Batalha, Luís & Batalha, João
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The Batalha brothers argue that scientific papers would benefit from an explicit "backstory" section, since the polished, isolated form of a published paper obscures the messier human process behind it — citing Richard Feynman's loss of enthusiasm for physics before a chance observation of a wobbling, spinning cafeteria plate reignited the thinking that led to his Nobel-winning QED work, Ian Goodfellow's account of conceiving GANs during a bar conversation, and Dijkstra inventing his shortest-path algorithm entirely in his head (with no pen or paper) during a 20-minute café sit. They extend this into a broader reflection on scientific personalities — Newton's deep, often-omitted engagement with alchemy and biblical numerology (which they suggest is worth understanding as part of the whole person rather than an embarrassing footnote), and Freeman Dyson's remarkable humility (declining to annotate a paper by claiming insufficient expertise despite a career of major contributions) — framing sustained "childlike curiosity" late into a distinguished career as a common trait among the scientists they most admire.
They describe Fermat's Library's origin as an informal journal club among friends from different academic backgrounds (physics, computer science) that evolved into a public annotation platform — named for Fermat's famously margin-constrained note about his Last Theorem — along with related tools: Margins (freely available annotation software used by universities for their own journal clubs), Librarian (a browser extension overlaying comment functionality directly onto arXiv), and their popular Twitter account, which shares bite-sized mathematical and scientific curiosities designed to give readers a "dopamine hit" of sudden understanding.
They offer a sustained critique of the current scientific publishing system: journals impose restrictive page/format limits that work against clarity; the peer review process typically depends on just a handful of unpaid, often under-incentivized reviewers; and the impact factor — originally intended (per Eugene Garfield's citation-mapping work, which they note directly inspired Larry Page and Sergey Brin's PageRank algorithm) as a descriptive measure of a paper's influence — has instead become a heavily gamed "accounting unit," pressuring high-profile journals like Nature toward attention-grabbing, media-friendly claims and pressuring lower-tier institutions into high-volume, low-quality publishing to boost university rankings. They describe this as a genuinely bizarre economic loop: governments fund the research, pay the reviewers' salaries indirectly, and then pay again (via library and university subscriptions) to access the resulting papers, which are largely paywalled by journals contributing comparatively little value. They cite a historical precedent — the NIH-backed 1960s "Information Exchange Group" preprint-sharing initiative, reportedly shut down under pressure from journal publishers (including opposition from Francis Crick) — as evidence this dynamic is neither new nor accidental, and note that even decades later only around 2% of biology papers first appear as preprints. They see hope in overlay journals built atop arXiv/bioRxiv (citing Discrete Analysis and Quantum, the latter partnered with Fermat's Library) and efforts by senior, already-tenured researchers like Tim Gowers to lend credibility to open publishing models, alongside funder mandates (from the EU and the Gates Foundation) requiring open access as a precondition of funding.
Discussing potential fixes to peer review itself, they and Lex discuss whether Amazon- or Stack Overflow-style crowdsourced review — many contributors, each reviewing to the level of their own expertise — could produce metrics more resistant to gaming than the current small, often anonymous review panel, while acknowledging (via a kind of "Heisenberg uncertainty principle" of metrics) that any new metric will eventually be gamed once adopted at scale, so metrics should be judged on resilience rather than permanence. They cite Tim Gowers's "Polymath Project" as evidence that large-scale, genuinely collaborative online mathematics is achievable for certain decomposable problems, and Terence Tao's public math blog (where an outside commenter's Sudoku-solving insight helped crack the Erdős discrepancy problem) as a case study in open, informal collaboration accelerating real research; they also discuss Tao's own writing about nearly failing out of his PhD program despite early prodigious talent, as a valuable, humanizing model of openness about struggle in science.
They discuss the case of Grigori Perelman at length as an emblem of disinterested devotion to pure mathematics: he published his Poincaré conjecture proof directly on arXiv (partly as protest against the paywalled publishing industry), later declined the Fields Medal after two Harvard-affiliated researchers republished a "sanded-down" version of his work while its recognition was still being publicly debated, and separately declined the $1 million Clay Millennium Prize, reportedly because its terms required conventional journal publication and because he had no interest in money from a "businessman" (Clay) uninvolved in mathematics itself. Lex and the brothers connect this to a broader observation (also drawing on Soviet-era mathematics and physics, and comparing it to state-run Olympic sports versus commercialized American professional sports) that removing money and credit-competition from an intellectual or athletic pursuit can, paradoxically, let genuine excellence surface more clearly — while noting Cédric Villani (Fields Medalist turned politician) as a counter-example of choosing to leverage scientific prestige toward direct societal influence instead.
On reading and studying papers, the brothers describe treating papers as inherently unoptimized for clarity (rather than assuming difficulty reflects one's own inadequacy), citing a technique attributed to Feynman and Fermi of reading a paper's conclusion first and trying to independently reconstruct the path to it; Lex adds his own practice of a breadth-first approach through related-work sections and citation trees, valuing related-work sections as comparatively low-agenda, "Wikipedia-style" summaries useful for triangulating a field's actual state and tensions. Both agree understanding often arrives as a sudden "quantum jump" after long stretches of near-zero comprehension while jumping between references. On note-taking, they describe the value of writing (or otherwise capturing, e.g. via audio) explanations aimed at one's own future, post-forgetting self — framing a person who just learned something as uniquely positioned to teach their later, forgetful self, since they alone know exactly where the conceptual difficulties were.
They discuss several favorite annotated papers: a mathematician's investigation (using tools like an improvised "iron sight" alignment method) into how 6th-century-BC engineers dug the Tunnel of Eupalinos on Samos from both ends to meet in the middle without modern surveying tools; Fermi's famous one-page, declassified "My Observations at Trinity" report, in which he estimated the atomic bomb's yield by tossing torn paper scraps and measuring their blast displacement (a technique João later replicated using a viral video of a bride's dress being displaced by the Beirut explosion, arriving at a similar energy estimate); the Bitcoin white paper (their platform's first annotated paper, explained with added background on public-key cryptography, hash functions, and Merkle trees to make it accessible to undergraduates); and Freeman Dyson's one-page paper introducing the "Dyson sphere" concept and proposing infrared radiation as a detectable signature of advanced civilizations.
The conversation closes on lighter territory: a differential-equations analysis João wrote (partly for fun during a work lunch) modeling the required kill ratio for the living army to defeat the reanimating army of the dead in Game of Thrones' Battle of Winterfell; the appeal of tightly bounded, universally understandable problems (Fermat's Last Theorem, the Riemann Hypothesis) as "intellectually democratic" entry points into serious mathematics; reflections on Cristiano Ronaldo versus Messi as an analogy for hard work versus innate genius (with Lex favoring Messi/Maradona for moments of aesthetic genius over Ronaldo's discipline-driven consistency); ideas for computer-vision analysis of sports (goal detection, ball/player tracking) and podcasts (silence-length as a proxy for thoughtfulness, as in a notably long pause by Steve Jobs before answering a question); and closing advice to follow one's curiosity iteratively and without concern for status, since — as Poincaré reportedly said of the ideal parental lesson — cultivating genuine enthusiasm for the world's mysteries, without traumatizing the process, is the real foundation of both intellectual growth and a meaningful life.
Excerpts
On the perverse economics of academic publishing:
“You have the government that is funding the research, is paying the salaries of the scientists, it's paying the salaries of the reviewers, and it's buying back all that — the product of their work — again. This is for me bizarre.”
On why the impact factor distorts scientific incentives:
“The impact factor is almost like a nobility title, because papers are born with impact even before anyone reads them... researchers don't have the incentive to care about if this paper is going to ever have a long-term impact on the world. Their end goal is [for] the paper to get published.”
On why Perelman rejected the Fields Medal:
“Just the fact that they doubted that Perelman had done that was enough for him to say, 'I'm not interested in this prize'... he's this kind of ideal of a Platonic ideal of what a mathematician should be — someone that deeply cares about mathematics, cares about fair attribution, and disregards money.”