Among all the elements analyzed in recent weeks on the success of the La Revuelta program, presented by David Broncano on TVE, there is one that has particularly caught the attention of those with advanced knowledge of mathematics. Every evening, located in a conspicuous place behind the presenter’s table, you can see a blackboard on the surface of which a series of symbols and a mysterious graph appear.
“I watch La Révolte with my son and I noticed it from the first day,” explains Raúl Ibañez, mathematician from the UPV/EHU. “Whoever put this knows mathematics or has contacted someone who knows, because the graph is well done and it is not something simple,” explains Eduardo Sáenz de Cabezón, mathematician and presenter of the Órbita Laika program , on La 2. “It is a work of art in mathematics,” says professor and popularizer Clara Grima.
The million dollar problem
What you see on the board is a representation of what is known as the Riemann hypothesis, first formulated by the German Bernhard Riemann in 1859 and whose demonstration has continued for over 150 years due to its implications in the distribution of numbers. . primary domains and areas such as physics, probability theory and applied statistics. It is so important that it is one of the seven millennium problems for which the Clay Institute of Mathematics is offering a million-dollar prize.
Previously, the hypothesis was one of 23 problems that German mathematician David Hilbert prioritized at the 1900 International Congress of Mathematicians in Paris. “Hilbert himself said that if he fell asleep and woke up in 500 years, the first thing he would ask would be whether the Riemann hypothesis has already been proven,” recalls Alberto Márquez, professor at the University of Seville.
Hilbert said that if he went to sleep and woke up in five hundred years, the first thing he would ask would be whether the Riemann Hypothesis has already been proven.
Alberto Marquez
— Professor at the University of Seville (United States)
“It is said that the great mathematician GH Hardy included solving the Riemann hypothesis each year at the top of his list of New Year’s resolutions, which ended with the assassination of Mussolini,” adds Clara Grima. “In the book Humans“, Matt Haig suggests that aliens come to Earth to kill the one who proved the Riemann hypothesis, because it is such important knowledge that humans will abuse it and could destroy the universe”, recalls Raúl Ibañez.
The cousins’ Rosetta Stone
Why is this hypothesis so important and what does it suggest? “Its importance lies in the fact that it makes very deep connections between different areas of mathematics and is one of the most fruitful avenues of mathematical work,” says Sáenz de Cabezón. For Alberto Márquez, this is perhaps the most interesting mathematical problem to solve. “Very briefly, what the image represents is a function called zeta and the hypothesis says that the values which make this function zero are all on a straight line,” he emphasizes. “If this hypothesis is true, there are many interrelationships with many very important problems,” he says. But above all, he admits, proving that the hypothesis is true would be “like finding the Rosetta stone of prime numbers”.
“This could have very important implications in the field of cryptography, but also in many other applications,” explains Raúl Ibáñez. One of the particularities of the distribution of prime numbers is that there is no model. For example, If you have the first 20, there is no way to calculate the rest. “If the Riemann hypothesis is proven, we could better approximate its frequency,” he says. “And whoever does it will go down in history at that very moment, like Grigori Perelman did by solving the Poincaré conjecture or Andrew Wiles for trying to explain Fermat’s last theorem; This is the level of importance.
Infinite sum sequences
Although there is no simple way to explain the Riemann hypothesis, Clara Grima admits, it is useful to go back to the origin of the problem and how it evolved. It all begins in the 14th century, when Nicolas Oresme undertook to test what is called the harmonic series (the infinite sum of 1 + 1/2 + 1/3 + 1/4…) to understand if the result will be finite or infinite. Later, other mathematicians realized the relationship between this series and prime numbers, but the problem remained stuck in intermediate solutions. “This is where Riemann, who had never worked in number theory, comes along and comes up with a brilliant proposal,” says Grima. “What he does is hack the function and add a hint so that the results stop giving infinity and you can work with them.
When designing the function to find times when the result is zero, you see that, except for a series of trivial cases, one property emerges and that is that all values lie on one line. “And he launches his hypothesis: they are all there,” summarizes the mathematician. “That’s what the straight line we see on the board means.”
To date, billions of values have been calculated that yield zero and they are all on the line, but the demonstration of why there is no non-trivial zero outside of this line is missing. “We must show that if a point is exterior, it cannot be zero, except in trivial cases,” summarizes the Sevillian mathematician. “If this is demonstrated, one of the consequences is that by working a little harder, we could find the distribution of prime numbers, which explains the mystique surrounding the Riemann hypothesis.”
We are used to seeing works of art as decoration, it’s time to use a mathematical masterpiece.
Clara Grima
— Mathematics
For Clara Grima, bringing this mathematical formula to the stage of the most watched television program is genius. “I think this was done by someone very brilliant, who will be a mathematician or physicist,” he emphasizes. “We are used to seeing works of art as decoration, it’s time to use a mathematical masterpiece.” “Broncano’s mother is a high school math teacher, so maybe that’s where the shooting is going,” Márquez speculates. “Perhaps they meant: we are going to pose here the most difficult problem that exists, as impossible to solve as winning the battle of the public,” jokes Sáenz de Cabezón. “Or better yet, can you imagine that they put the Riemann Hypothesis there in case a viewer got interested in it, started investigating it, solved it and it became, then yes, the most famous program in the world. television?”
For the moment, the management of “La Revuelta” prefers to maintain the mystery and not reveal any further information. “As for why it is there and who put it,” assures the program director, Ricardo Castella, to elDiario.es, “I fear that you will also have to continue to formulate hypotheses.”
