's a similar example, actually. Such a fascinating human story.

Another very famous conjecture (a 'conjecture' is something mathematicians believe is true, but it's never actually been proved) was called The Poincaré Conjecture. The best of the very best in the world had tried and failed to make any progress at all for a whole century.

Then a brilliant, eccentric, reclusive Russian, Grigori Perelman (https://en.wikipedia.org/wiki/Grigori_Perelman), succeeded. When he mentioned that he'd proved it, at first no-one believed him. But then others checked, out of intense curiosity, and realized that he was 100% right. He'd really done it.

He was awarded the Fields Medal (this is like the Nobel Prize for Math), but he declined it. Then he was awarded a million dollars cash, which was a longstanding prize for whoever might possibly prove the Poincaré conjecture. And he turned down the million dollars, too, though he was living in his mother's apartment in genuine poverty.

He said: "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo."

This article describes Perelman quite well, after he'd refused the million dollar prize:



World's top maths genius jobless and living with mother
https://telegraph.co.uk/news/1526782/Worlds-top-maths-genius-jobless-and-living-with-mother.html


Homo Erectus would find all that hard to understand, too. :)

~~~

A little more about Perelman, who has fastidiously avoided journalists and any form of publicity. Even the author of the book about him, Perfect Rigour: A Genius and the Mathematical Breakthrough of the Century, was unable to meet him.

One journalist who managed to reach him on his cellphone was told: "You are disturbing me. I am picking mushrooms."

Now that, Homo Erectus would understand. :)

Totally get the magic of living the most simple life, would not be able to do myself but it's charming in several ways and honestly i feel very attracted to it sometimes :)

I think he's way more smart than he let's people know, and he just simply figured out that the way to happiness was just to have some potato & mushroom soup LOL

No worries in the world but to have something tasty to eat and a place to sleep, your tea and a book or two to read, and you can just let life go easy and go sleep without any worry. Maybe I'm biased but I totally get that :)

[johnf]

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

[Agape]

Well, I have been told I am good at math.....but I stopped at "These two mutually alien copies of conventional scheme theory are glued together" and my mind began to wander....and I was staring out the window wondering what my dog was digging up.......

Got slightly ahead to where “alien copies of conventional scheme theory are glued together” by θ factor 😀
What’s θ than an attempt for limitless synchronicity between two time-space continuums. While we can prove or disprove it as real number for small integers
it would be nearly impossible to prove it real number “ad infinitum”.

Example: two unrelated galaxies holding together by unknown θ algorithm for a long time before they drift away. The binding factor θ is an abstract unknown to residents of both galaxies. Once they discover it they can pass through a wormhole to see each other. But then: do they have anything else in common than θ?

Taking next step would be like crossing to “alien galaxy”. The problem of θ is dissolved by moving through the θ worm hole but then the galaxies aren’t longer alien.
By that foolish act alone the value of θ starts increasing till it reaches another approvable value. Then it collapses to itself and one can start anew.
But it’s quite impossible to prove any θ has value set in infinite or as some kind of really large integer.

It would be nice if it was so, however 🐨

I’m going to think about it for the rest of the day 🙏 then read some more pages ..

[Sunny-side-up]

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 (https://www.galoisrepresentations.com/2017/12/17/the-abc-conjecture-has-still-not-been-proved/) 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 (https://www.galoisrepresentations.com/2017/12/17/the-abc-conjecture-has-still-not-been-proved/) 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 (https://en.wikipedia.org/wiki/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]

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...
_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]

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 (https://en.wikipedia.org/wiki/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.