Same thing as with em dashes. Some of us have been using em dashes from before ChatGPT.
My English professor criticized me for allegedly excessive use of em dashes in 1973.
Once I started self-publishing in the 1990s, I disregarded her opinion.
Readit NewsCurtMonash commented on Product of Additive Inverses susam.net/product-of-addi... · Posted by u/blenderob
ab and (-a)(-b) can each be quickly proved to be the additive inverse of (-a)b. So they equal each other. No intermediate theorems are really needed.
But what does somebody do with a PhD at age 17? I can’t imagine hiring them as a prof when they’re so young. It’s not a bad idea to just take a couple years to continue your already productive collaboration while getting mentored on the non-math parts of being a mathematician.
I was one of several math grad students who started at Harvard at age 16 or 17 aroud the same time. Ofer Gabber and Ran Donagi went on to conventional academic math careers. I took a less straightforward career path.
But I was offered an assistant professorship at the Kellogg School of Business at age 21, and have often wondered whether I should perhaps have taken that, or else the research position I was offered at RAND.
> there are numerous examples of productive older mathematicians
Curious about the extreme cases. Did any centenarians ever managed to come with an outstanding original math result? If it didn't happen before, I hope to see it happening in the next decades, given current demographic trends.
I was told that a book published in honor of Oscar Zariski's 80th birthday included a paper by Oscar Zariski, either proving or at least making progress on a longstanding conjecture by Oscar Zariski.
I was in the relevant department at the time (Harvard math), but I wasn't much of an algebraic geometer, so I took that at face value without probing for details.
CurtMonash commented on Anthropic's AI-generated blog dies an early death techcrunch.com/2025/06/09... · Posted by u/Sourabhsss1
Arguably, the opposite is true. Ars Technica and others have written about this extensively [0].
Having summarized results appear immediately with links to the sources is preferable to opening multiple tabs and sifting through low-quality content and clickbait.
Many real-world problems aren't as simple as "type some keywords" and get relevant results. AI excels as a "rubber duck", i.e., a tool to explore possible solutions, troubleshoot issues, discover new approaches, etc.
Yes, LLMs are useful for junior developers. But for experienced developers, they're more valuable.
It's a tool, just like search engines.
Airplanes are also a tool. Would you limit your travel to destinations within walking distance? Or avoid checking the weather because forecasts use Bayesian probability (and some mix of machine learning)? Or avoid power tools because they deny the freedom of doing things the hard way?
One can imagine that when early humans began wearing clothing to keep warm, there were naysayers who preferred to stay cold.
The most creative people I know are using AI to further their creativity. Example: storytelling, world building, voice models, game development, artwork, assistants that mimic their personality, helping loved ones enjoy a better quality of life as they age, smart home automations to help their grandmother, text-to-speech for the visually impaired or those who have trouble reading, custom voice commands, and so on.
Should I tell my mom to turn off Siri and avoid highlighting text and tapping "Speak" because it uses AI under the hood? I think not.
They embrace it, just like creative people have always done.
[0] https://arstechnica.com/gadgets/2024/05/google-is-reimaginin...
Socrates had a skeptical view of written language, preferring oral communication and philosophical inquiry. This perspective is primarily presented through the writings of his student, Plato, particularly in the dialogue Phaedrus.
I confirmed that from my own memory via a Google AI summary, quoted verbatim above. Of course, I would never have learned it in the first place had somebody not written it down.
I stopped reading early, when the article said that in the 1970s one big relational database did everything.
In fact, relational databases did nothing in the 1970s. They didn't even exist yet in commercial form.
My first prediction as an analyst from 1982 onwards was that "index-based" DBMS would take over from linked-list DBMS and flat files. (That was meant to cover both inverted-list and relational systems; I expected inverted-list DBMS to outperform relational ones for longer than they did.)
My favorite:
"Very well. Let's have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit."
"Love and tensor algebra? Have you taken leave of your senses?" Trurl began, but stopped, for his electronic bard was already declaiming:
Come, let us hasten to a higher plane,
Where dyads tread the fairy fields of Venn,
Their indices bedecked from one to n,
Commingled in an endless Markov chain!
Come, every frustrum longs to be a cone,
And every vector dreams of matrices.
Hark to the gentle gradient of the breeze:
It whispers of a more ergodic zone.
In Riemann, Hilbert or in Banach space
Let superscripts and subscripts go their ways.
Our asymptotes no longer out of phase,
We shall encounter, counting, face to face.
I'll grant thee random access to my heart,
Thou'lt tell me all the constants of thy love;
And so we two shall all love's lemmas prove,
And in our bound partition never part.
For what did Cauchy know, or Christoffel,
Or Fourier, or any Boole or Euler,
Wielding their compasses, their pens and rulers,
Of thy supernal sinusoidal spell?
Cancel me not - for what then shall remain?
Abscissas some mantissas, modules, modes,
A root or two, a torus and a node
The inverse of my verse, a null domain.
Ellipse of bliss, converge, O lips divine!
The product of our scalars is defined!
Cyberiad draws nigh, and the skew mind
Cuts capers like a happy haversine.
I see the eigenvalue in thine eye,
I hear the tender tensor in thy sigh.
Bernoulli would have been content to die,
Had he but known such a^2 cos 2 phi!
-- Cyberiad. Stanislaw LemI'd completely forgotten that one!!
I just recall the (non-mathematical) poem about the haircut.
Certainly that section generally comes more to mind these days in the age of LLMs ..
Robert Heinlein's "... And he built a crooked house" is both hilarious and mathematical, although perhaps in different parts of the same story.
Like many classic science fiction "novels", including Foundation, Poul Anderson's Operation Chaos is really a collection of linked novellas.
The last one has the hero and heroine recruiting the spirit of Lobachevsky to help them recover their daughter from non-Euclidean hell.
That's what makes it such a good giveaway. I'm happy to be told that I'm wrong, and that you do actually use the proper double long dash in your writing, but I'm guessing that you actually use the human slang for an emdash, which is visually different and easily sets your writing apart as not AI writing!
I never use hyphens where em dashes would be correct.
I do have issues determining when a two-word phrase should or shouldn't be hyphenated. It surely doesn't help that I grew up in a bilingual English/German household, so that my first instinct is often to reject either option, and fully concatenate the two words instead.
(Whether that last comma is appropriate opens a whole other set of punctuation issues ... and yes, I do tend to deliberately misuse ellipses for effect.)