Grant Sanderson urges math to reward "motivated explanations," not just proofs
In a guest post on Terence Tao's blog, the 3Blue1Brown creator proposes giving expository, intuition-building math work academic credit similar to proofs.
What to know
- Grant Sanderson, known for 3Blue1Brown, proposes that mathematics formally define "motivated explanations" and give them academic credit comparable to proofs.
- The proposal responds to concern that machine-generated proofs without accompanying human understanding devalue proof as a proxy for mathematical insight.
- Sanderson acknowledges his own bias as a non-academic math communicator whose career centers on explanation rather than problem-solving.
- The essay draws on prior work, including Michael Nielsen's concept of "discovery fiction," to argue this kind of explanatory work is already valued informally and deserves formal recognition.
Grant Sanderson Creator of 3Blue1Brown, guest essay authorTerence Tao Mathematician, blog hostMichael Nielsen Coined the term "discovery fiction"
How it unfolded 1 development · click the chart to see its coverage articlesposts
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Essay surfaces on Hacker News, gains traction
The post reached Hacker News's front page, accumulating 53 points and 24 comments, indicating notable interest within the technical and math-adjacent community.
“When proofs can be generated without that understanding, it undermines their value as a proxy.”
— Grant Sanderson, Guest essay author, 3Blue1Brown creator · source -
I remember hating math from late primary school to all through high school. I never learned my times tables properly. They were just absolutely boring AF. What I didn't realize at the time though was that I basically set myself up for failure. When the basic building blocks are hard, everything else on top gets unnecessarily hard.I remember…
2 more of the top 3 · 45 posts in this stretch
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Mathematicians: “Math isn't really about proofs, it's about understanding!” Physicists: 👀 https:// terrytao.wordpress.com/2026/09 /18/if-math-is-more-than-proof-we-need-to-better-celebrate-the-rest-of-it/
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I find myself less worried about it than at first. I think what we'll see are that some things are low-hanging fruit and can be solved just by tireless search. Maybe half the millennium and other such high-visibility problems will fall this way.Others, I think, will be beyond both human and AI. And so what then? Mathematicians just throw in the…
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background
Sanderson publishes essay on Tao's blog proposing "motivated explanations" — Grant Sanderson, in a guest post introduced by Terence Tao, argues the math community should define and academically reward "motivated explanations" that build intuition, alongside proof-generation, partly in response to fears that proof-generating machines are making mathematicians obsolete.
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first by HN Best, 5d ago · also HN Frontpage
What people are saying 21 voices from 2 sites · best of 45 · verbatim
- Sep 20
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I think it says quite a bit that I had already been thinking of Outside In before it was even mentioned in this article. Outside In truly is one of the great works of math communication.I'd argue that its format, a dialog between a novice who is yet still sharp (is able to be the one that makes the connections between ideas) and an expert who…
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Just my experience with a broader version of intuition and not being able to describe the things around me. This is very true. I have a lot of intuition, yet I am often unable to name what I am intuiting, and sometimes I even have difficulty describing it!It is not just with math, either. I independently arrived at both a cognitive fallacy and a…
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I posted nine days ago in another thread:As much as I hate it, I don't think we'll ever get a proof of the four color theorem that isn't enumerating cases.When you have an integral or the sum of an infinite series that comes out to pi, you know there must be some satisfying explanation involving a circle.Contrast with "Examples of patterns that…
- Sep 19
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This is, as always from Grant Sanderson, thought provoking and opens new insights.It occurs to me on reading this that there’s a connection to other computerized mathematical activities.Occasionally some computer lab in the past would announce that they have computed pi to more digits than ever before; or a new Mersenne prime will be found.These…
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I was about to link the "discovery fiction" article [0] by Michael Nielsen, but halfway through saw Grant mention it as an inspiration. It's one of my favorite styles of writing that lets you settle into a cozy read of a narrative around a problem while slowly exposing you to the rigor and nuances of tackling it. It's definitely deserving of a…
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https:// terrytao.wordpress.com/2026/09 /18/if-math-is-more-than-proof-we-need-to-better-celebrate-the-rest-of-it/
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> There’s a wonderful book, How to Prove It by Daniel Vellemanthe name sounds familiar but i don't think i have read that one, i did enjoy "introduction to mathematical reasoning" by eccles.personally my relationship with mathematical proofs has been complicated. it took some work to understand basic proofs (dedekind cuts, ideas vs. instructions…
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I have been losing interest in this proof-oriented approach into extremely abstract concepts (what seems to be the core of academic mathematics today). Obviously, proofs are very attractive because they are the closest thing we have to a universal truth (at least under the assumed axioms). Having mechanisms to reliably show a proof, and…
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Well, so Tao now invites literal industry boosters to lure mathematicians into a pro-AI stance. This is the guest poster:https://www.3blue1brown.com/talentThe only concrete step any mathematician on the internet, including on the other AI concern site https://proofsandprompts.com/ , is demanding funding for an academic frontier AI.Strange that the…
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I'm not sure that this new approach will be AI-resistant. Why would people not use AI to help in creating the "motivated explanations". Maybe they can't be one shotted today, but AI also makes this easier.Assume in 2 years we have a heap of these motivated explanations, all as high quality as Grant's videos and the best books. But who will read…
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If this suggestion were to come to pass, I wonder how new math PhDs would think about choosing between a 'normal' R1 faculty job vs. the "teaching route" (teaching professorships, lectureships, community college professorships, or SLAC professorships).It's been my understanding that traditionally the ones who care about "motivated explanations" in…
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> we might imagine what it could look like to have an analog of the Millennium Prize Problems for open exposition problemsThe core idea seems to me that we should shift the standards for professional evaluation from generating proofs to generating explanations. Makes sense that such a proposal would come from the 3B1B guy, and I actually agree…
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It would be interesting to see what would happen if we had two competing mathematical institutes, a sort of First/Second Foundations:1) Rejection of AI for anything but trivial applications while still using computers at their full capacity. Researchers would ensure full human understanding of proofs and methods.2) Unrestricted, all-embracing use…
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Hmmh. I like motivated explanations, but, as acknowledged in the text, this is a subjective thing to measure. What is a great motivated explanation for Tao, might be hard to grasp for me. So I guess judging how well an explanation motivates something depends on two things: 1) My way of thinking, and 2) what I already know and how well I recall it…
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Part of the controversy here is that now the skill advantage that some Field Medalist had is much narrower. The fact that fields medals have an age limit implies that it favors brain power over understanding. And that was the guiding light award of the community. So i find it "funny" (and natural) when they are offended by AI. That is the main…
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If I have to take the risk of simplifying,1. We humans have managed to take huge amount of information and compress it using a loss function containing some bias we have about the information.2. We now ask ourselves to decompress the same information with some additional cross-entropy. As a side effect of this process we sometimes spurt out…
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The last days we are served these high goals about understanding, "digestion" and so on.But if you look at the practice of present mathematics, in the last 20 years it is all about publishing solutions to problems.There are famous problems to be solved, there is a hierachy of conjectures to be solved. A quick search here on HN gives pearls like…
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Similarly, programming is also a precise language of communication. Initially, we focused on direct machine behavior but every abstraction above the hardware (including assembly) has been to make that behavior legible to humans.Developed notations and shared procedural abstractions have made thinking about computation more intentionally human and…
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The math field is confronting something that coders have been dealing with for a few years now, only far more violently. Today's moat for software seems to be that AI can automate tasks but not a full job (yet). But for a large proportion of mathematicians, doing these tasks really was _the_ job - complete a sufficiently difficult set of them and…
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I’m reminded of that famous debate between Poincaré and Hilbert at the International Congress of Mathematicians in Paris in 1900. It was then that everyone decided to follow Hilbert’s path, and proof came to be valued more than intuition. I think modern math at school and at applied university kind of lost this intuitive part. I try to teach my…
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While I understand and emphatically with Tao's concern I'm afraid it's missing the forest from the trees. Unless you can make a claim that AI will never be able to perform intellectually at the same level as any human at a much lower cost, there's an outstanding utility problem that remains unaddressed. Sure enough, the AI may not have taste or…