A follow-up to Shmuel Weinberger’s post
First, the not so serious part: emotions
Someone was shouting in her vernacular accent: “Because all the relationships are emotional!” just now, at 11pm.
It was so loud that I heard it as clearly as possible from the fifth floor.
It broke my concentration and made my mind switch to something different: maybe instead of saying I am a mathematician which actually made me feel nervous because i am no longer in a math department, I should say I am someone that have a deep relationship with it. How do i prove it? Because I have had and plan to continue having so many strong emotions with it!
Here is a list:
Euphoria: When I proved something successfully, blimey, I am the happiest person in the world.
Empowered: I am so grateful that I can understand a lot of physics, biology, chemistry, computer science or music because I know maths.
Humbled: Why are large number so large? Why are we still knowing so little about everything?
Dread: I was not good at maths during high school, and maths exams at that time gave me tremendous nerves. I think it was to the level of panic attacks.
Sublimity: To me the Euler equation is like a Flemish painting I could hang on my wall; the aesthetic experience of an elegant is as haughty as listening to Bach’s music, but a little bit scary when thinking about higher dimensional space and topology (see, for example, this video).
Anticipation: When I was going to learn a new topic, I would feel super excited.
Repose: I remember, for example, going over lecture notes for revision, and seeing all the definitions and theorems and lemmas connecting with each other makes me feel extremely organized and calm.
Camaraderie: The quarrels between you and your teammate can get so intense and heated that outsiders wouldn’t understand, but when the problem’s solved, we are the best teammates together.
Isolation: I felt sour when all my friends went out on Friday night.
Desolation: Does the never-ending tunnel resonates with you?
Tenacity: Is it about faith in myself, faith in the conjecture, or just because there is no exit?
Grounding: As I am doing CS, formal verification of things and some provable bounds give me something i can grip on and feel grounded by.
Bewilderment: Just dazed and confused.
Second, are they really not so serious?or, what are emotions good for?
I travelled to an AI conference recently focused on integrating reasoning and learning; one of the main goals of this community (check inductive logic programming, for instance) is automated discovery, defining new entities and finding relationships between them, from atoms to genes. This is not a new dream either. As brought up by keynote speaker Prof. Stephen Muggleton, Turing1 once pondered a question about whether a machine can generate new ideas like a nuclear chain reaction.
Discovery to me is the most exciting, and grandiose objective of AI, as it has truly propelled the development of our civilization.
As for mathematical creation, it feels like these mysterious emotions, like the sense of “rightness”, or surprise, curiosity are like the little fairies guiding us to the destinations.
And this is the part current AI has not be able to do yet.
Maybe partially it’s because AI doesn’t have emotions yet but we do?
Maybe our human emotions will still make us better mathematicians, sometimes, and for a while?
Maybe we should try to always keep it this way?
And be wary that when we work with AI, our feelings seem to be less deep, and less varied.
Received 24 September 2026.
- The passage (responding to Lady Lovelace’s objection that a machine can only do what it’s told) reads: a person can “inject” an idea into a mind or machine, and it will respond to some extent and then die away like a piano string struck by a hammer. Turing then extends the simile to an atomic pile below critical size: an injected idea corresponds to a neutron entering the pile from outside, causing a disturbance that eventually dies away unless the pile is large enough, in which case the disturbance keeps growing until the whole pile goes up.
He then applies this directly to minds: most human minds seem to be “sub-critical,” meaning an idea presented to them gives rise, on average, to less than one idea in reply, while a smaller proportion are “supercritical,” where an idea can set off a whole cascade of secondary and tertiary ideas. He notes animal minds seem clearly sub-critical, and then poses the question your talk seems to have been built around: can a machine be made to be super-critical? ↩︎
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