From University Lecturer to Chief Academician

Eighty years ago, there was only one known multiplication method, which was the conventional vertical calculation method learned in textbooks.

When multiplying numbers with a small number of digits, the vertical calculation method is very fast and convenient, but when calculating the multiplication between multipliers with millions of digits or billions of digits, the vertical calculation method It seems powerless, for example, calculate pi or find a larger prime number.

Then came the 'Karatsuba algorithm', which breaks down the multiplier of a number into smaller parts and recombines these parts in such a way that a small number of additions and subtractions can be used instead of a large number of multiplications.

This algorithm completes the multiplication calculation of two n-digit numbers, and only needs 'n to the 1.58th power' multiplication of single digits, instead of the previous 'n square' times.

Later, two scientists worked together to improve the multiplication algorithm of large numbers by using the method of "introducing fast Fourier transform". You can complete the multiplication calculation of large numbers, where log n is the logarithm of n.

This improvement is a leap-forward innovation, and the subsequent continuous improvement of the multiplication algorithm of large numbers is based on this method.

Wang Hao's research results are also carried out in the way of "introducing fast Fourier transform", so he will use "improvement and innovation" to describe his own achievements. His explanation also starts from the "Fourier transform algorithm".

Expand with the 'Fourier Transform Algorithm', assist other calculation methods, and construct a digital area containing the 'result'.

This is where the innovation comes in.

His research does not carry out normal step-by-step calculations, but delimits the 'value set that may become the result', for example, 25*25, you can simply delineate the result in the range from 400 to 900, and pass some necessary screening , such as 'the mantissa is 5', cross out the numbers in the set one by one until only one number remains, and it will be determined as the final result.

Of course, the multiplication of very large numbers is much more complicated. The introduction of "fast Fourier transform" and other calculation methods will make the delineated range more accurate.

If you are calculating '25 times 25', you can directly delineate the range between the three numbers '725, 625, and 525', and then you can quickly exclude 725 and 525, and finally get the result of 625.

"After comparing the numbers of each digit, you can continue to narrow the range..."

"The result of multiplying each carry digit can help continue to exclude numbers within the range. The higher the digit, the larger the excluded range. We can see that when it is close to the highest digit..."

"When it comes to more precise screening, you need to use..."

As the explanation slowly unfolded, everyone in the audience became very serious and interested, because what they heard was a very novel calculation method.

Prior to this, all multiplication calculation methods were calculated step by step and step by step, instead of delineating a set for screening. The new method is more like the method of "human brain thinking" and "fuzzy mathematics".

Similar to the 'human brain' and 'fuzzy mathematics', it is only the part that delimits the scope at the beginning, and the subsequent step-by-step screening is all detailed calculations.

In the first row of judges' seats, a white-haired Joseph Sfakis whispered to Wolfgang Kilian, "I read his paper and know this method, but I don't know whether it is accurate or not. It is unclear whether the number of calculations is as small as the paper says."

"Now, I'm sure."

Joseph Sfakis said with some pride, "I insisted on keeping this paper."

Wolfgang Kilian said with a smile, "It's really interesting, the method is very novel, the logic is very rigorous, there should be no problem. This will be an innovation of multiplication, a very meaningful innovation."

on stage.

Wang Hao's explanation was very detailed, and it took another half an hour to explain all the 'screening steps' one by one.

Then, with his hands on the desk, he concluded with a smile on his face, "Through this screening process, only one number will be obtained in the end. That is the final result."

"According to this method, when calculating the multiplication of super-large digits, the number of calculations required is less than 'n/3 of n×log n' calculations, which should already be one of the fastest known methods."

The audience was quiet for a while.

Then, sparse applause sounded, and the applause became louder and louder as it approached, quickly filling the entire lecture hall and lasting for a long time.

In the middle of the second row, someone did not applaud.

It's Gorelix.

Yesterday, Gorelix's report was confirmed to be wrong by Wang Hao. After he went back, he examined the whole process. As Wang Hao pointed out on the spot, there were indeed mistakes.

However, Gorex would not be grateful to Wang Hao for this. In other words, as long as he is not a legendary saint, it is impossible for him to be grateful to the person who pointed out the mistake after being pointed out in public.

Gorelix was humiliated, and was pointed at by others while walking on the road.

Of course, the main reason is that his report was wrong, but he couldn’t help secretly hating Wang Hao. Don’t expect top scholars to be broad-minded, tolerant, and examine their own mistakes.

Top scholars are mostly the kind of people who like to dig into the horns of the dead. They may not care about many daily things, but when it comes to issues in the professional academic field, many of them are more careful and grudge than ordinary people. Opposites, but look down on each other, do not say a word when they meet, and even become enemies.

Gorelix is ​​such a person. He came to listen to Wang Hao's report not to 'learn something', but to find an opportunity to 'taunt' the other party. The other party's report is scheduled for the next afternoon, so it must be just a joke. Small results.

A small achievement?

Still have the face to give a report at the STACS meeting? So many people came to 'support', what a disappointment!

Gorelix had already thought up his lines, but he didn't expect that Wang Hao's achievements would be so great, so big that he directly innovated a "screening" multiplication calculation method.

He quickly calculated in his mind, knowing that Wang Hao's statement that "the number of calculations is less than n×log n times" was not an exaggeration, and he was even modest when he said "one of the fastest calculation methods".

This new method may make the number of calculations less than 'n/fifths x log n times', and it will also become the fastest method for multiplication calculations of very large numbers.

However, he still found the problem.

When there was still sparse applause in the lecture hall, Gorex suddenly stood up.

Suddenly, the venue was quiet.

Everyone looked at Gorelix and showed interest. They all knew the conflict between Gorelix and Wang Hao, and wanted to see what Gorelix had to say.

Gorex asked, "Mr. Wang Hao, how do you prove that using this method, you will only get one number in the end?"

"Your method is to delineate the scope and then do the screening, but how do you prove that your screening process is perfect? ​​Will you screen out all non-result numbers?"

This question made everyone in the venue stunned, and many people also nodded.

Many people followed the train of thought and understood the process. They also felt that the screening mechanism was perfect, but the feeling was just a feeling. The screening mechanism was not perfect, so the report could be said to be wrong.

Gorex's questions were very good, and it can be said that he asked the voices of many people.

Everyone looked at the stage again.

Wang Hao smiled slightly and said, "Thank you Mr. Gorelix for your question, because this is exactly my next job."

"A proof of reverse process!"

He walked to a blank whiteboard on the left and wrote a line, "Suppose, two different numbers are obtained through screening, a and b..."

Then he started from the last step of the screening mechanism, made a one-by-one check, and recorded the properties of a and b respectively.

Slowly found out through comparison——

The digits of a and b are the same; the highest digits of a and b are the same; the single digits of a and b are the same; the middle area numbers of a and b are the same; a and b...

Continuous checking calculations can quickly obtain a series of identical properties.

Wang Hao completed the last step of checking the calculation, showed the content on the whiteboard to the audience, nodded and said, "Should there be no need to continue? All the digits of a and b are the same, so it can be concluded that a and b are the same A number."

"So, it can be determined that the screening mechanism is perfect!"

immediately.

The audience applauded thunderously and lasted for a long time.

The white-haired old Joseph went directly to the cabinet next to the wall, took the champagne on the top, walked to the stage and handed it to Wang Hao, shouting, "It can be confirmed in advance, your thesis is optimal!"

Wang Hao took the champagne and shook hands with Old Joseph to express his gratitude, "Thank you! Old Joseph."

"This is what you deserve!"

Old Joseph said and gave him a hug.

During the interaction between the two, the applause became more enthusiastic. Gorelix in the second row sat on a chair, stared at Wang Hao on the podium for a long time, and finally joined the others to clap a few times vigorously. Chin palm.

He has nothing to say about this research.