AI will bring the next generation of math.

AI will revolutionize mathematics. This tool brings new types of accuracy for calculations. When mathematicians try to prove some math problems right or wrong. The system. It can be used for extremely long quantum decimal numbers that can prove formulas true or false. Another thing is that even if the AI finds the zero points in things. Like the Riemann Zeta function (Riemann Hypothesis), that doesn’t make it an unusable tool. 

The AI can have many ways. To use that function. The simplest way is that. The AI will not use those points in the zeta function. 

The AI can create prime numbers in the computer memory. So. In those cases, the system can transform those prime numbers into a series. The system. It can delete all numbers other than prime numbers from that series. The system. It can put those numbers into the frame. And then mix their locations in the series. When the system requires encryption. It must only send. The number of the frame. There is a prime number that the encryptor requires. If those numbers are in a table that looks like a chessboard. 

The transmitter must only tell. It uses the prime number from frame G:2. The golden rule is that the key must not be sent with the message. So, the system can be random. The tables that it will use. Then it sends those tables to the receiver. And then. The system that decrypts data can find the same binary number. 

The simple encryption table. It could look like this. (Quanta)  

The attacking system doesn’t know what prime numbers the encryption system used. If the attacking system uses a brute force attack, it tries to guess the right prime number. And we know that things like algorithms are not guessing. They try each number to open the message. The system can also cut the data line into pieces. And use different prime numbers for each data package. The system can use multilevel encryption. 

That means that. The first stage of encryption happens. When the message is left on a personal computer. Then at the point of the router, the system can use another count by using random prime numbers. And there can be multiple systems that count and share information. And the message. It can also travel by using different physical lines. 

The system that receives information. That can use decryption in similar points. As the encryptor encrypted the data. A router-computer can divide the numbers in the message. The transmitter router is used for encryption. Then the final decryption happens on a personal computer. The system can share encryption and decryption for different independent systems. That minimizes damages. If a code-breaking catastrophe occurs in one system. The other systems can stand the attack. The attacker must find and break all of those systems separately. 

When AI calculates things like azimuth angles. It can use extremely high accuracy for those numbers. This kind of accuracy brings new ideas for geometry. 

https://www.quantamagazine.org/the-ai-revolution-in-math-has-arrived-20260413/

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

The new model for prime numbers.

Prime numbers play a vital role in cryptology. The cryptological process requires big numbers. There is always the possibility that the number is virtually big. The system can divide those big numbers to smaller and that makes it possible to crack the code. The prime number is divided by 1 and itself. That makes it impossible to find the smallest possible factor in the number. If the attacking system finds that the smallest known common factor it makes easy to crack the message. If the number that the system uses to encrypt messages is pairer the system can simply use the 2 and then count it with itself to find the right number. 

There is a possibility that prime numbers involve secret code. If that code exist there is the possibility to calculate the series of the prime numbers very fast. Prime numbers require that the attacking system must always generate the entire number. And today the system uses the Riemann zeta function for that purpose. 

The problem with that function is it always gives the same prime number points. When the system drives Riemann zeta function, known as the Riemann conjecture, there are always certain points that the function gives. The attacking system can create the right prime number simply using the more powerful systems. And the AI driven neural network can make that attack quite fast, if it begins to create the right prime number by using the certain point of the number series that  Riemann Conjecture created. So, there must be some more effective way to find the right prime number. Or there must be a method that doesn’t depend on the Riemann Zeta function. 

There is a possibility to increase the encryption safety by using the multi stage encryption. When the data travels through one encryption line that line counts those ASCII numbers using the quantum decimal prime numbers. Those extremely long decimal prime numbers that are many times counted to the ASCII codes can make the message safer. The other way is to share those ASCII numbers to smaller series like series that involve three numbers. That makes the attacker to detect the data from those 3 number series.  

Above: Riemann Zeta function

Researchers uncovered the connection between prime numbers and the integer partitions. Those two things might not seem to have any connection. But mathematicians found that there is a connection. Before this and Riemann's zeta function there was a method to detect and identify the prime numbers. 

“To appreciate the significance of this breakthrough, we must journey back to the third century BCE. It was then that the Greek scholar Eratosthenes devised an elegantly simple method to identify prime numbers—known today as the “Sieve of Eratosthenes.” This technique involves systematically eliminating the multiples of each integer, leaving only those that remain indomitable: the primes. “ 

“Despite its antiquity, the sieve remains one of the most effective tools for sifting through these unique integers. This enduring relevance underscores the complexity of the problem at hand: even after more than 2,000 years of research, no straightforward algorithm or universal formula can predict where the next prime number will appear.” (Sustainability Times, “Prime Numbers Had a Hidden Code”: Mathematician Cracks 2,000-Year-Old Mystery That Could Rewrite Number Theory)

“This ancient method highlights the persistent challenge prime numbers pose. While it is a rudimentary yet powerful tool, the quest to fully comprehend primes continues, emphasizing their profound mystery and significance in mathematics.” (Sustainability Times, “Prime Numbers Had a Hidden Code”: Mathematician Cracks 2,000-Year-Old Mystery That Could Rewrite Number Theory)

When we think about the number theorem and other kinds of things we must realize that the prime numbers have one rule. That rule is that the prime number is unpaired. That means it will always end in numbers 0,1,3,(5), 7, 9. Five is in brackets because there is a big possibility that the number that ends to five is composite to five like 15.  That means if the number is a prime number it must not end in a pair. There is also risk with 9 that it can divide by using number 3. The 9 is not a prime number alone. 

The other rule is that there should not be series like 222 or 555. And the number must not involve sequences like 1313. Those rules are made to determine the prime number. If there are repeating  sequences, the same number or the number is pairer it is not prime number. The prime numbers are required in cryptology. The system generates a long and big number that it uses for encrypting data. The encryption process means that the ASCII number of the letter or number will count by using that prime number. And if an attacker finds that number the defender is in trouble. There is a possibility to increase layers to the encryption process. But that thing requires more powerful machines. Or it requires the new types of encryption systems. 

https://www.geeksforgeeks.org/maths/riemann-zeta-function/

https://www.sustainability-times.com/research/prime-numbers-had-a-hidden-code-mathematician-cracks-2000-year-old-mystery-that-could-rewrite-number-theory/

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