July 15, 2019 report

# Ramanujan machine automatically generates conjectures for fundamental constants

A team of researchers at the Israel Institute of Technology has built what they describe as a Ramanujan machine—a device that automatically generates conjectures (mathematical statements that are proposed as true statements) for fundamental constants. They have written a paper describing their device and have uploaded it to the *arXiv* preprint server. They have also created a webpage for people who wish to allow the network to use their computer's process cycles, suggest a proof or develop code toward new mathematical structures.

The Ramanujan machine is named for famed Indian mathematician Srinivasa Ramanujan, a self-taught mathematician who grew up in India and was "discovered" by fellow mathematician G.H. Hardy. After moving to England, he became a fixture at Cambridge, where he shook up the math world with his unorthodox mathematics—instead of pounding away at math proofs, he obtained results to famous problems through intuition and then let others find the proofs for them. Because of this, he was sometimes described as a conjecture machine, pulling formulas out of thin air as if they received from a higher being—sometimes in dreams. In this new effort, the researchers in Israel have sought to replicate this approach using computing power.

The Ramanujan machine is more of a concept than an actual machine—it exists as a network of computers running algorithms dedicated to finding conjectures about fundamental constants in the form of continued fractions—these are defined as fractions of infinite length where the denominator is a certain quantity plus a fraction, where a latter fraction has a similar denominator, etc.) The purpose of the machine is to come up with conjectures (in the form of mathematical formulas) that humans can analyze, and hopefully prove to be true mathematically. The team that created the machine is hoping that their idea will inspire future generations of mathematicians—to that end, they note that any new algorithms, proofs or conjectures developed by a participant will be named after them. The researchers note that their machine has already discovered dozens of new conjectures.

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**More information:**Gal Raayoni et al. The Ramanujan Machine: Automatically Generated Conjectures on Fundamental Constants arXiv:1907.00205v1 [cs.LG]: arxiv.org/abs/1907.00205

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**Citation**: Ramanujan machine automatically generates conjectures for fundamental constants (2019, July 15) retrieved 21 August 2019 from https://phys.org/news/2019-07-ramanujan-machine-automatically-conjectures-fundamental.html

## User comments

knowphiselfknowphiself(and I'm bad at math)

a math paper should not require citations

Spaced out EngineerDone. I did the computer's homework.

Whydening GyreWell, then. Have some 100 proof Vodka...

Doug_Nightmaredoogsnova3.144605511....

julianpenrodHitchens said anything proposed without proof can be dismissed, which means that, if someone doesn't provide proof or evidence of a statement, that automatically makes it untrue! Essentially, only the person making an assertion has to prove it. If someone opposes it, they don't have to do anything since the other not providing evidence "proves" it untrue!

Those who hate God, who hate the truth use this with abandon. They denounce statements not hateful of God, they denounce conspiracy theories. Those saying God is present, that a conspiracy seems to be acting ask for opponents' proofs otherwise and the opponents merely insist that only the first person in an argument has the burden of proof!

To be philosophically pure, PhysOrg must denounce Ramanujan or Hitchens. They can't both be accepted!

julianpenrodI then looked at the scatter graph of (p(i)/p) - [p(i)/p], which is the fractional part of each prime that is expressed in sin(p(i)). The result is a series of parallel pencils of parallel straight lines, ten in each pencil, with a space between pencils big enough for another line.

This is empirical, but it can be looked at and possibly even provide a direction to finding a universal connection between the sine, p, and the prime numbers.

julianpenrodIf f(j) = p^(1+sin(1+sin(p^(1+sin(j^(1/p)))))), if someone calculates (j*f(j))^(1/p), for j ranging from 1 to i, then sums those values to get S(i), and then multiply S(i) by the term ((ln(i)^(3/p))/(i^(1/p)) to produce p*(i), p(i)/p*(i) will produce a curve that, up to i=100,000, falls mostly between .98 and 1.02. It seems this is approaching the value 1 or a value close to 1. This can provide a means of calculating an approximation for p(i) that could make finding the exact value of p(i) quicker. This is empirical but it seems to work.

ProtoplasmixjulianpenrodWhat isn't realized is that the depravity of Hitchens' "tenet" is no search for knowledge. It was never anything more than a political swindle. Intended to give "ammunition" to the degenerates who hate God and declare He is not present and those who insist that conspiracy theories must be wrong. out of the hate Democratic Rackets followers have for anyone who isn't a Democratic Rackets deviate.

Note that no one who received doctorate accreditation in philosophy or "science" condemned Hitchens' "tenet". That can be called a conspiracy against God.

ProtoplasmixDa SchneibStudentofSpiritualTeaching= 4 / sqrt (Phi)

Let the Ramanujan machine confirm it, as current mathematicians are too proud for admitting the historical mistake.

MayILogic or Light is crucial, although Love is most important.

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