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Numbers and Narratives

Did Professor Denis-Charles Cisinski, University of Regensburg, always aspire to be a mathematician? “Actually, I preferred literature to mathematics. I read everything - from poetry and novels to science fiction and philosophy.” The passionate reader was eager to learn anything. Becoming a mathematician, teaching as a professor firstly was not on the agenda. Within the tapestry of existence, certain occurrences unfold spontaneously. Right? Some things just happen.

Letters

To the delight of the editor, Cisinski suggests they meet in a café for the interview. A throwback to the non-digitized era, the favored haunt of writers. Recollecting his high school days, Cisinski reminisces about an exceptional teacher who blended mathematics and literature. “We delved into rather advanced concepts and explored the works of Leibniz, Cauchy, and other intellectuals of the 19th century,” he shares. The respective math teacher loved to code authors, either as an illustration or a description. “My first encounter with mathematical functions was intertwined with poetry - Arthur Rimbaud’s Voyelles.” There was also Paul Valéry, until today one of Cisinski’s favorite poets.

Hailing from Paris, Cisinski appreciates bustling megacities not less than the scenic landscapes of the French Midi or Greek islands. Initially contemplating philosophy, he understood mathematics “as a tool to organize my thoughts, providing a foundation for philosophy.” Is mathematics the tool to understand the world? For the professor, mathematics transcends mere utility: “It is a component of general knowledge. I like to understand what we do at university as general knowledge. I do not like to separate disciplines. There is no reason to do that.”

Symbols

As a professor in pure mathematics, Cisinski navigates the labyrinths of mathematical concepts and structures, his research touches upon algebraic geometry. Cisinski’s warning regarding what his research is about, is more than legitimate. Even if another mathematician asked him, it would be difficult to answer, he says. His research involves crafting a specialized geometric language using symbols, notations, and terms. In such a language of geometry, symbols act as the equivalent of words, playing distinct roles in articulating the properties and relationships of geometric shapes – akin to words in natural languages – such as verbs, adjectives, or nouns playing different roles in a sentence.

Cisinski's focus extends to topology, addressing the properties of geometric objects under continuous deformations, such as twisting or stretching. This intellectual journey seeks to refine the language of geometry, creating a nuanced vocabulary to describe and differentiate shapes and topological transformations. The objective is to express intricate concepts and relationships more concisely.

Counting

Mathematics plays a crucial role in gaining new insights, discover new phenomena, experiencing advances. “The way we hint certainty in mathematics is much more radical than most of other human activities you might think of. It is built on activity; on things we can check.” Cisinski states. What can be checked is computation. It is based on certain tools that allow repeating the same computation many times. The general idea is to reduce the newly developed symbolic language until you receive a reduced computation.

Such computations have not necessarily to be about numbers: “Computation just means you manipulate symbols with specific rules and then you only use these rules.” This way, it becomes a mechanical process, and you obtain a result. “If you do the same computation thousands or millions of times and you get essentially all the time the same results – with very few exceptions, as you got tired for instance, – then it starts to be sensible. Or at least plausible.” Cisinski laughs: “This is the kind of radicality we have. We look for ways to express ourselves in a way that will be eventually reduced to just a computation.”

Far from it if you think that's the end of the story. Subsequently, “you need to elaborate a discourse – and this is human activity - which explains why a certain mechanical process actually expresses something you want to understand.” Cisinski considers UR’s Faculty of Mathematics to be a hub for such intellectual challenges. He also finds joy in teaching and the open participation of students across all levels in seminars, making the academic environment both stimulating and inclusive.

Artificial Intelligence

Are pure mathematicians ready for artificial intelligence? “The principles on which AI is built is bad,” Cisinski says a tiny bit annoyed. “Let me be provocative: If I ask AI mathematical problems it will provide an answer, but never a proper answer.” Why? “It should be able to tell – what you ask me, I cannot answer. Therefore, we should have a basic constraint on all AI we have today.”

He argues that the principles underpinning AI are flawed, emphasizing the importance of context-awareness, reminding of the inherent biases embedded in the questions posed. For the moment, “AI gives you the average answer, without a second check of the content.” To give a simple example: If the average human being asking the question is a racist, the AI answer will be racist.

The second reason why Cisinski doesn’t like AI is the lack of transparency when it comes to the models. The respective companies would not make their code - the actual program on which their AI is based -, public. “There is no way to access the information,” Cisinski says, questioning the ethics of embracing technology without understanding its underlying principles.

Coda

As the room fills up, the steaming of the coffee machine increasingly mingles with the murmuring at the neighboring tables. The conversation touches on the Middle East, German history, requests for humanity, and issues of identity. “Identity must not be fixed once and for all. I don’t like that we fix anything.” Cisinski smiles, becoming swiftly thoughtful again. “Identity means different kinds of stories. We must tell stories to ourselves, to others. I think we exist along realities, maybe several realities. We can exist in many different ways at the same time. Being a mathematician is a story. Being in Germany or other parts of Europe is also a story.” Both would affect him as a human being, Cisinski says. “Each story affects us as a human being.”

Among those stories is living in a global polycrisis. It affects the researcher not less than others. At the end of the 20th century, Cisinski shared with many others much hope. “Just think of the fall of the Berlin Wall, it was amazing!” The decades after, particularly in recent years, the optimism faded. Do you have dark vision of humankind in general? “Well, it is not that it is dark, but somehow maybe the only thing I see is that we are just a physical process. What is possible will happen.” Being in control, being (finally) on the good side of history, we should still be able to believe that, no?! “Sure, we could do amazing things,” Cisinski says with a huge smile. “And there is this illusion, that, whatever we built, will last.”

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