An artificial intelligence system developed by Technion researchers, combining the UMAPS algorithm with large language models, mapped hundreds of formulas to the constant π and found that most of them are related to each other – a first step towards a unified theory of π formulas to be presented at the NeurIPS conference
Since the dawn of history, mathematicians have sought ways to calculate significant mathematical constants, most notably π – the ratio of the circumference of a circle to its diameter, which cannot be represented precisely as a quotient of whole numbers. As early as ancient Egypt (16th century BC), approximate values of π were used to measure land areas. Archimedes (3rd century BC) was among the first to develop a method for approximating it, and over the generations, additional approaches have developed: from the Indian mathematician Madhava (14th century AD), through the giants of science Euler, Newton, Leibniz, and Gauss, to the mathematical genius Srinivasa Ramanujan (20th century) – after whom the Ramanujan Machine research group led by Prof. Ido Kaminer from the Viterbi Faculty of Electrical and Computer Engineering at the Technion is named.
Although π and other constants have fascinated mathematicians for thousands of years, no single theory has yet emerged that explains the full range of formulas that have accumulated. This reflects a common challenge in science and mathematics: human knowledge is built up as a collection of separate discoveries, while the internal connections between them often remain hidden.
New research from Ramanujan's group, to be presented at the upcoming NeurIPS conference – the world's largest conference on artificial intelligence and machine learning – demonstrates how artificial intelligence can help unify different theories in science. The research proposes a new approach to mathematics – using artificial intelligence to find connections between mathematical formulas – and demonstrates the effectiveness of this approach in uncovering hidden mathematical principles.
The development of the system was led by Tomer Raz, a member of the reserve's elite "Barkat" program and a master's student under the supervision of Prof. Ido Kaminer. Ramanujan Machine group members Michael Shalit, Dr. Elyashiv Livtag, Rotem Kalish, Shahar Weinbaum and Dr. Yaron Hadad also participated in the research.
The system combines UMAPS – an innovative mathematical algorithm – with large language models (LLMs). Based on more than 455 thousand scientific articles, the system identified thousands of formulas for calculating the constant π, filtered them into 385 unique formulas, and proved that most of them (94%) are related to each other. Thus, Ramanujan's group recorded an unprecedented success – discovering a connecting thread between various "classical" formulas such as those of Madhava, Euler and Gauss. To their surprise, the researchers discovered that many of the ancient formulas are also related to "modern" formulas, including new formulas discovered by the algorithms developed in recent years by the Ramanujan machine group. According to Prof. Kaminer, "We expect that further improvements to the system will make it possible to classify all π formulas into a few categories and thus create a unified theory. Looking ahead, our approach could help map connections in other worlds of mathematics and other fields of science. This is an especially important process in an era when the amount of knowledge is growing at an enormous rate."
The research was supported by the Schmidt Sciences Foundation.
Authors of the article: Tomer Raz, Michael Shalit, Dr. Elyashiv Livtag, Rotem Kalisch, Shahar Weinbaum, Dr. Yaron Hadad and Prof. Ido Kaminer.
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Hello Avinoam. The article is based on research published in a peer-reviewed journal. When your materials are published in a scientific journal, I would be happy to publish them as well. We do not have an evaluation team to conduct peer review ourselves.
Avi Shalom.
You can save the prestige of the scientist, and the prestige of Prof. Ido Kaminer, if you remove the article about constant pi from the article. I already explained this in my previous response, which revealed that a closed circular line must be curved to a certain extent.
If it is short, its curvature is large. This explanation leads directly to the idea that for every size of a closed circular line, there is a private pi number, and its value varies between 3.14 and 3.16. Follow my publications, and save your scientific prestige.
With great respect, Avinoam Abeba
I wrote to you – only one response to the article
My last comment disappeared.
A geometric mathematical theorem, by cosmologist Avinoam Esfa.
The degree of curvature of a closed circular line is reflected in its private pi number.
Infinite individual pi numbers vary from 3.14 – to a closed circular line with a diameter of infinite mm, (zero curvature)
For 3,16 in a closed circular line with a diameter of zero mm. (infinite curvature)
It seems to me that here I ended my many years of struggle with mathematicians, who believed in a fixed number pi (3.14) that corresponds to all closed circular lines, and they did not know that by this belief, they delayed the development of geometry, and it remained with the geometry of straight line segments for thousands of years.
Now the way has been opened to the geometry of closed circular lines, which is exhibited in the world's first geometric museum, in my home in Ramat Efal, Ramat Gan.
Many thanks to the newspaper "Hidaan" for allowing me to express myself with complete scientific freedom and thereby promoting the development of science.
Avinoam Abaeva, the explorer of the universe
The cosmologist Avinoam Esva announces that he has been engaged in his research for 40 years, using his natural knowledge – with enthusiasm and a wonderful feeling of satisfaction. And in two months I will be 86 years old.
During these wonderful years, I invented the precise measuring device – the scope – that proved the idea of the variable pi – experimentally, and no respected and recognized scientific body was willing to go back on the experiment.
Last year, I opened the world's first private geometric museum in my home, where I presented the geometry of closed circular lines, with the idea of a changing pie.
The museum houses the scope, where the historic scope experiment that proved the idea of variable pi was conducted.
This museum actually showcases my life's work,
Many thanks to the newspaper website and its veteran editor, Mr. Avi Blizovsky.
The freedom of expression you granted me contributed to the development of geometry, and removed the stagnation in science in the study of the universe.
Every person can explore the universe with the help of their natural knowledge.
That's what I did too, and the title of the first book I published testifies to that.
The magical journey of a nerd on the wings of natural knowledge.
Every living creature has its own natural knowledge, and artificial intelligence, which is a machine, has no natural knowledge –
All artificial intelligence can do is recite the work of a person who possesses natural knowledge.
Every living creature has its own natural knowledge, which it is born with.
I was fascinated by the wonders of natural reality, and I began to explore the wonders of natural reality with the help of my natural knowledge, which you didn't even know existed - today I know that natural reality is all a wonder of wonders.
And the great wonder is the natural knowledge of all living beings.
Every person can explore the universe with the help of his natural knowledge, and perhaps he will discover absolutely new things.
Best regards
Cosmologist Avinoam Abeba
I published my most important response yesterday, summarizing the topic of the geometry of closed circular lines.
And I don't see her. Thank you for your attention.
Avinoam Sadness
I sent 2 replies.
Who would have believed that mathematics is based on faith?
It really happened….
Mathematicians believe that the ratio of the diameters of two random circles
Exactly equal
The ratio of the circumferences of the circles
This is the stupidest belief of mathematicians, and it has stopped the development of geometry.
A. Asbar
The natural science of geometry was corrupted by the interference of mathematicians.
A natural geometer, he first identified a line, its length, and its shape. { Open straight line, (Closed circular line.)
This natural science gave the name geometric (closed circular lines to circles)
Geometry is the exact science of line lengths, and the most precise expression of line length is in measurement.
Measurement can become more and more accurate, but perfect measurement does not exist in reality.
Mathematics has hindered the development of the geometry of circles, which are essentially "closed circular lines."
Shame on mathematicians who did not themselves repair the damage caused to the first of the exact sciences - geometry.
The second exact science is physics, which measures, and therefore mathematics, which performs calculations, cannot harm it.
How mathematics has damaged geometry,,,,
Mathematicians believe
Because if the diameter of circle A is 4 times larger than the diameter of circle B,
So the circumference of circle A will also be 4 times larger than the circumference of circle B.
From this foolish belief, which no mathematician has ever proven, arose the false number 3.14 – which states,
For all the circles in the world, from the smallest to the largest – there is a single number 3,14 which says, ,,,,,,,,,,,,,
How many times larger is the circumference of any circle than its diameter? —–This is how the false number 3,14 came into being.
The belief in the false number 3.14 has hindered the development of circular geometry for thousands of years, and is
It remained in this state until a nerve appeared, which canceled the false number 3,14 that supposedly corresponds to all circles,
And he established the following rule
Every length of a closed circular line has a specific pi number, and they all lie in a narrow range between 3,14 and 3,16.
The newspaper "Hadayan" is asked to take on a public mission, and save geometry from the clutches of mathematicians, who are hindering the emergence of a new geometry - of closed circular lines, discovered by Nefer.
The geometry of the straight line has existed for thousands of years, and mathematics is delaying the emergence of the geometry of closed circular lines. If the newspaper had come to me, it would have been recorded in the history of science, along with the nerve.
Who believed that mathematics would hinder the development of geometry?
Mathematics is just a language of abstract quantities expressed in numbers, and it is mistakenly presented as the queen of sciences when it should be presented as the handmaid of the exact sciences,
Numbers reflect quantities of length, area, volume, time, and energy.
There is nothing in mathematics, except that it is a language of abstract quantities, using numbers that have abstract quantities.
A. Asbar
Readers of the journal are asked to publish the new science of neuroscience,
A. Asbar
Avi Blizovsky's answer reduces the importance of the newspaper "Hidaan" to a gossip newspaper.
If there is no news report whose writer fights for the truth, then the news report becomes a gossip newspaper.
A scientist can replace the truth he holds with another truth, and that's how science advances.
But we fight for the truth.
This is a truth that must be fought for.
All mathematicians truly believe that if the diameter of circle A is 5 times larger than the diameter of circle B,
So the circumference of circle A is also 5 times larger than the circumference of circle B,
This is a false belief, and from it follows that all circles have a single number, expressing how many times larger,
The circumference of any circle is its diameter. Thus was born the false number 3,14, which Naber has been fighting for 25 years.
Nerve is considered a scientific Don Quixote fighting a losing battle against mathematicians who believe in the false number 3,14.
But Nerver continues to fight, and he invented the scope device, which he proved by experiment.
If the diameter of circle A is 5 times greater than the diameter of circle B
So the circumference of circle A will never be 5 times larger, but another number close to 5, but never 5.
This is how the false belief of mathematicians was disproved,
That the ratio of the diameters of two circles is (equal) to the ratio of their circumferences.
This result cannot be reached by mathematical calculation, but only by practical experiment, by very, very precise measurement.
The precise circumference device reached this result 10 years ago, but mathematicians who hold the false belief that the ratio of diameters is equal to the ratio of circumferences refuse to repeat the circumference experiment, and they are following the development of geometry. The geometry of closed circular lines is waiting to be discovered, but mathematicians are hindering the development of science. Aber opened the Museum of Closed Circular Lines, a private museum located in Aber's house in Ramat Efal, and it is slowly entering the public consciousness. The circumference device is in this museum
A. Asbar
In the comments, no one claims to be providing authoritative scientific material. But I asked you to stop with this article, you have exaggerated the number of comments.
Did Archimedes believe in the false number 3.14?????
I dont think so
The false number 3.14 that fits all circles probably appeared hundreds of years ago, and I would appreciate it if someone could correct me.
A. Asbar
Avinoam, I think you have exhausted your responses to this article.
Technion scientists are being asked to save the prestige of the Technion and declare that 3.14 is the false number of mathematics.
A. Asbar
interesting.
I would be happy to expand on the connections found between the various formulas for pi. What kind of connections and how the categories of the formulas are constructed. Thank you
The mathematics education system is steeped in the lie of the number 3,14
The mathematics education system has no way to test itself, and it will continue to teach the false number 3,14.
For thousands of years, the system has taught the false number 3,14, and the mathematician who discovered it is considered an eccentric and is persecuted by the mathematical community. The mathematician also discovered the new geometry of closed circular lines, but the mathematical community ignores him as if he does not exist,
Nerves were persecuted by the mathematical community, and Galileo was persecuted by the church.
Galileo answered his persecutors with the eternal saying, "And yet, move, move."
And Nerber answered his pursuers with an eternal saying,,,,,,,,,,and yet,
Galileo and Nerves believe that practical experiment in actual reality determines physical truth.
Galileo discovered new physics through a simple and not-so-precise practical experiment (free movement on an inclined plane)
And Neber discovered a new geometry, by means of a not-so-simple and very precise practical experiment, (the perimeter experiment).
For these innovations, Galileo was persecuted by the church, and Nerva was persecuted by the community of mathematicians.
The parallel between Galileo and Nerva is perfect, both were pioneers in science.
Galileo discovered new physics, and Aberdeen discovered new geometry.
A, nervous
There are two types of geometry in the world.
of the straight line
And of the closed circular lines. (Discovered by Nerve in the circumference experiment)
A. Asbar
1976, 9th grade at Ort Singlowski, physics teacher Krieger gave us a special lesson on pi and e and their relationship to statistics and mathematics in general.
So what is Bigil?
Mathematicians believe that if the diameter of circle A is 4 times larger than the diameter of circle B,
Then the circumference of circle A will also be 4 times greater than the circumference of circle B.
This is the stupidest belief of mathematicians, and from it it follows that for all circles, from a diameter of zero mm
And up to an infinite diameter of millimeters, there is a single number that expresses – how many times larger – the circumference of each circle is than its diameter.
The value of this number, ——–a little more than 3,14 and I call it the —- lie number 3,14
The false number 3,14 stripped mathematics of its unjustified title – the queen of sciences – and transformed it into a simple language of quantities, since numbers express abstract quantities that are not perceived by the senses.
To understand my extreme reaction, it must be recognized that I discovered a new geometry by a simple but very precise experiment.
This is the geometry of closed circular lines. Just as Galili discovered new physics by a simple experiment on an inclined plane, so you discovered new geometry with the scope device I invented.
Galili and Naber were persecuted for their discoveries, by the church, and by the community of mathematicians.
The pursuit of Galili has already ended, but it continues after Naber.
No mathematician believes the idiot who claims a specific pi number for each diameter of a circle, from a diameter of zero mm to a diameter of infinite mm.
Soon everyone will believe, and the false number 3,14 will disappear from science.
I inform all mathematicians that I have opened my private geometric museum, in my home in Ramat Efal, and it is the museum of closed circular lines, in which the perimeter is displayed.
The ancient geometry was of the straight line; the new geometry is of closed circular lines.
Follow the science of nerves
A. Asbar