I’ll leave the questions on this subject to someone with a firmer grasp of math theory than I can claim.

Japanese mathematician claims to have solved a notorious maths problem, but nobody understands it

The ABC conjecture
Shinichi Mochizuki of the Research Institute for Mathematical Sciences at Kyoto University is such a mathematician. In August 2012, he posted a series of four papers on his personal web page claiming to prove the ABC conjecture, an important outstanding problem in number theory.

A proof would have Fermat’s Last Theorem as a consequence (at least for large enough exponents), and given the difficulty of Wiles’ proof of Fermat’s Last Theorem, we should expect a proof of the ABC conjecture to be similarly opaque.

The conjecture is fairly easy to state. Suppose we have three positive integers a,b,c satisfying a+b=c and having no prime factors in common. Let d denote the product of the distinct prime factors of the product abc. Then the conjecture asserts roughly there are only finitely many such triples with c > d. Or, put another way, if a and b are built up from small prime factors then c is usually divisible only by large primes.

Here’s a simple example. Take a=16, b=21, and c=37. In this case, d = 2×3×7×37 = 1554, which is greater than c. The ABC conjecture says that this happens almost all the time. There is plenty of numerical evidence to support the conjecture, and most experts in the field believe it to be true. But it hasn’t been mathematically proven – yet.

Enter Mochizuki. His papers develop a subject he calls Inter-Universal Teichmüller Theory, and in this setting he proves a vast collection of results that culminate in a putative proof of the ABC conjecture. Full of definitions and new terminology invented by Mochizuki (there’s something called a Frobenioid, for example), almost everyone who has attempted to read and understand it has given up in despair.

Add to that Mochizuki’s odd refusal to speak to the press or to travel to discuss his work and you would think the mathematical community would have given up on the papers by now, dismissing them as unlikely to be correct. And yet, his previous work is so careful and clever that the experts aren’t quite ready to give up.

Sometime on the morning of 30 August 2012, Shinichi Mochizuki quietly posted four papers on his website.

The papers were huge — more than 500 pages in all — packed densely with symbols, and the culmination of more than a decade of solitary work. They also had the potential to be an academic bombshell. In them, Mochizuki claimed to have solved the abc conjecture, a 27-year-old problem in number theory that no other mathematician had even come close to solving. If his proof was correct, it would be one of the most astounding achievements of mathematics this century and would completely revolutionize the study of equations with whole numbers.

Mochizuki, however, did not make a fuss about his proof. The respected mathematician, who works at Kyoto University’s Research Institute for Mathematical Sciences (RIMS) in Japan, did not even announce his work to peers around the world. He simply posted the papers, and waited for the world to find out.

A possible answer to the question “why now?” Is that these papers have just appeared for the first time in English, having been in Japanese before.

Abstract. The present paper is the first in a series of four papers, the
goal of which is to establish an arithmetic version of Teichm¨uller theory for number
fields equipped with an elliptic curve — which we refer to as “inter-universal
Teichm¨uller theory” — by applying the theory of semi-graphs of anabelioids,
Frobenioids, the ´etale theta function, and log-shells developed in earlier papers by
the author. We begin by fixing what we call “initial Θ-data”, which consists of
an elliptic curve EF over a number field F, and a prime number l ≥ 5, as well as
some other technical data satisfying certain technical properties. This data deter-
mines various hyperbolic orbicurves that are related via finite ´etale coverings to the
once-punctured elliptic curve XF determined by EF . These finite ´etale coverings
admit various symmetry properties arising from the additive and multiplicative
structures on the ring Fl = Z/lZ acting on the l-torsion points of the elliptic curve.
We then construct “Θ±ellNF-Hodge theaters” associated to the given Θ-data. These
Θ±ellNF-Hodge theaters may be thought of as miniature models of conventional
scheme theory in which the two underlying combinatorial dimensions of a
number field — which may be thought of as corresponding to the additive and
multiplicative structures of a ring or, alternatively, to the group of units and
value group of a local field associated to the number field — are, in some sense,
“dismantled” or “disentangled” from one another. All Θ±ellNF-Hodge theaters
are isomorphic to one another, but may also be related to one another by means of a
“Θ-link”, which relates certain Frobenioid-theoretic portions of one Θ±ellNF-Hodge
theater to another in a fashion that is not compatible with the respective conven-
tional ring/scheme theory structures. In particular, it is a highly nontrivial
problem to relate the ring structures on either side of the Θ-link to one another. This
will be achieved, up to certain “relatively mild indeterminacies”, in future papers
in the series by applying the absolute anabelian geometry developed in earlier
papers by the author. The resulting description of an “alien ring structure” in terms of a given ring structure will be applied in the final paper of the series to
obtain results in diophantine geometry. Finally, we discuss certain technical results
concerning profinite conjugates of decomposition and inertia groups in the tem-
pered fundamental group of a p-adic hyperbolic curve that will be of use in the
development of the theory of the present series of papers, but are also of independent interest

Not an easy read.

Cool. Found a question.

Would this proof confine randomness within physics?

Postpocelipse said:

Cool. Found a question.

Would this proof confine randomness within physics?

Please explain question.

PS. If this is the future of mathematics, why are mathematicians still not getting past the integers? Surely by now mathematicians should be taking an interest in real numbers.

mollwollfumble said:

Postpocelipse said:

Cool. Found a question.

Would this proof confine randomness within physics?

Please explain question.

I am only making intuitive sense of the paper so far. The theorem suggests a calculability to physics randomness such as decay moment etc.

PS. If this is the future of mathematics, why are mathematicians still not getting past the integers? Surely by now mathematicians should be taking an interest in real numbers.

The title was chosen on the basis this guy is onto something and there may be a new field to investigate. My question related to physics randomness obtaining a real number nature through this proof, possibly.

in the future maths teachers will be dressed in silvery one piece suits , very much GORT from the day the earth stood still

all maths teachers will use the special “google helmet” with heads up display to project maths formula to the teacher

the google helmet in action against tardy behaviour and unruly students

Chips for the brain

Id like a math and physics chip installed in my brain

If someone can do that in the future that would be good

they can make other chips for the brain too, like trade chips, woodworking, silversmith, electrician, plumber, beginner, mechanic, software programmer etc

(maths)

Spiny Norman said:

(maths)

(meh)

Postpocelipse said:

mollwollfumble said:

Postpocelipse said:

Cool. Found a question.

Would this proof confine randomness within physics?

Please explain question.

I am only making intuitive sense of the paper so far. The theorem suggests a calculability to physics randomness such as decay moment etc.

PS. If this is the future of mathematics, why are mathematicians still not getting past the integers? Surely by now mathematicians should be taking an interest in real numbers.

The title was chosen on the basis this guy is onto something and there may be a new field to investigate. My question related to physics randomness obtaining a real number nature through this proof, possibly.

:-) Good. (backing off)

CrazyNeutrino said:

Id like a math and physics chip installed in my brain

Id like a math and physics chip installed in my computer! My computer keyboard doesn’t even have genuine minus, times or divide-by signs, even the first calculator had those. Also missing all the other useful maths symbols.

Maths journals won’t accept equations and papers typed in Microsoft. Has to be from Linux, using a typesetting program that hasn’t improved its maths typesetting since 1978. Windows calculator for Windows 10 has lost all its scientific and engineering functions. Fortran hasn’t added any new maths functions since 1977. Excel hasn’t added any new maths functions since the version I used with Windows 3.11.

Microsoft’s equation editor now is (apart from better kerning) much worse than it was back in Windows 3.11. Much more difficult to find symbols font (needed by maths) in Office than it was back in Windows 3.11. Excel has never handled subscripts and superscripts correctly.

So let’s have a math and physics chip for the computer – as well as a keyboard with printed mathematical symbols.

mollwollfumble said:

CrazyNeutrino said:

Id like a math and physics chip installed in my brain

Id like a math and physics chip installed in my computer! My computer keyboard doesn’t even have genuine minus, times or divide-by signs, even the first calculator had those. Also missing all the other useful maths symbols.

Maths journals won’t accept equations and papers typed in Microsoft. Has to be from Linux, using a typesetting program that hasn’t improved its maths typesetting since 1978. Windows calculator for Windows 10 has lost all its scientific and engineering functions. Fortran hasn’t added any new maths functions since 1977. Excel hasn’t added any new maths functions since the version I used with Windows 3.11.

Microsoft’s equation editor now is (apart from better kerning) much worse than it was back in Windows 3.11. Much more difficult to find symbols font (needed by maths) in Office than it was back in Windows 3.11. Excel has never handled subscripts and superscripts correctly.

So let’s have a math and physics chip for the computer – as well as a keyboard with printed mathematical symbols.

my keyboard has ½ of them…

mollwollfumble said:

Windows calculator for Windows 10 has lost all its scientific and engineering functions. Fortran hasn’t added any new maths functions since 1977. Excel hasn’t added any new maths functions since the version I used with Windows 3.11.

Err, if you select calculator under Win 10 and then check the scientific section I’d imagine that this would bring up the normal scientific bits.

How many new maths functions need to be added to excel?

sibeen said:

mollwollfumble said:

Windows calculator for Windows 10 has lost all its scientific and engineering functions. Fortran hasn’t added any new maths functions since 1977. Excel hasn’t added any new maths functions since the version I used with Windows 3.11.

Err, if you select calculator under Win 10 and then check the scientific section I’d imagine that this would bring up the normal scientific bits.

How many new maths functions need to be added to excel?

the possibilities are near-∞

Have you seen the OLED configurable keyboard?

link below

there are also some on screen maths keyboards for android, apple and Unix

some for windows

https://www.cs.tut.fi/~jkorpela/math/kbd.html

https://msdn.microsoft.com/en-us/goglobal/bb964665.aspx

alt codes

http://usefulshortcuts.com/alt-codes/maths-alt-codes.php

https://www.cs.tut.fi/~jkorpela/math/syms.html

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

http://askubuntu.com/questions/228050/is-there-a-tool-to-quickly-create-custom-keyboard-layouts-for-international-keyb
https://github.com/simos/keyboardlayouteditor

related

http://blog.wolframalpha.com/2010/02/05/a-new-way-to-type-on-the-wolframalpha-app/

http://tex.stackexchange.com/questions/1979/good-keyboard-layouts-for-typing-latex/1985#1985

https://www.autohotkey.com/

OLED Keyboard with configurable keys

http://www.artlebedev.com/everything/optimus/popularis/

Postpocelipse said:

I’ll leave the questions on this subject to someone with a firmer grasp of math theory than I can claim.

Japanese mathematician claims to have solved a notorious maths problem, but nobody understands it

The ABC conjecture
Shinichi Mochizuki of the Research Institute for Mathematical Sciences at Kyoto University is such a mathematician. In August 2012, he posted a series of four papers on his personal web page claiming to prove the ABC conjecture, an important outstanding problem in number theory.

A proof would have Fermat’s Last Theorem as a consequence (at least for large enough exponents), and given the difficulty of Wiles’ proof of Fermat’s Last Theorem, we should expect a proof of the ABC conjecture to be similarly opaque.

The conjecture is fairly easy to state. Suppose we have three positive integers a,b,c satisfying a+b=c and having no prime factors in common. Let d denote the product of the distinct prime factors of the product abc. Then the conjecture asserts roughly there are only finitely many such triples with c > d. Or, put another way, if a and b are built up from small prime factors then c is usually divisible only by large primes.

Here’s a simple example. Take a=16, b=21, and c=37. In this case, d = 2×3×7×37 = 1554, which is greater than c. The ABC conjecture says that this happens almost all the time. There is plenty of numerical evidence to support the conjecture, and most experts in the field believe it to be true. But it hasn’t been mathematically proven – yet.

Enter Mochizuki. His papers develop a subject he calls Inter-Universal Teichmüller Theory, and in this setting he proves a vast collection of results that culminate in a putative proof of the ABC conjecture. Full of definitions and new terminology invented by Mochizuki (there’s something called a Frobenioid, for example), almost everyone who has attempted to read and understand it has given up in despair.

Add to that Mochizuki’s odd refusal to speak to the press or to travel to discuss his work and you would think the mathematical community would have given up on the papers by now, dismissing them as unlikely to be correct. And yet, his previous work is so careful and clever that the experts aren’t quite ready to give up.

I wish that we could stop the Septic Tanks from fucking around with the ENGLISH language, apart from other fuck ups, it is maths not math From Principa Mathematica the title of the original document by Newton “PrincipleS of MathematicS both words plural hence the “s”.

bob(from black rock) said:

Postpocelipse said:

I’ll leave the questions on this subject to someone with a firmer grasp of math theory than I can claim.

Japanese mathematician claims to have solved a notorious maths problem, but nobody understands it

The ABC conjecture
Shinichi Mochizuki of the Research Institute for Mathematical Sciences at Kyoto University is such a mathematician. In August 2012, he posted a series of four papers on his personal web page claiming to prove the ABC conjecture, an important outstanding problem in number theory.

A proof would have Fermat’s Last Theorem as a consequence (at least for large enough exponents), and given the difficulty of Wiles’ proof of Fermat’s Last Theorem, we should expect a proof of the ABC conjecture to be similarly opaque.

The conjecture is fairly easy to state. Suppose we have three positive integers a,b,c satisfying a+b=c and having no prime factors in common. Let d denote the product of the distinct prime factors of the product abc. Then the conjecture asserts roughly there are only finitely many such triples with c > d. Or, put another way, if a and b are built up from small prime factors then c is usually divisible only by large primes.

Here’s a simple example. Take a=16, b=21, and c=37. In this case, d = 2×3×7×37 = 1554, which is greater than c. The ABC conjecture says that this happens almost all the time. There is plenty of numerical evidence to support the conjecture, and most experts in the field believe it to be true. But it hasn’t been mathematically proven – yet.

Enter Mochizuki. His papers develop a subject he calls Inter-Universal Teichmüller Theory, and in this setting he proves a vast collection of results that culminate in a putative proof of the ABC conjecture. Full of definitions and new terminology invented by Mochizuki (there’s something called a Frobenioid, for example), almost everyone who has attempted to read and understand it has given up in despair.

Add to that Mochizuki’s odd refusal to speak to the press or to travel to discuss his work and you would think the mathematical community would have given up on the papers by now, dismissing them as unlikely to be correct. And yet, his previous work is so careful and clever that the experts aren’t quite ready to give up.

I wish that we could stop the Septic Tanks from fucking around with the ENGLISH language, apart from other fuck ups, it is maths not math From Principa Mathematica the title of the original document by Newton “PrincipleS of MathematicS both words plural hence the “s”.

Looks around…
I left that s off to annoy people

CrazyNeutrino said:

bob(from black rock) said:

Postpocelipse said:

I’ll leave the questions on this subject to someone with a firmer grasp of math theory than I can claim.

Japanese mathematician claims to have solved a notorious maths problem, but nobody understands it

The ABC conjecture
Shinichi Mochizuki of the Research Institute for Mathematical Sciences at Kyoto University is such a mathematician. In August 2012, he posted a series of four papers on his personal web page claiming to prove the ABC conjecture, an important outstanding problem in number theory.

A proof would have Fermat’s Last Theorem as a consequence (at least for large enough exponents), and given the difficulty of Wiles’ proof of Fermat’s Last Theorem, we should expect a proof of the ABC conjecture to be similarly opaque.

The conjecture is fairly easy to state. Suppose we have three positive integers a,b,c satisfying a+b=c and having no prime factors in common. Let d denote the product of the distinct prime factors of the product abc. Then the conjecture asserts roughly there are only finitely many such triples with c > d. Or, put another way, if a and b are built up from small prime factors then c is usually divisible only by large primes.

Here’s a simple example. Take a=16, b=21, and c=37. In this case, d = 2×3×7×37 = 1554, which is greater than c. The ABC conjecture says that this happens almost all the time. There is plenty of numerical evidence to support the conjecture, and most experts in the field believe it to be true. But it hasn’t been mathematically proven – yet.

Enter Mochizuki. His papers develop a subject he calls Inter-Universal Teichmüller Theory, and in this setting he proves a vast collection of results that culminate in a putative proof of the ABC conjecture. Full of definitions and new terminology invented by Mochizuki (there’s something called a Frobenioid, for example), almost everyone who has attempted to read and understand it has given up in despair.

Add to that Mochizuki’s odd refusal to speak to the press or to travel to discuss his work and you would think the mathematical community would have given up on the papers by now, dismissing them as unlikely to be correct. And yet, his previous work is so careful and clever that the experts aren’t quite ready to give up.

I wish that we could stop the Septic Tanks from fucking around with the ENGLISH language, apart from other fuck ups, it is maths not math From Principa Mathematica the title of the original document by Newton “PrincipleS of MathematicS both words plural hence the “s”.

Looks around…
I left that s off to annoy people

Well you certainly got your moneys worth out of me, so go to the “naughty corner” and promise not to annoy bob(from black rock) again.

bob(from black rock) said:

I wish that we could stop the Septic Tanks from fucking around with the ENGLISH language, apart from other fuck ups, it is maths not math From Principa Mathematica the title of the original document by Newton “PrincipleS of MathematicS both words plural hence the “s”.

I mostly thought pluralising a word in a title was unnecessary. How wrong I was……

Postpocelipse said:

bob(from black rock) said:

I wish that we could stop the Septic Tanks from fucking around with the ENGLISH language, apart from other fuck ups, it is maths not math From Principa Mathematica the title of the original document by Newton “PrincipleS of MathematicS both words plural hence the “s”.

I mostly thought pluralising a word in a title was unnecessary. How wrong I was……

I don’t think you could have been any wronger.

Have been wondering what the word “heuristics” meant. Looking it up was worth it. Interesting subject and reading up on it led me to the word ‘satisficing’. I’ll be looking for a sentence to use it in.

Peak Warming Man said:

Postpocelipse said:

bob(from black rock) said:

I wish that we could stop the Septic Tanks from fucking around with the ENGLISH language, apart from other fuck ups, it is maths not math From Principa Mathematica the title of the original document by Newton “PrincipleS of MathematicS both words plural hence the “s”.

I mostly thought pluralising a word in a title was unnecessary. How wrong I was……

I don’t think you could have been any wronger.

Well at least I’m doing something useful and marking a boundary for people.

Postpocelipse said:

Have been wondering what the word “heuristics” meant. Looking it up was worth it. Interesting subject and reading up on it led me to the word ‘satisficing’. I’ll be looking for a sentence to use it in.

here is an example of using Satisficing in a sentence

Satisficing is a decision-making strategy or cognitive heuristic that entails searching through the available alternatives until an acceptability threshold is met.

Science journalists have discovered cohort, the statistical cohort and they have gone absolutely bananas with it lately.

CrazyNeutrino said:

Postpocelipse said:

Have been wondering what the word “heuristics” meant. Looking it up was worth it. Interesting subject and reading up on it led me to the word ‘satisficing’. I’ll be looking for a sentence to use it in.

here is an example of using Satisficing in a sentence

Satisficing is a decision-making strategy or cognitive heuristic that entails searching through the available alternatives until an acceptability threshold is met.

I don’t find that definition very satisficing.

The Rev Dodgson said:

CrazyNeutrino said:

Postpocelipse said:

Have been wondering what the word “heuristics” meant. Looking it up was worth it. Interesting subject and reading up on it led me to the word ‘satisficing’. I’ll be looking for a sentence to use it in.

here is an example of using Satisficing in a sentence

Satisficing is a decision-making strategy or cognitive heuristic that entails searching through the available alternatives until an acceptability threshold is met.

I don’t find that definition very satisficing.

wouldn’t be much of a definition if it did.