Eighty years ago, there was only one known method of multiplication, 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. However, when calculating the multiplication of multipliers with millions or billions of digits, the vertical calculation method There is nothing you can do about it, for example, calculating pi or finding larger prime numbers.
Later came the 'Karatsuba algorithm', which breaks the multiplier of a number into smaller parts and reassembles the parts in such a way that a large number of multiplications can be replaced by a small number of additions and subtractions.
This algorithm only requires '2 to the nth power' single-digit multiplications to complete the calculation, instead of the previous 'n square' times.
Later, two scientists worked together to use the method of 'introducing fast Fourier transform' to improve the large number multiplication algorithm, which only required 'n×log n×log (log n)' single-digit multiplication. 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 subsequent continuous improvements in large number multiplication algorithms are based on this method.
Wang Hao's research results are also conducted in the same way as "introducing Fast Fourier Transform", so he uses "improvement and innovation" to describe his results. His explanation also starts from the "Fourier Transform Algorithm".
Expand with the 'Fourier transform algorithm' and assist other calculation methods to construct a digital area containing the 'result'.
This is where innovation comes in.
His research is not a normal step-by-step calculation, but a "set of values that may become the result". For example, 25*25, you can simply delineate the result in the range of 400 to 900, and go through some necessary screening , for example, 'The mantissa is 5', cross out the numbers in the set one by one until there is only one number left, which is determined as the final result.
Of course, multiplication of very large numbers is much more complicated. By introducing 'Fast Fourier Transform' and assisting other calculation methods, the delimited range will be more accurate.
If you are calculating '25 times 25', you can directly circle the range between the three numbers '725, 625, and 525', and then quickly exclude 725 and 525, and finally get the result 625.
"After comparing each digit, you can continue to narrow the range..."
"The result of multiplying each carry digit can help to continue to exclude numbers within the range. The higher the digit, the larger 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 calculation methods were calculated step by step, rather than delineating a set for screening. The new method is more like the techniques of 'human brain thinking' and 'fuzzy mathematics'.
Similar to the 'human brain', 'fuzzy mathematics' is just the initial delineation of the scope, and the subsequent step-by-step screening is all detailed calculations.
In the first row of the judges' bench, the white-haired Joseph Sifakis whispered to Wolfgang Killian, "I read his paper and I know this method, but I don't know whether it is accurate or not. It’s unclear whether the number of calculations is as small as the paper says.”
"Now, I'm sure."
Joseph Sifakis said with some pride, "I insisted on keeping this paper."
Wolfgang Kilian smiled and said, "It is indeed very interesting. The method is novel and the logic is very rigorous. There should be no problem. This will be an innovation in multiplication, a very meaningful innovation."
On stage.
Wang Hao explained very carefully, and it took him more than half an hour to explain all the 'screening steps' one by one.
Then, he put his hands on the desk and concluded with a smile, "Through this screening process, you will only get one number in the end. That is the final result."
"According to this method, when calculating the multiplication of very large digits, the number of calculations required is less than 'one-third n × log n' calculations, which should be one of the fastest methods currently known."
There was silence in the audience.
Then, sparse applause rang out, and the applause got 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, there was someone who did not applaud.
It's Gorlix.
Yesterday, Gorliks' report was confirmed to be wrong by Wang Hao. After he went back, he reviewed the entire process, and as Wang Hao pointed out on the spot, there was indeed an error.
However, Gorlix 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 feel grateful to the person who pointed out the error after being pointed out in public.
Gorlix 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 can't help but secretly hate Wang Hao. Don't expect top scholars to be broad-minded, tolerant, and review their own mistakes.
Most of the top scholars are people who like to get into trouble. They may not care about many daily things, but when it comes to issues in the professional and academic fields, many are more petty and vindictive than ordinary people. Some top scholars even go to the research and development field because of Opposing each other, but looking down upon each other, not saying a word at all when meeting, and even becoming enemies.
Gorliks 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, so it was definitely just a Small results.
A small achievement?
Do you still have the nerve to give a report at the STACS meeting? So many people came to 'support', but the result was so disappointing!
Gorlix had already thought of his lines, but he didn't expect that Wang Hao's achievements would be so great, that he would directly innovate a 'screened' multiplication calculation method.
He quickly made calculations in his mind, knowing that Wang Hao's statement that 'the number of calculations is less than one-third n × log n times' was not an exaggeration. He said that 'one of the fastest calculation methods' was even modest.
This new method may allow the number of calculations to be less than 'n×log n times five times', and 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, Gorlix stood up suddenly.
Suddenly, the venue fell silent.
Everyone looked at Gorliks and showed interest. They all knew the conflict between Gorliks and Wang Hao and wanted to see what Gorliks was going to say.
Gorliks asked, "Mr. Wang Hao, how can you prove that using this method, you will only get a number in the end?"
"Your method is to draw a range and then screen, but how do you prove that your screening process is perfect? Will all non-result numbers be screened out?"
This question stunned everyone in the venue, and many people nodded.
Many people have followed the train of thought and understood the process. They also feel that the screening mechanism has been perfected, but they just feel that if the screening mechanism is slightly imperfect, the report can be said to be wrong.
Gorlix's questions were very good, and it can be said that he asked many people's opinions.
Everyone looked back to the stage.
Wang Hao smiled slightly and said, "Thank you Mr. Gorliks for your question, because this is my next work."
“A proof of the reverse process!”
He walked to a blank whiteboard on the left and wrote a line, "Suppose, through screening, two different numbers, 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.
Through comparison, I slowly discovered——
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 digits of a and b are the same; a and b...
Through continuous verification, a series of similar properties are quickly obtained.
Wang Hao completed the last step of 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, you can be sure that the screening mechanism is perfect!"
Suddenly.
The audience applauded thunderously and continuously.
The white-haired old Joseph walked 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, "You can also confirm in advance that 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 even more enthusiastic. Gorliks, who was sitting on a chair in the second row, stared at Wang Hao on the podium for a long time, and finally joined the others in clapping a few times. Chin palm.
He had nothing to say about this research.
