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

- experimental
- concrete
- algorithmic
- computational

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.

Doron Zeilberger's Opinion's Table of Content