2026-10-24T13:30:08Z https://nostr.now C.B. Aberlé https://nostr.now/npub1s28a6qpzcu243guvp3snypltaxxcgfwrcdfv8ngjuanlgdgx4hdqv5f7ya https://media.mathstodon.xyz/accounts/avatars/111/098/917/412/284/257/original/b755ebcbb13ffa92.jpg https://media.mathstodon.xyz/accounts/avatars/111/098/917/412/284/257/original/b755ebcbb13ffa92.jpg https://nostr.now/nevent1qqs23tt997tavfl8cvw0edt5jxxwch25555pvmu25teyzjnwlunuv4qzyzpglhgqytr32k9r3sxxzvs8a05cmpp9c0p49s7dztnk0ap4q6ka500ltnf one nice thing about working on more niche problems with less public attention around them is that there&#39;s fewer vultures circling them. 2026-09-09T00:46:56Z https://nostr.now/nevent1qqsq6f3kl6r06372hwmhx0npmpvmhnmsz2833pqp7rmj5j2pjx8ux0qzyzpglhgqytr32k9r3sxxzvs8a05cmpp9c0p49s7dztnk0ap4q6ka5c7lfjw In reply to <a href='/nevent1qqsrq834d790evsz22ac0zz4nlm2rus7pmk56q9n7sk9k0spq0uf3qgx8phdc'>nevent1q…phdc</a><br/>_________________________<br/><br/>Having spent several years in the trenches of formalized mathematics by now, I&#39;m actually more sympathetic <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> &#39;s line of thinking than I used to be, but I think there&#39;s nothing about formalized mathematics *per se* that forces this to be the case.<br/><br/>The way I&#39;ve come to use proof assistants/etc. over the years actually, counterintuitively, ends up making math more &#34;empirical,&#34; in a way. My informal proofs and ideas become &#34;hypotheses&#34; I can &#34;test&#34; by attempting to find a formalism and suitable abstractions that make them checkable by a computer. And like any good scientific experiment, this quickly becomes an iterative process—take some informal ideas, attempt to formalize them, get some data back about what ends up being difficult, refine the ideas, repeat until a satisfactory equilibrium is found. And this process itself can lead to a lot of &#34;a ha&#34; moments and &#34;radical&#34; new ideas, itself.<br/><br/>As already noted, however, this process carries the risk of railroading one&#39;s thoughts into those ways of thinking that are more easily formalized in a particular system. But imo this is a failure of that particular system to be sufficiently syntactically/semantically flexible, and not of formalism/interactive theorem proving in general.<br/><br/>The future I hope for, and which I am actively building toward, is one in which we have general systems for defining, simulating, and verifiably translating between different logical/formal systems, so that if someone has a new mathematical idea they want to try out it&#39;s easy to get up and running with a system for testing it and relating it to other frameworks.<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub18a63tjqchu08dmrzfs644v3wysydjq4kdqjx2xh66qdx02zk4a9qtkszuj" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Andrej Bauer</span> (<span class="italic">npub18a6…szuj</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1vlchukd4yknuculh52a5xzq98k4fcndnp4ptnl9jx7gr6j5nqsls06mzqq" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>DougMerritt (log😅 = 💧log😄)</span> (<span class="italic">npub1vlc…mzqq</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub14a5755aglz3euvetuy8z7x25akaz42lgvrgkr8qj2a55ghpwaelqjf9fse" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Martin Escardo</span> (<span class="italic">npub14a5…9fse</span>)</a></span> [@JacquesC2](<a href="https://types.pl/@JacquesC2">https://types.pl/@JacquesC2</a> ) [@pigworker](<a href="https://types.pl/@pigworker">https://types.pl/@pigworker</a> ) <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1vzxa0v32meu5krw7989cfnladxlel8x5wuqzaquzqmrgedueajuq7fncd7" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Kevin Buzzard</span> (<span class="italic">npub1vzx…ncd7</span>)</a></span> 2026-03-31T17:27:24Z https://nostr.now/nevent1qqs0eks7hh3k0pvre8nxkgsq2jyhwr3ay0l6p233pztu8qexew5azxczyzpglhgqytr32k9r3sxxzvs8a05cmpp9c0p49s7dztnk0ap4q6ka5j4v4v2 In reply to <a href='/nevent1qqsz86gpdrvuvg2vme379zwzjjd7ywtuh4jkhklwn00uqwhhketj95ca3smxc'>nevent1q…smxc</a><br/>_________________________<br/><br/>Fixed! Thanks, John! 2026-03-23T00:55:44Z https://nostr.now/nevent1qqswkq452tqrv7s9e7k3y5ukesuwgqkh0aq4nzsamwnwq032g0ync6gzyzpglhgqytr32k9r3sxxzvs8a05cmpp9c0p49s7dztnk0ap4q6ka5r4u52e New blog post up on my website: How Algebraic is Algebraic Geometry? <a href="https://cbaberle.com/Blog/How+Algebraic+is+Algebraic+Geometry%3F">https://cbaberle.com/Blog/How+Algebraic+is+Algebraic+Geometry%3F</a><br/><br/>This post was the result of me trying to wrap my head around some of the central concepts of modern algebraic geometry and its generalizations from the perspective of someone more at home in type theory, category theory, programming languages, etc. In particular, I&#39;ve been watching much of the recent work on &#34;synthetic algebraic geometry&#34; with some interest, and also have had a passing interest in the programme of trying to develop geometry over &#34;the field with one element,&#34; due to my longstanding interest in the Riemann Hypothesis and the various research programmes it has spawned. If any of that sounds interesting to you, then I hope that this blog post can be as illuminating for you to read as it was for me to write :)<br/><br/>Tagging a few people who I think might find this interesting and/or whose writings on these and related topics have been stimulating to my thinking on this subject: <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1jxf7pzy53pjcqsvzyglscnjamewcru5zcg9chp8jec30p4977s9qmp0dxv" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>npub1jxf7pzy53pjcqsvzyglscnjamewcru5zcg9chp8jec30p4977s9qmp0dxv</span> (<span class="italic">npub1jxf…0dxv</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1englp98pffr30xnchxeexqlf2t8jf96n45atdph2nl4tt3fzc9xqupzqfn" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Tim Hosgood</span> (<span class="italic">npub1eng…zqfn</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub17yd3krguvj7u7z7s5kh47arlzlwk9wcwz205gg7qg582rzazzyds4v03sq" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>David Wärn</span> (<span class="italic">npub17yd…03sq</span>)</a></span> <br/><br/>Comments, feedback, and criticism are much welcomed! In particular, please do let me know if I got anything wrong! Like I said, I&#39;m very much an outsider to these subjects trying to understand them better for myself. 2026-03-23T00:34:05Z https://nostr.now/nevent1qqs22hf8rst2055q5m3t56kugwlcduz9q95acytjffjhnw3df2lv8nczyzpglhgqytr32k9r3sxxzvs8a05cmpp9c0p49s7dztnk0ap4q6ka5l0z4xu In reply to <a href='/nevent1qqsw7v5czs08xj9jppxrlh8l2qt3h3vfn46r62txjqc76k55kqyhthc8md3c8'>nevent1q…d3c8</a><br/>_________________________<br/><br/>yes, absolutely! :) 2026-02-10T22:05:19Z https://nostr.now/nevent1qqsg2d36drvv8x0zmj8m02tjmy3td4l4r693gm6ghhjv83t9yx7c25gzyzpglhgqytr32k9r3sxxzvs8a05cmpp9c0p49s7dztnk0ap4q6ka55d64j3 In reply to <a href='/nevent1qqsvsxd90wng2w2hlz0su9a2ffasn90gs0yp5pv4ce8t4hxrwpyflxc7t0d39'>nevent1q…0d39</a><br/>_________________________<br/><br/>thank you so much, John! 2026-02-10T00:58:30Z https://nostr.now/nevent1qqs9r0yag5jmhqtwxefsfryvnpz9zs3apae5wvrxpnysq9t0gnlre2gzyzpglhgqytr32k9r3sxxzvs8a05cmpp9c0p49s7dztnk0ap4q6ka5w7vcqv First up on the list of recent additions to my website: something that&#39;s a bit different from my usual work on type theory, etc., but that&#39;s also very near and dear to my heart—The Music of the Primes ( <a href="https://cbaberle.com/Blog/The+Music+of+the+Primes">https://cbaberle.com/Blog/The+Music+of+the+Primes</a> ) a blog post exploring the fascinating connections between musical tuning, the Riemann Zeta function, and linear algebra over the integers!<br/><br/>Some others on this server (e.g. <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> ) have touched on these topics before, but they&#39;ve been a pet obsession of mine for the last several years, owing to my joint musical and mathematical background, and this blog post is a fairly comprehensive write up of my findings! Check it out if you&#39;re interested! 2026-02-09T16:52:50Z https://nostr.now/nevent1qqsryt4k5633ekfea3m2ylu5tk0zp6qawh2w6gkku9kqvhyalzkphwgzyzpglhgqytr32k9r3sxxzvs8a05cmpp9c0p49s7dztnk0ap4q6ka5dke8ky In reply to <a href='/nevent1qqst2w6gdmc76a73zluqn9xp9vskqkdmjlul70tsgysc2pwltvcghyq44q4tr'>nevent1q…q4tr</a><br/>_________________________<br/><br/>&#34;We train young men to drop fire on people, but their commanders won&#39;t allow them to write &#39;fuck&#39; on their airplanes because it&#39;s obscene!&#34;—Walter Kurtz (Marlon Brando), Apocalypse Now<br/><br/>also, as others have already said, thank you so much for talking about this 🏳️‍⚧️❤️ 2025-03-08T01:14:28Z https://nostr.now/nevent1qqs2q4px3es66h7axwk8s008hcka3es2wcawzal4ezgjepw230ru3cszyzpglhgqytr32k9r3sxxzvs8a05cmpp9c0p49s7dztnk0ap4q6ka5mwd976 In reply to <a href='/nevent1qqsyxfmqv7h76fu49h0z005jhs7uhupg8q7wtxyprg0ensaffl4fp6g2reul9'>nevent1q…eul9</a><br/>_________________________<br/><br/> <img src="https://media.mathstodon.xyz/media_attachments/files/113/862/547/372/284/063/original/0631ed21d04d7d43.jpeg"> <br/> 2025-01-20T20:23:51Z