Meeting of math minds fails to clear up ABC conjecture proof

December 17, 2015 by Bob Yirka report
Shinichi Mochizuki

(Phys.org)—A group of mathematicians specializing in arithmetic geometry met for five days earlier this month in an attempt to understand a proof constructed by Shinichi Mochizuki, of Kyoto University posted online back in 2012—it is called the "inter-universal Teichmuller" (IUT) theory and runs more than 500 pages. To date, no one has been able to verify the proof, or even understand it. This latest meeting was an attempt to overcome some of the hurdles that have impeded progress by other mathematicians in understanding what Mochizuki has done.

The proof, Mochizuki claims, offers a solution to the ABC conjecture which involves expressions of the form a + b = c and connecting the that are factors of a and b with those that are factors of c. While seemingly simple to describe, no one prior to Mochizuki has been able to create a proof for it. If other mathematicians in the field do one day come to understand the proof, and verify it as correct, it would mark a truly historic day for mathematics. But, unfortunately, as it stands now, that day may never come.

In the three years since Mochizuki posted his proof, many experts in the field have looked at it, but all have failed to grasp what Mochizuki has tried to show. Making things more difficult is that Mochizuki appears to be shy, and even more hesitant to travel outside of his home country of Japan. This latest meeting was held, oddly, at Oxford University. Mochizuki, as expected, refused to attend, though he did make a virtual appearance via Skype.

The circumstances surrounding the proof and the difficulty others in the field are having with it offers a contrast of extremes—on the one hand, the experts working to understand it are generally a highly intelligent bunch, yet their failure to grasp what their colleague has wrought has almost certainly led to issues with pride. The result over the past three years has been the voicing of frustration, anger and perhaps a hint of hesitation—no one wants to be the guy that spent years working to understand a proof, only to find that it was not really a proof after all.

Several of the people that attended the recent meeting have publicly expressed some degree of relief because it appears that there is at least some level of understanding of the overall concepts of the proof now, and they apparently look promising. Others have stated that the meeting did little to build on what had already been known. A workshop follow-up has been scheduled this summer, in Kyoto, which will likely see Mochizuki attending and perhaps offering some new insights on his work so that others may come to understand and perhaps one day verify his proof.

Explore further: Mathematician announces that he's proved the ABC conjecture

More information: via Nature, Newscientist

Related Stories

Mathematician announces that he's proved the ABC conjecture

September 12, 2012

(Phys.org)—In all of history there are very few names that stand out in the field of mathematics, at least among those not in the field: Euclid, Newton, Pythagoras, etc. This is likely due to several reasons, chief among ...

Researchers look into the brains of chronic itch patients

June 15, 2015

It's long been known that scratching evokes a rewarding and pleasurable sensation in patients with chronic itch. Now, researchers in the Department of Dermatology and Temple Itch Center at Temple University School of Medicine ...

Recommended for you

New paper answers causation conundrum

November 17, 2017

In a new paper published in a special issue of the Philosophical Transactions of the Royal Society A, SFI Professor Jessica Flack offers a practical answer to one of the most significant, and most confused questions in evolutionary ...

Chance discovery of forgotten 1960s 'preprint' experiment

November 16, 2017

For years, scientists have complained that it can take months or even years for a scientific discovery to be published, because of the slowness of peer review. To cut through this problem, researchers in physics and mathematics ...

8 comments

Adjust slider to filter visible comments by rank

Display comments: newest first

marcush
4 / 5 (4) Dec 17, 2015
Perhaps he may make a more concerted effort at explaining it if people chose to otherwise ignore it.
axemaster
5 / 5 (5) Dec 17, 2015
Making things more difficult is that Mochizuki appears to be shy, and even more hesitant to travel outside of his home country of Japan... A workshop follow-up has been scheduled this summer, in Kyoto, which will likely see Mochizuki attending and perhaps offering some new insights on his work

This guy seriously needs to quit hiding in his room with his waifu, and explain how the heck this proof works.
Sonhouse
not rated yet Dec 17, 2015
Where is Terence when you need him:)
adam_russell_9615
2.5 / 5 (2) Dec 17, 2015
If no one understands your proof then I think it is more likely to be invalid than valid.
zaxxon451
5 / 5 (1) Dec 18, 2015
If no one understands your proof then I think it is more likely to be invalid than valid.


Look at his picture, if anyone can come up with the proof, my money's on this dude.
swordsman
5 / 5 (1) Dec 18, 2015
"..solution to the ABC conjecture which involves expressions of the form a + b = c and connecting the prime numbers that are factors of a and b with those that are factors of c."

"factors of..."? That covers a wide field, in which case use 7,5,2 for a,b,c.
antigoracle
2.6 / 5 (5) Dec 19, 2015
If no one understands your proof then I think it is more likely to be invalid than valid.

I don't understand your reasoning, therefore you are invalid.
adam_russell_9615
3.7 / 5 (3) Dec 20, 2015
If no one understands your proof then I think it is more likely to be invalid than valid.

I don't understand your reasoning, therefore you are invalid.

"My proof:
a implies b
b implies c
c implies j
and since j implies k
then a implies k"

"Wait, I dont see how you got from c to j. Did anyone understand line 3"?
crickets
"Sir can you explain why you say c implies j"?
crickets

If its a valid proof then someone should understand each step of the logic and if there is a step in doubt its just common sense that the author should explain himself. He doesnt need to leave Japan to do so. We have email now.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.