by Herbert Harris

Is mathematics created or discovered? For over two thousand years, that question has puzzled philosophers and mathematicians alike. In Plato’s Meno, Socrates encourages an uneducated boy to “discover” a geometrical truth simply by answering a series of guided questions. To Plato, this demonstrated that mathematical knowledge is innate, that the soul recalls truths it has always known. The intuitionists of the early twentieth century, however, rejected this idea of eternal forms. For thinkers like Poincaré and Brouwer, mathematics was not revelation but construction: an activity of the human mind unfolding in time.
The debate continues today in an unexpected new arena. As artificial intelligences start to generate proofs, conjectures, and even entire branches of formal reasoning, we are prompted to ask again: what does it mean to do mathematics? Current systems excel at symbol manipulation and pattern matching, but are they truly thinking in any meaningful way, or just rearranging signs? The deeper question is how humans do mathematics. What happens in the brain when a mathematician recognizes a pattern, intuitively sees a relation, or invents a new kind of number?
In what follows, I’ll trace that question from ancient philosophy to modern neuroscience and then to the newest foundations of mathematics. We’ll see that mathematical invention may be the natural expression of the brain’s recursive, embodied intelligence, and that this perspective could transform how we think about both mathematics and AI. Read more »

Throughout most of the UK (Northern Ireland is 
In June 1932, half a year before Adolf Hitler was sworn in as German Chancellor, Victor Klemperer watched Nazis on a newsreel marching through the Brandenburg Gate in Berlin. A professor of Romance languages at the Technical University of Dresden, whose area of specialization was the 18th century and the French Enlightenment, Klemperer (1881-1960) was unpleasantly gripped by this first encounter with what he termed “fanaticism in its specifically National Socialist form,” and by the “expression of religious ecstasy” he discerned in the eyes of a young spectator as the drum major passed by, balanced precariously on goose-stepping legs while he robotically beat time.
When my mother was a teenager in the early 1940s, a NY-area radio station ran a weekly contest, asking listeners to vote for their favorite singer among two: Crosby or Sinatra? How people made this preference known remains unclear to me: did you need a phone in your house to make a call to the station or was sending a postcard enough? Whatever the method, the winner would be announced each Sunday afternoon. While Sinatra often took the prize, Crosby occasionally outpaced the Jersey boy who grew up two towns south of Cliffside Park, my mother’s hometown. On those occasions, she told me, she’d stamp around my grandparents’ railroad apartment, enraged at the abject stupidity of her fellow listeners. When she’d tell this story, my mother would marvel at her parents’ forbearance, the way they’d accept these outbursts without comment, though they were highly disciplined, gloomy people for whom the idea of having an “idol,” or caring about his fate on a weekly radio show was surely alien. I like this insight into them, a softer side that I myself had only witnessed a few times.
Anushka Rostomji. Waq Waq Tree, 2023, of the Flesh and Foliage Series.
Jersey City is a medium-size city on the West bank of the Hudson River across from Lower Manhattan. Up through the middle of the 20th century it was a port and a railroad hub but that disappeared when containerized freighter became too deep to travel that far up New York Bay. Without any freighters the railroads were no longer needed. Light industry disappeared as well. Jersey City became back-offices and bedrooms to Manhattan-based business.
We have slid almost imperceptibly and, to be honest, gratefully, into a world that offers to think, plan, and decide on our behalf. Calendars propose our meetings; feeds anticipate our moods; large language models can summarize our desires before we’ve fully articulated them. Agency is the human capacity to initiate, to be the author of one’s actions rather than their stenographer. The age of AI is forcing us to answer a peculiar question: what forms of life still require us to begin something, rather than merely to confirm it? The best answer I’ve been able to come up with is that we preserve agency by carving out zones of what the philosopher 




When promoting her new book in September, Supreme Court Justice Amy Coney Barrett stated in an interview as quoted in Politico : “I think the Constitution is alive and well.” She went on – “I don’t know what a constitutional crisis would look like. I think that our country remains committed to the rule of law. I think we have functioning courts.”
During covid, amid the maelstrom that was American healthcare, a miracle happened. State medical boards suspended their cross-state licensure restrictions.

