Eighty years ago, there was only one known method of multiplication, and that was the conventional vertical method learned in textbooks.

The vertical method is very quick and convenient when multiplying numbers with few digits, but when it comes to multiplying multipliers of millions or billions of digits, it is not possible to do so, for example, to calculate pi or to find larger prime numbers.

Later, the 'Karatsuba algorithm' was developed, which broke down the multiplier of a number into smaller parts and recombined those parts in such a way that a small amount of addition and subtraction could be used instead of a large number of multiplications.

This algorithm completes the calculation by multiplying the single digits of '2 to the nth power' times, instead of the previous 'n squared' times.

Later, two scientists worked together to improve the multiplication algorithm of large numbers by using the method of 'introducing fast Fourier transform', which only needs to multiply the single digits of 'n×log n×log(log n)' to complete the multiplication of large numbers, where log n is the logarithm of n.

This improvement is a leapfrog innovation, and the subsequent continuous improvement of the large number multiplication algorithm is based on this method.

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

The 'Fourier transform algorithm' is used to construct a numerical region containing the 'result' with the assistance of other calculation methods.

That's where innovation comes in.

For example, 25*25, you can simply delineate the results in the range of 400 to 900, and through some necessary filters, such as 'the mantissa is 5', the numbers in the set are crossed out one by one, until there is only one number left, which is determined as the final result.

Of course, multiplying very large numbers is much more complicated, and the introduction of the 'fast Fourier transform' and the assistance of other calculation methods will make the delineation of the range more accurate.

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

"After comparing each digit of the number, you can continue to narrow it down......"

"The result of multiplying each carry digit can help to continue to exclude the number in the range, the higher the number, the greater the range of exclusion, we can see that when approaching 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 very interested, because what they heard was a very novel calculation method.

Prior to this, all multiplication calculations were calculated step by step, rather than delineating a set for screening, and the new method was more like 'human brain thinking' and 'fuzzy mathematics'.

Similar to 'human brain' and 'fuzzy mathematics' are only the parts that delineate the scope at the beginning, and the subsequent step-by-step screening is a detailed calculation.

In the first row of judges, the white-haired Joseph Sfakith whispered to Wolfgang Killian, "I read his paper and know this method, but I don't know if it's accurate, and I don't know if the number of calculations is as low as it says in the paper." ”

"Now, I'm sure."

Joseph Sfakis said with some smugness, "I insisted on leaving this paper. ”

Wolfgang-Killian smiled, "It's really interesting, the method is very novel, the logic is very rigorous, and there should be no problem." This will be an innovation in multiplication, a very meaningful innovation. ”

Stage.

Wang Hao explained very carefully, and it took more than half an hour to explain all the 'screening steps' one by one.

Then, he propped up the lectern with his hands and concluded with a smile, "Through this screening process, you will only get one number in the end." That's the end result. ”

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

There was a moment of silence in the audience.

Then, sparse applause rang out, approaching that the applause grew louder and louder, quickly filling the entire lecture hall and continuing for a long time.

In the middle of the second row, there was a person who did not applaud.

It's Gollix.

Yesterday, Gorlix's report was confirmed by Wang Hao to be wrong, and after he went back, he examined the whole process, just like Wang Hao pointed out on the spot, there was indeed an error.

However, Golix would not be grateful to Wang Hao for this, or that as long as he was not a legendary saint, it was impossible for him to be grateful to the person who pointed out the mistake after being pointed out in public.

Gorlix was embarrassed, and he was pointed at by others when he walked on the road.

Of course, the main reason is that his report is wrong, but I can't help but secretly hate Wang Hao, don't expect top scholars to be broad-minded, tolerant, and examine their own mistakes.

Top scholars, most of them like to drill the horns of the bull's horns, they may not care about a lot of daily things, but when it comes to professional academic issues, many are more cautious than ordinary people, more resentful, some top scholars, even because of the opposition in the field of research and development, and look down on each other, do not say a word when they meet, and even become enemies.

Gollix 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 was scheduled for the afternoon of the next day, and it must have been a small achievement.

A small result?

And the face to give a presentation at the STACS meeting? So many people came to 'cheer', what a disappointment the result!

Gollix had already thought of the lines, but he didn't expect that Wang Hao's achievements would be so big, so big that he directly innovated a 'filtered' multiplication calculation method.

He quickly made calculations in his mind, knowing that Wang Hao's words about 'less than one-thirds of the number of calculations × log n times' were 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/× log n times' and become the fastest method for multiplying very large numbers.

Still, he figured out the problem.

While there was still sparse applause in the lecture hall, Gollix stood up suddenly.

Suddenly, the venue fell silent.

Everyone looked at Gollix and showed interest, they all knew the contradiction between Gollix and Wang Hao, and wanted to see what Gollix was going to say.

Gollix opened his mouth and asked, "Mr. Wang Hao, how do you prove that using this method, you will only get one number in the end?" ”

"Your approach is to do the screening after the scope, but how do you prove that your screening process is perfect? Will all non-result numbers be filtered out? ”

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

Many people have understood the process along with the train of thought, and they also feel that the screening mechanism has been perfected, but the feeling is just a feeling, and the screening mechanism is imperfect, and the report can be said to be wrong.

Gollix's questions are very level, and it can be said that they have asked the voices of many people.

Everyone looked back at the stage.

Wang Hao smiled slightly and said, "Thank you, Mr. Gollix, for your question, because this is exactly what I will do next." ”

"A proof of the push-back process!"

He walked over to a blank whiteboard on the left and wrote a line, "Suppose, sift through two different numbers, A and B......"

He then started with the screening mechanism of the last step, made a one-to-one check, and wrote down the properties of A and B respectively.

Through the comparison, it was slowly found that -

A and B have the same number of digits; The highest digit of a and b is the same; A and B have the same single digits; The numbers in the middle area of A and B are the same; A & B......

Successive checks quickly result in a series of identical properties.

Wang Hao completed the last step of the calculation, showed the content on the whiteboard to the audience, and nodded, "There shouldn't be any need to continue, right?" All digit digits of A and B are the same, and it can be concluded that A and B are the same number. ”

"So, you can be sure that the screening mechanism is perfect!"

Suddenly.

The applause from the audience was thunderous and enduring.

The white-haired old Joseph walked directly to the cabinet next to the wall, took the champagne placed on the top, walked to the stage and handed it to Wang Hao, shouting, "You can also determine in advance, your paper is the best!" ”

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

"You deserve it!"

Old Joseph said and gave him a hug.

In the interaction between the two, the applause became more enthusiastic, and Gollix in the second row sat on the chair, stared at Wang Hao on the podium for a long time, and finally slapped a few times together with others.

He had nothing to say about this research.