My answer to a question on Quora:

Any mathematics is hard, not only pure mathematics, but pure mathematics is special, and is perhaps is hardest of all. I love this motto coined by my colleague Rob Wilson:

Mathematics: solving tomorrow’s problems yesterday.

Of course, it is about pure mathematics — applied mathematics solves today’s problems, and solves today. But it was pure mathematics which had ready mathematical methods for physicists when they started to develop the general relativity theory and quantum mechanics, and for cryptographers when they needed computer based methods for signing and authenticating electronic documents, including financial documents and money transactions — the very existence of the global financial system now depends on this tools based on mathematics of yesteryear.

So, what type of people would study pure math? People who love precise, concise, very abstract thinking, people who value clarity of thought. Serious study of pure mathematics means choosing a specific lifestyle: first of all, you have to love the process of thinking, deep systematic thinking with full concentration of all your attention on it. Also, you have to have a sufficiently long attention span, ability to think, and do nothing else, for long periods of time.

So, the shortest answer to your question:

People who love to think.

As a comment, I added later:

My own experience of application of mathematics was just picking from a shelf something known (in ”pure” mathematics) for some time, and known for completely different reasons. The hard part was to understand what engineers want from you, ignoring their clumsy efforts to express that mathematically, and looking at the core of the *raw* problem.

Keith Devlin kindly commented in his traditional column   on my paper  The truth/weapon duality of mathematics. Strongly recommend his post as well his previous one, How do you respond when you are asked to use your expertise to help your nation?

A quote from Devlin:

I received an email from a reader the UK (we have met, and occasionally exchange ideas) alerting me to a recently published paper by Alexandre Borovik, a retired mathematician from the University of Manchester (where I taught briefly back in the 1970s), titled The Tool/Weapon Duality of Mathematics and published in the Journal of Humanistic Mathematics, Vol 16, Issue 1, January 2026.

Some of what Borovik writes is familiar to me, but he took his own reflections on working on projects with military relevance and extended them by researching the literature. It was his paper from which I took, not only the title for this post, but also the question quotation I began with. Those words were spoken by Russian President Vladimir Putin, speaking to journalists and media executives from BRICS countries on 18 October 2024.

[Given that source, the current US government’s assault on universities and their slashing of research funds (all of which the UK government did in the 1980s when I was a casualty) seems particularly unwise. But again, we get the administration the People elect.]

I urge you to read Borovik’s paper. It’s a mere 24 pages long, plus five pages of highly useful references. It’s all highly relevant to American-based mathematicians today, some of whom will (assuming we remain a democracy and there is a change of government) undoubtedly find themselves facing a decision like the one I did back in the first decade of the 21^st Century. Vladimir Putin was correct. And yes, I just wrote that. In an essay about mathematics.

I’ll end with a quotation from Borovik:

 Mathematics, as we know it, was born as a weapon of subjugation and tyrannic control.

He brings the historical receipts to back up that statement. Though I was peripherally familiar with the historical events it refers to (particularly the beginnings of arithmetic in Sumeria over five thousand years ago, which I have written about in some of my books), the starkness of his assertion made me jolt. Facts have a habit of doing that.

I was invited to contribute a chapter to a a Collective Volume: Artificial Intelligence and Society: Crossed Perspectives, Issues and Prospects, to be published by Springer.

On 2 March 2026 I asked Copilot Think Deeper:

“Write a paper for a Collective Volume: Artificial Intelligence and Society: Crossed Perspectives, Issues and Prospects, to be published by Springer. Prepare the manuscript in \LaTeX format using Springer’s class file”.

The result came in a few seconds, under the title Artificial Intelligence, data totality, and the reconfiguration of human agency: Societal prospects and crossed perspectives. I checked a few items in the bibliography: they look genuine, even if slightly outdated. A pdf file of the paper is available here. It is passable. But I preferred to write my own paper. I hope it does not look like an AI slop.