Opinion 180: The Ramanujan Machine is a Harbinger of Mathematics becoming a Science again (and Fun again!)

By Doron Zeilberger

Written: Feb. 16, 2021

Last week an account of the amazing Ramanujan machine appeared in the "top scientific journal", Nature. It is very rare that any math is ever published in Nature, and, indeed, "officially" it was labeled AI. But it is math at its best, and the best kind, experimental mathematics!

Some naysayers, and I won't mention any names (hint: he has an equally brilliant brother), went as far as calling it an "intellectual fraud", and went on to claim that there was "nothing new" and "it all follows from Gauss and Euler". This reminds me of the joke

A: My dog can play chess

B: Wow, he is a genius!

A: Not really, I beat him most of the times

Here is a machine, that without any prior knowledge rediscovered something that it took Euler and Gauss some effort to find.

Besides, this dismissive "high-brow" number theorist, was not quite right, and some of the conjectures made by the Ramanujan machine are new and some, I think, still unproved. To prove his point, the above-mentioned brilliant brother picked a "random" discovery that was labeled "unproved" and went on to prove it. The proof is far from trivial, and uses some fairly sophisticated analysis. This reminds me of another joke

A math professor says in a lecture "such and such is trivial". A student asks him "why is it trivial?" The professor thinks and thinks and can't answer. Then he leaves the room, and two hours later returns and says "indeed it is trivial" and then fills the board with a long explanation.

Another naysayer is a good frenemy of mine, that will also remain nameless, who asserted that calling it "The Ramanujan machine" is ``over the top''. I disagree! Ramanujan would have loved it, and the machine does exactly what Ramanujan excelled at, make interesting conjectures (most of which he did not bother to prove, leaving it to Bruce Berndt and his students). That same frenemy of mine also claimed that the conjectures made by the Ramanujan machine "do not give any insight". Perhaps, but they give something much more important, they give meta insight.

The great significance of the Ramanujan machine, and why I love it so much, is that it is a harbinger of a new kind of doing mathematics. A new methodology and even ideology, and if you wish a new religion, to replace the current forbidding, intimidating, elitist, "mainstream pure mathematics", that the above mentioned brother is one of its priests. The Ramanujan machine is

In other words, it is fun! and this kind of methodology will make most of the current papers in Annals of Mathematics obsolete in fifty years.

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