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Have breakthroughs in mathematics been discovered through artificial intelligence?

The researchers of the Faculty of Electrical and Computer Engineering at the Technion developed an algorithm for discovering new formulas and new relationships between mathematical constants

The picture of the mathematician Remanjuan next to a complicated formula that he developed Photo credit: Technion spokespersons
The picture of the mathematician Remanjuan next to a complicated formula that he developed Photo credit: Technion spokespersons

Artificial intelligence is a tool that is rapidly changing the world - in image processing, speech recognition, disease diagnosis, new drug development, autonomous transportation, writing and translation, and even creative production of texts, images and videos.

Number theory is a field that so far has not received much attention from AI researchers, and this is where a new article by Technion researchers in the group of Prof. Ado Kaminer from the Viterbi Faculty of Electrical and Computer Engineering. led the research Rotem Elimelech, who was an undergraduate student while working on the research now published inPNAS, and is currently a master's student at the faculty. The researchers explain that "new discoveries in number theory - for example, the discovery of formulas for previously unknown mathematical constants - are considered a creative challenge that requires moments of human inspiration, so it was customary to assume that there was no place for artificial intelligence in this field."

It is customary to assume - and wrongly. The Technion researchers presented a breakthrough in connecting the two fields about three years ago. In 2021 they are Published In the journal Nature, a "hypothesis generator" that produces mathematical formulas. They called the hypothesis generator the "Ramanjuan machine" after the mathematician born in India, one of the greatest mathematical geniuses of all time. 

One of Ramenjuan's rare abilities was in formulating mathematical formulas intuitively and without proof. Technion researchers sought to reproduce or imitate the same intuition using algorithms and large computing power. Indeed, the new machine produced several hypotheses, some of which were familiar and some of which were completely new.

In the new article recently published inPNAS Prof. Kaminer's research group presents the "Remanjuan Machine 2.0", focused on the issue The relationships between the various mathematical constants and shows how computer generated results provide clues for mathematicians. The new research is a breakthrough in the field called AI for Science - scientific progress through artificial intelligence.

According to Elimelech and Prof. Kaminer, "On a philosophical level, our work explores the interrelationships between algorithms and mathematicians. The new article shows that algorithms can indeed provide the information necessary to produce creative insights and lead to the discovery of new formulas and new relationships between mathematical constants."

Mathematical constants such as pi, Euler's constant, and the golden ratio are numbers that appear naturally in mathematical developments and their value does not change. Many of them have enormous value not only in mathematics but also in other fields including biology, physics, and ecology.


The work on the original task, discovering new constants, yielded some dramatic "by-products":

  • Demonstrating the effectiveness of "virtual laboratories", where computer experiments are conducted that simulate "physical" experiments in the natural sciences. In these laboratories it is possible to produce new mathematical formulas and even new mathematical hypotheses through algorithms. Hypotheses that are based on examples and try to generalize them are the driving force of mathematical research. The more examples there are that support the hypothesis, the stronger it is and the more likely it is to be true.
  • As an example of such success, the researchers used the formulas discovered by the algorithm to construct a simple proof of the irrationality of a famous constant named after Roger Epfrey, who proved this property in 1979. His proof is known as a surprising breakthrough, based on an extraordinary intuition in a more than 100-year-old hypothesis, the mathematical logic behind which until now was cumbersome and difficult to understand.
  • Expanding the use of distributed computing - computing based on many computing units (many computers, many processors). According to the researchers, some of the mathematical discoveries are not possible without the power inherent in distributed computing. In this aspect, the researchers collaborated with Prof. Mark Zilberstein From the Viterbi Faculty of Electrical and Computer Engineering at the Technion and made use of it In the infrastructure of a distributed calculation supported by thousands of volunteers from all over the world who "contributed their computers to science" and ran the algorithm and contributed to my discoveries.
  • The new Remanjoan machine, combined with distributed computing, can be used by other researchers in producing search algorithms that serve their purposes, so that in any case that the algorithm manages to find a "tip", it will help direct the research of human researchers to examine new phenomena in promising areas. 

Wolfram Brandt, Carlos de la Cruz Manguel, Ofir David, Prof. Mark Zilberstein, Yaron Haddad, Ratem Kalish and Michael Shalit participated in the study.

for the article inPNAS

8 תגובות

  1. Avi Belizosky.

    Block him

    Asbar again returned to flood the comments with obsessive pseudo-science. He is not in control of himself.

    Block him because you're fed up.

    Half of the comments here are from one person who comes back like a broken record and floods the comments

  2. Avi Belizosky

    Asbar again returned to flood the comments with obsessive pseudo-science. He is not in control of himself.

    Block him because you're fed up.

    Half of the comments here are from one person who comes back like a broken record and floods the comments

  3. Maybe stop publishing the comments of the gentleman who calls himself sad? I go in to read scientific articles and get repetitive pseudo-science.

  4. Don Quixote the Alsabian man of Jerusalem
    A searcher is responsible for a tragic mathematical conception, which has halted the development of geometry for the past 2000 years.

    All mathematicians since Archimedes believed that each size of a circle corresponds to a single pi number whose value is 3.14

    Asbar did not believe the mathematicians, and he discovered that each size of a circle has a private pi number that is in a narrow range, between 3.14 and 3.16

    It is about an infinite number of private pi numbers of circles (whose diameter appears between zero mm, and infinity mm) and the formula for finding them is known to everyone.

    But the mathematicians don't believe in getting upset, and they continue to teach the lie of a single pi number 3.14, which is supposed to fit all circles.

    And since Asbar has already been fighting for 30 years with the number pi 3.14, he is considered a scientific Don Quixote dealing with a lost war in advance.

    A call to the Einstein Institute of Mathematics
    Accept the task of correcting this tragic math mistake, and one hour early.
    Look at the book
    "Esbar's magical journey on the wings of natural knowledge"

    Barcode
    for the experiment
    the scope

  5. The mathematician is waiting 2000 years for a breakthrough, on the subject of pie.
    The neurotic Don Quixote, the man of Jerusalem, is responsible for a tragic mathematical concept that has stopped the development of geometry for the past 2000 years.

    All mathematicians since Archimedes believed that each size of a circle corresponds to a single pi number whose value is 3.14
    Asbar did not believe the mathematicians, and he discovered that each size of a circle has a private pi number that is in a narrow range, between 3.14 and 3.16

    It is about an infinite number of private pi numbers of circles (whose diameter appears between zero mm, and infinity mm) and the formula for finding them is known to everyone.

    But the mathematicians don't believe in getting upset, and they continue to teach the lie of a single pi number 3.14, which is supposed to fit all circles.

    And since Asbar has already been fighting for 30 years with the number pi 3.14, he is considered a scientific Don Quixote dealing with a lost war in advance.

    A call to the Einstein Institute of Mathematics
    Accept the task of correcting this tragic math mistake, and one hour early.
    Look at the book
    "Esbar's magical journey on the wings of natural knowledge"

    Barcode
    for the experiment

    A. Asbar

  6. Inspiring and giving hope. The fear is hype like in the dotcom bubble 25 years ago. Right now it looks like it's going to good and productive places. I wish he would continue. The contribution to the prediction of protein folding is enormous. We are at the beginning of a revolution that will change the world and make it more efficient.

  7. There is nothing new in mathematics, and there never will be.
    Artificial intelligence is not capable of breaking through and discovering anything absolutely new.
    Such a breakthrough belongs to natural intelligence, which is based on natural knowledge that man has.
    The machine has no natural knowledge, and is only capable of reciting "noises of words"

    On the other hand, there is something new in physics, and it is presented in a short article - the physical forms of matter

    This article will replace all physical theories of science, from ancient times to the present day.

    These theories appear in Wikipedia, and they all failed to understand the word substance.

    Matter appears in reality as elements such as iron, carbon, hydrogen, zinc, and each element is a physical form.
    Those interested in following the development of the concept of "physical form" will follow Asbar's publications on the Hedao website, and in Asbar's books published by Niv.

    A. Asbar

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