Ramanujan machine automatically generates conjectures for fundamental constants

mathematical constant
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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 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 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 —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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Celebrating the mathematical genius Ramanujan

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
Journal information: arXiv

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Jul 15, 2019
math need proof like vodka

Jul 15, 2019
seriously and this surprised me when a friend said his dad said the same.
(and I'm bad at math)
a math paper should not require citations

Jul 15, 2019
2^500 conjectures to find on the basis of finistic distinguishability of perturbation for rank and the existent constants.

Done. I did the computer's homework.

Jul 15, 2019
2^500 conjectures to find on the basis of finistic distinguishability of perturbation for rank and the existent constants.

Done. I did the computer's homework.

Well, then. Have some 100 proof Vodka...

Jul 15, 2019
Having had my second glass of Pinot Noir, I say this is a fine homage to Srinivasa Ramanujan.

Jul 15, 2019
Too bad your Pi value is wrong, suckers.
3.144605511....

Jul 16, 2019
Ramanujan is violating the Hitchens tenet!
Hitchens 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!

Jul 16, 2019
In looking at the relationship of the primes numbers, p(i) and the trigonometric function sin(x), I constructed the scatter graph of sin(p(i)). The result was a plot that resembled so many overlapping sinusoidal waves, something like a Lissajous figure, with a regular gap between the sinusoidal waves. This suggested a connection between p, which can be used to represent pi, and the primes. The primes coordinate with the value of p.
I 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.

Jul 16, 2019
Using the indicated connection between p, being used here for pi, the sine function and the primes p(i), I derived a formula that produce approximations for the primes which, when divided into the primes, provide a ratio that appears to be close to 1.
If 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.

Jul 16, 2019
Hitchens 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!
So the hypothesis about the non-trivial zeros of the Riemann zeta function all having real part one-half can be dismissed? You may wish to read what Godel said...

Jul 17, 2019
If Hitchens' "tenet' is accepted, then the assertion that all the zeroes, z, of the zeta funtion must have Re(z) = 1/2. Likewiose, such thingsa s athe Goldbach Conjecture and Fermat's Last Theorem must be declared untrue, they must be declared "proved" untrue.
What 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.

Jul 17, 2019
What isn't realized is that the depravity of Hitchens' "tenet" is no search for knowledge. It was never anything more than a political swindle
These days "political swindle" is redundant. It's not likely Hitchens intended his statement to be applied rigorously to mathematics, fairly obvious not one mathematician would agree with it. Keep working on your conjectures about the primes, julianpenrod, one way of looking at the Sieve of Eratosthenes is seeing each prime as a sine wave whose wavelength is twice the prime's magnitude and which intersects the x-axis at each of the composites the prime is a factor of...

Jul 17, 2019
It's kinda stoopit to talk about "math without a proof" in a formal paper. The paper is, you know, where you present the proof. Then everyone in the math community gets to check it for errors and stuff. Duhhhhh ummm.

Too bad your Pi value is wrong, suckers.
3.144605511....

= 4 / sqrt (Phi)
Let the Ramanujan machine confirm it, as current mathematicians are too proud for admitting the historical mistake.

Jul 27, 2019
Before one may count, it must have some thing to count.

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

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