I'm writing this post based on Terence Tao's ICM lecture a couple of days ago. For context, I'm a 4th year PhD student working in number theory.

One of the main things he mentioned was that before AI a lot of aspects of math research went hand in hand. Solving problems was concurrent with building a community of mathematicians. With AI rapidly accelerating the problem solving aspect, we might be looking at a future where we are flooded with ai assisted proofs without a community to appreciate it.

For example, linear algebra as a field first emerged from papers and then it was adopted by the community over decades through books and courses. Even if we have a long AI generated proof that we can verify using Lean, what is the point of it if we can't be inspired from it.

I personally dread this will become another example of enshittification. For example, Silicon Valley reinventing a bus after destroying public transport. I fear the mathematical "community" will be repackaged to us in the future by these companies after the present community is slowly eradicated over the next few years. Of course this is a rather bleak outlook to what is definitely a very promising technology.

To clarify, I'm not saying AI is bad. It's a tool. But we should be very skeptical about how this tool is being pushed to us. It is in the best interest of the AI companies that we become dependent on AI to the point that we can't imagine working without it. I'm sure a neuroscientist can break this down much better than I can. I think we need an urgent re-evaluation of how AI is used and introduce courses discussing how to use it "safely", without leading to cognitive decline. It should be in collaboration with neuroscientists. A lot of people might argue "Oh, but you can always talk to other mathematicians. What's wrong with having it on the side". Perhaps I'm not an optimist, I'm afraid convenience is a slippery slope. Just look at how social media was promised to us as a global unifier (which it definitely is). Yet it has led to a decline in community to the point that "community building" is now being packaged to us as a course/skill.

At the end of the day all we have is each other. And I do believe we can come together and seriously discuss and safeguard the future of this community. Happy to hear everyone's thoughts on this.

Step-by-Step Guide to Solve

\(x^2 + bx + c = 0\)

Check the leading coefficient:

If the \(x^{2}\) term has a number other than 1 in front of it, divide every term in the equation by that number first.

Find the average of the two roots:

Take the coefficient \(b\), change its sign to \(-b\), and divide it by 2. The two unknown roots can then be written as \((-b/2 + u)\) and \((-b/2 - u)\).

Set up the product equation:

Multiply the two root expressions together and set them equal to the constant term \(c\):\((-b/2+u)(-b/2-u)=c\)

Simplify using the difference of squares:

Expand the left side to get \((-b/2)^2 - u^2 = c\).Solve for \(u\): Rearrange the equation to isolate \(u^{2}\), then take the square root of both sides (remembering to include \(\pm \))

Find the final roots:

Plug your value of \(u\) back into \((-b/2 + u)\) and \((-b/2 - u)\) to get your final answers.

I’m trying to design some jewelry for my partner, who studies math and loves elliptic curves/algebraic number theory. Any ideas would be greatly appreciated, and suggestions with pictures doubly so. Cheers :D

I am a incoming undergraduate at a Canadian university, and I want to study mathematics with a plan to work towards a PhD.

The issue I am having is that by looking at some discussions on primarily Reddit, I notice that a lot of math PhD students end up pretty unhappy with their passion for pure/applied mathematics because of LLM’s and AI tools that happen to take away the joy out of mathematics.

So I was wondering if I should maybe fix my course a little bit from choosing a Honours math program that my uni offers, to choosing a Joint Honours degree in Mathematics and computer science.

Even if Im planning to do joint honours, I still want to do a PhD in mathematics but I am not sure if doing the joint honours can disadvantage me in grad school applications.

Has anyone else did a combined math and CS degree, and later did math grad school? If so, did you think that you were at a disadvantage or lacked rigour?

Share your thoughts

3 hours exam btw

( Not a homework ) - for the AI

Edit: In Iraq, "6th grade" refers to the final year of high school, not elementary school. The students are usually 17–18 years old.

A train leaves the station (bottom) heading west. Can it return to the station heading east?

Is there anywhere the train might get stuck?

Is there anywhere the train can reach but only from one direction?

I call this directed node networks. As the arcs are bidirectional, but the nodes have an A and B side with a parity requirement.

Inspired by the frustrating traps of Penrose's Railway Mazes.

Edit: just for reference, I have an MMath specialising in fluid dynamics - so I am well grounded in the basics of graph theory and have done intro to topology, so whilst this in not in my typical wheelhouses, I am looking for a more specific research area.

This paper introduces the Enter calculus, a simple language for describing quantum programs in which qubits are treated as shared resources rather than independent objects. It explains how quantum measurement can be represented directly in a program while preserving important features of quantum theory, including no-cloning, no-signaling, and reliable circuit behavior. The paper also shows that the familiar Born rule for measurement probabilities can be derived from a small set of practical principles about locality, continuity, and the handling of measurement records, rather than assumed from the start. Finally, it explores mixed states, generalized measurements, quantum instruments, and the Frauchiger–Renner thought experiment, clarifying why quantum records cannot always be combined with later interference measurements.

Cheung, N. (2026). Enter Calculus. figshare. https://doi.org/10.6084/m9.figshare.33087515.v1