Mathematicians are a fascinating breed. They look at problems and new fields of study for discoveries and then plug away on a single problem or set of problems for amazing amounts of time. They do this by attacking the problems from every direction using every mathematical tool they have. They use intuition and experience to find patterns, similarities to other problems, and even brute force methods. The goal is to seek out patterns, make sense of those patterns by stating conjectures, and then prove those conjectures into theorems. This often takes mathematicians years or decades – if they ever solve it at all. If nothing else, mathematicians are a persistently curious lot.
The Ramanujan Machine
With all this potential tedium, is there a way to speed some of this up? Could one automate some of the work? AI algorithms are amazing at pattern matching, so what if we use machine learning to start the ball rolling? Enter the Ramanujan Machine – after the famous Indian mathematician that saw patterns where others did not (and had no less than 2 movies made about him). This kind of software may be transformative to how mathematics is done – and some are raising questions about what it means for the field.
The concern is that the Ramanujan Machine does much more than just pattern match. The machine consists of a set of algorithms that seek out conjectures, or mathematical conclusions that are likely true but have not been proved. Researchers have already used machine learning to turn conjectures into theorems on a limited basis — a process called automated theorem proving. The goal of the Ramanujan Machine is more ambitious. It tries to identify promising conjectures in the first place.
The algorithms in the Ramanujan Machine scan large numbers of potential equations in search of patterns that might indicate the existence of formulas to express them. The programs first scan a limited number of digits, perhaps five or 10, and then record any matches and expand upon those to see if the patterns repeat further. When a promising pattern appears, the conjecture is then available for an attempt at a proof.
So far, the Ramanujan Machine has generated more than 100 intriguing conjectures so far – and several dozen have been proved.
The question for the field is now: what does this tool mean for us.
I have already written about the problem of scientific discovery and Epistomology. Machines can now pattern match and come up with equations and descriptions that can describe physical realities, but at what point can we say that we ‘know’ something?
If a machine observes a system and spits out an answer/mathematical description, we often do not know how it arrived at that answer. Can we really say we ‘know’ a thing and are accurately describing it? Without understanding the interplay of the underlying principles that got us to that answer, it might only hold for that set of inputs.
Some would argue, that’s how we’ve always done science. Despite our best efforts, science pushes ever forward and sometimes refutes past theories. We have seen this most dramatically in medical discoveries and regularly in the fields of cosmology and quantum mechanics. However, in mathematics, this is not so. Proven theorems have held for millennium.
So where does this leave us
Honestly, I think software like the Ramanujan machine is the next logical step in mathematics and pure sciences. Just like the calculator became a tool that helped transform math 100 years ago, AI enhanced pattern matching is a next logical tool in the toolbox. Instead of relying on intuition and years of grunt work, it’s unbiased and methodical approach could help us see patterns we have missed, and do it massively faster. After all, correctly formulated mathematical proofs are proofs no matter what the source was.
While it likely cannot replace a well-trained expert, it certainly could help augment their efforts. Speeding up our rate of discoveries by orders of magnitude sounds like a very solid contribution to me.
Try out the machine here: https://www.ramanujanmachine.com/
Read more here: https://www.livescience.com/ramanujan-machine-created.html
Or even download the code here: https://github.com/ShaharGottlieb/MasseyRamanujan/