ABC conjecture is an interesting conjecture that will lead to many other consequences in number theory. For example, Fermat’s last theorem can be easily derived from it. No proof of abc conjecture has been found since mid-1980s, when it was first proposed.
The conjecture is stated in terms of three positive integers, a, b and c (hence the name), which have no common factor and satisfy a + b = c. If d denotes the product of the distinct prime factors of abc, the conjecture essentially states that d is usually not much smaller than c. In other words: if a and b are composed from large powers of primes, then c is usually not divisible by large powers of primes.
In August 2012, Japanese mathematician Shinichi Mochizuki claimed to have proven it, but his proof is to long and complex that nobody understands it. There is another problem however. Those interested in understanding the proof are in USA, but Mochizuki has no interest to stay in USA for a few months and explain it.
Attempts at verifying Mochizuki’s work are severely hampered by his refusal to leave his home university and lecture on his new mathematics, as is standard in the academy.
If his proof stands, it will revolutionize number theory for the next 100 or 1000 years, because of the other associated consequences (a short list here), but Mr. Mochizuki is not in hurry. Moreover, when questions arise about his proof, he merely posts revisions or updates on his website.
We first came across Shinichi Mochizuki’s name, because he is also suspected to be the creator of mathematical algorithm behind bitcoin.