What mathematical subfield do you think is going to make the next biggest change in human history?

what mathematical subfield do you think is going to make the next biggest change in human history?

Tom Brady

Arithmetic Deformation Scheme Theory.

Computer science. Specifically, graph theory applied to sift through large amounts of data to replicate structures we can't see ourselves.

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I support this. I am too much of a pleb yet to understand the theory but just considering its goal it is clear that this will be a revolution. "Roughly speaking, arithmetic deformations change the multiplication of a given ring, and the task is to measure how much the addition is changed". That is amazing. The only bad part is that I believe this will be the end of number theory. Understanding the secrets of arithmetic deformation will make us gods of numbers. There will be no conjecture left. Everything will follow trivially from the fundamental results that will soon be discovered.

THE END.

i'm a drooling retard, what are the implications of this theory?

To put it simply, the hardest problems in number theory are those who in some way relate multiplicative properties and additive properties. To give an easy example, consider the twin prime conjecture. What primes p exist such that p+2 is also prime? Primes are a multiplicative property of the integers, and we are relating that to addition +2. Now compare this to the following problem: Find all the primes p such that [math] 2p [/math] is prime. The solution? TRIVIAL. None. This version of the problem is so simple because it only has multiplication.

Another easy problem would be this. Solve the following diophantine equation: [math] x+y+z = a+b+c [/math]. So easy. Just isolate a variable and parametrize. Trivial.

So in other words, the harder problems in number theory are all about finding how multiplication relates to addition and vice versa. A fundamental example is the ABC conjecture (which arithmetic deformation theory already solved). Which basically related the sum of integers with the prime factorization of the numbers. Super hard question because this relation between addition, gcd and prime factorization is non-trivial so a lot of study is necessary.

And what arithmetic deformation theory does is look behind numbers to find explicitly what the relation between addition and multiplication is. Which means that Mochizuki is pretty much trying to hack number theory from the inside. After Mochizuki's theory gains popularity, only analytic number theory will be safe and not even that safe as many analytic properties of integers are closely related to algebraic ones.

(Algebraic) Number Theory will die with Mochizuki because he will solve everything.

sadly, this

im no mathematician but i can tell you its graph theory, ala network science and its applications in computation and the life sciences

>Arithmetic Deformation Scheme Theory.
don't use this meme name, fesenko only pretends to understand IUT

>To put it simply, the hardest problems in number theory are those who in some way relate multiplicative properties and additive properties. To give an easy example, consider the twin prime conjecture.
But work on the twin prime conjecture has had tons of progress, compare that to a problem like the Riemann hypothesis which has had essentially 0 progress in 150 years and isn't to do with multiplication/addition links

Triple integrals. Such a shame so few people can even begin understanding it.

Mathematical Biology

what other name would you give it? gigauniverse theory?

There is absolutely nothing special about those, except that they look a bit alien. They are known for a long time now.

this and probabilty theory (stochastic analysis)

>what other name would you give it? gigauniverse theory?
what's wrong with IUT?

>But work on the twin prime conjecture has had tons of progress
What does progress have to do? It still incredibly hard.

> compare that to a problem like the Riemann hypothesis which has had essentially 0 progress in 150 years

Well, that's because the Riemann Hypothesis is much more fundamental. Cracking it gives so much information about prime numbers. If RH was easy then number theory would be trivial. It is like that saying "If the brain was so simple we could understand it, we wouldn't".

>what mathematical subfield do you think is going to make the next biggest change in human history?

None of them.

Math theory could build computable models nanostructures, nanomaterials,semiconductors,genetics,medicine, new kind study materials.

Dynamical systems theory