Neuroscientist | Assitant Research Professor @FlorianMerkle lab | @Cambridge_Uni and @ClareCollege | Neurodegeneration | Still in awe of Biology
South East, England
Joined March 2018
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Edward Harding retweeted
Fermat: “I have discovered a truly marvelous proof of this, which this margin is too narrow to contain”
Anthropic: “13 million lines of code”
Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help.
Last month, Claude completed the first formalized proof of Fermat’s Last Theorem, one of the most famous theorems of all time. This was a project experts thought would take many years. It is the largest Lean proof ever written.
Fermat’s Last Theorem was first proven in 1995 by Sir Andrew Wiles, more than 350 years after it was conjectured. Our proof, which totals over 13 million lines of code, provides machine verification. More importantly, it proves over 29,000 other theorems that the proof requires, across many areas of math which had never before been formalized.
We see this as a major step in the long process of firming up the core of mathematical knowledge, building on work from three centuries of mathematicians and hundreds of contributors to Lean and Mathlib. We are optimistic that AI-assisted verification of mathematical proofs will help reduce the burden of refereeing mathematics in an era where more proofs are being produced than ever before.
You can read about the process on our Science Blog: anthropic.com/research/forma…
And see the complete proof on GitHub: github.com/anthropics/fermat…
Edward Harding retweeted
Beyond “non-significant” results: Why and how to test for practical equivalence | PNAS pnas.org/doi/10.1073/pnas.26…
Edward Harding retweeted
IMO, we could cross the valley of death more often if more teams were funded to use their better bridging skills to build between validated points.
But most funders don't put enough time into comparing tech specs of proposals, even if they'd do that when buying a car or phone.
Edward Harding retweeted
Lovely example of incrementally beneficial steps in cancer medicine. Dementia barely at the start of this process.
Edward Harding retweeted
This is an incredible time. After 1000+ years, math is becoming a semi-empirical science where you understand things to be correct because they have been computer verified, and not because you personally understand them from first principles.
I am guilty of this myself. I am about to submit an AI-derived mathematical proof to arXiv that I don't completely understand but which addresses a problem in theoretical biology with a neat solution. I understand the problem, the approach and the result, but I don't understand all the details of the proof. It's been an exciting experience that has occupied the better part of the last month for me. I am transparent about my limitations in understanding the proof and welcome human review that proves it right or wrong (you learn something important about AI in either case).
In general, I consider it an entirely good thing for people who are not specialized to use AI for solving problems in their field using tools from other fields that they don't fully understand. But I agree that it is placing a serious burden on human verifiers. Unless, of course, the AIs become so good at verifying that we don't need humans.
Edward Harding retweeted
Risk of transmission of amyloid β pathology via transfused blood produ... sciencedirect.com/science/ar…
Edward Harding retweeted
Risk of transmission of amyloid β pathology via transfused blood produ... sciencedirect.com/science/ar…
Edward Harding retweeted
Video of myosin proteins "walking" along actin. Insane that we can image this!
It was made by Toshio Ando's group using atomic force microscopy. All of their papers are a goldmine; they've also recorded a Cas9 protein cutting DNA and ATP synthase spinning.
Edward Harding retweeted
Do you remember your university interview? 🤔
Prime Minister @andyburnham @10DowningStreet does!
We were delighted to see this reunion with Professor John Mullan, who taught the PM during his time studying English at @FitzwilliamColl Cambridge.
Turns out you can never escape your old teachers 🤣
This was a lovely surprise for me, on a very big morning for thousands of young people.
Good luck to everyone getting their A-level, T-level and BTec results today. Whatever it says in those envelopes, you should be proud of the hard work that got you here. And remember, there isn't just one route to success.
Edward Harding retweeted
Today 18yo daughter got offered a place at Oxford University (4 A*) We aren't posh, we live in by postcode a deprived area, she goes to a normal state school, she's had no extra tutoring, just her own hard work and determination. Since Year 7 she's wanted to go to Oxford!
Edward Harding retweeted
Cannibalism is common among insects, but so-called killer flies take it to another level.
Small and extremely fast, these predatory insects view any airborne moving object as a potential target—including when that object is another killer fly. This behavior makes mating dangerous: Males risk becoming lunch if they try to make contact with a female or even fly near her.
New research finds one way males avoid this fate: by approaching females in a winding, unpredictable flight pattern and then repeatedly dodging as she launches her attack. Learn more: scim.ag/3TvBOKk @NewsfromScience
Edward Harding retweeted
Up & downs in research science thats what I tell my students. My h-index hit 100 yesterday and I thought great that’s a milestone. Then I was stung by a wasp and my ankles itching like hell and I was so enthusiastic to chomp a burger I bit off the tip of my tongue. Rollercoaster.
Edward Harding retweeted
Today, we’re announcing a £400 million investment in UK life sciences, including plans to establish a new flagship R&D centre in Cambridge. The new site on the city’s Biomedical Campus, one of the world’s leading life sciences ecosystems, will be a catalyst to fuel collaboration and accelerate GSK R&D.
Edward Harding retweeted
This is the result of many bad legacy decisions taken by UKRI hastily and without proper consultation, overseen by a government department that no longer exists. Surely the new @andyburnham government will want to take time to review this.
Edward Harding retweeted
MIT filmed the single hour that makes all of calculus one subject instead of two. Free, uncut, chalk only. Almost nobody watches it.
This is 18.01, Single Variable Calculus, lecture 19, taught by David Jerison. The First Fundamental Theorem of Calculus.
Slopes and areas were separate problems for centuries. Different tools, different people, different questions. This lecture shows they were the same thing pointed in opposite directions.
Every gradient computed in every training run rides on that connection. Most engineers use it daily and have never seen the proof that makes it legal.
Watch the board work in the middle. He builds the link line by line, real students in the room, no software, no animation.
A machine learning engineer I know rewatched it before an interview and said the chain from loss to update finally read as 1 object instead of 3 tricks.
Full course free on YouTube under Creative Commons.
You've been using the theorem. You've never seen it earned.
Edward Harding retweeted
Today, the FDA approved a subcutaneous starter dose of Leqembi, marking the first anti-amyloid treatment that can be given by injection (at a doctor’s office or at home) throughout the full course of treatment.
Until now, Leqembi could only be administered through IV infusions every two weeks at a hospital or infusion center.
Today’s FDA action gives people and families more options.
Read our full statement:
alz.org/news/2026/alzheimers…
Edward Harding retweeted
MIT put its full multivariable calculus course online in 2007 and charged nobody a dollar for it.
Lecture 34 is the final review. A professor in an orange sweater writes Unit 1 on a chalkboard and starts working through the whole semester.
The camera never moves much. No editing, no music, no production budget visible anywhere.
MIT OpenCourseWare launched in 2001 with 50 courses. The plan was to publish materials from every course the university taught.
Faculty were told they would get no royalties and no extra pay. Most agreed anyway.
The catalog passed 2,400 courses. Downloads run past 300,000,000 and the site draws millions of visitors a year from countries with no equivalent institution.
Universities charging 60,000 dollars a year watched a peer give the lectures away and kept charging.
The thing people pay for was never the lecture.
Edward Harding retweeted
脳でオートファジー(細胞内の掃除機構)をオン/オフできるマウスを作成しました。一度神経細胞内が「汚く」なり機能が悪くなっても、オートファジー(掃除)を再開すれば細胞の状態と運動・認知機能が回復しました。神経には、病的変化後も回復能力があるかもしれません。
science.org/doi/10.1126/scie…