We Need Mathematicians More Than Ever

In Richard McElreath’s excellent book on Bayesian methods, Statistical Rethinking, he opens with a little story about the Golem of Prague. The Golem was a mythical, supernatural figure that once stalked the alleyways of Prague’s Jewish ghetto in the 16th century. Legend has it that the renowned Rabbi Löw, also known as the Maharal of Prague, was seeking a way to protect the local Jewish people from pogroms and the whim of unpredictable rulers. Endowed with the power to transform the four elements into living things, he moulded a superhuman from the mud of the Vltava. To bring the Golem to life, Rabbi Löw had to insert a shem (a clay tablet bearing the name of God) into its mouth.

The Golem would do whatever it was instructed to do. It was intelligent, but it was not wise. It could not make its own independent decisions and would just keep doing what it was told. Rabbi Löw would deactivate his creation for the Sabbath, to allow the creature to rest according to the Jewish custom. However, one day he forgot, and the Golem went raging through the ghetto, destroying everything in its path. Rabbi Löw was reciting Psalm 92 in the synagogue when he was interrupted and told of the chaos the Golem was causing. He eventually confronted the monster outside the synagogue, where he managed to remove the shem. The Golem was never revived and allegedly was later stored in the synagogue’s attic, which remained locked for centuries. To this day, Psalm 92 is recited twice during services in Prague’s most famous synagogue.

In Yiddish, the word Golem means ‘stupid’ or ‘lazy’ — an interesting description despite its amazing superhuman powers. But an appropriate one. Executing intelligence is easy — executing it with wisdom is hard. Recent developments in technology has made the execution of intelligence easier, but have made no progress on the execution of wisdom.

If we don’t develop a future generation of Mathematicians, I believe that we may be unleashing bigger and bigger Golems on the world without sufficient means to control them and ensure they act with wisdom. I’d like to lay out some particular concerns I have in this regard.

We May Be Losing Good Mathematicians to Data Science

Data Science and Mathematics are two very different things. The Python package scikit-learn offers a Data Scientist pre-packaged tools to run advanced mathematical algorithms like Support Vector Machines or Gradient-boosted Trees. They can engineer their algorithmic pipelines with the convenience of not having to engage deeply with the underlying mathematics of what they are doing. Parameters are often selected with little wisdom, and trial and error is often the main method used to determine their values.

Today’s young mathematicians are increasingly being reconditioned as data scientists, often lured by higher salaries and the temptation of a career in the new ‘world’s sexiest job’. As part of this reconditioning, they risk becoming engineers and not mathematicians. They risk losing their wisdom to critique and interpret their methods, and increasingly fall into the trap of trial-and-error execution. You don’t need to be a mathematician to engineer or execute a pipeline.

It’s worth remembering that all of the methods that are packaged up neatly in languages such as Python, R or Julia rely on methods developed by professional mathematicians. If the number of professional mathematicians decline, who will develop better methods in the future? One possible long term consequence of a decline in professional mathematicians is a reduction in the speed of mathematical method development and innovation. This is something we need to keep a close eye on.

The advent of AI threatens a laziness of mathematical rigor

I’ve already been asked numerous times at various speaking events and panels if AI will replace the need for mathematicians. The fact that some people may believe this terrifies me more than a little. Anyone who engages with even the very latest Generative AI developments, or who understands how Generative AI works, knows that it is a very poor replacement for a sharp mathematical mind.

An excellent recent piece in the New Yorker described ChatGPT as ‘a blurry JPEG of the web’. This is a very apt description. In mathematical thought and reasoning, a blurry JPEG is a lazy answer that will be lacking in precision and often plainly incorrect, no matter how well articulated it is.

For example, it’s obvious that this answer is wrong since 2⁴ = 4², but ChatGPT would have us think otherwise using its blurry JPEG response engine:

Again, consider the consequences of a decline in professional mathematicians and an increasing reliance on this kind of technology to answer math questions. We need a healthy future cadre of mathematicians to stop these kinds of Golems from going rogue.

So, if you are lucky enough to be a young person interested in Mathematics as a career, you have my encouragement and support — you may end up saving the world from the Golems!

What did you think of some of the points I am raising in this article? Feel free to comment!