We're 99.9% sure this pattern is true, but no one can prove it

when I started phd in mechanical engineering at university of New Hampshire in 2018. Professor Zhang already achieved this feat, got offered Assistant Professorship in UCSB, and left UNH. Older grad students told me Zhang was a soft spoken guy, very nice to students, and often seen pacing up and down the hallway, pondering the problem. Apparently, Zhang's PhD thesis at Purdue refuted his PhD advisor's earlier paper, and made the advisor unhappy and refused to write him any recommendation letters. He indeed had to find work in many places before finally got a chance to settle a bit at UNH.

The hardest Prime to find is Optimus. It likes to disguise itself.

24:45 I like how the most replayed part is the 67 prime

24:49 now we know why you chose the range 20-40

The fact that Yitang Zhang bypassed the collective groupthink of the 2005 AIM conference by simply not being there is the ultimate testament to independent research. While the world's top experts were busy proving why pushing past theta = 1/2 was structurally impossible, Zhang was quietly engineering a way to force error-term cancellations on a smooth subset of step sizes. Incredible breakdown of the GPY weighted averaging machine.

Zhang Yitang not only solved the "impossible problem", he also is a true inspiration to solve the problem at age 57, considering most mathematicians and scientists had their peak achievements before age 35, in his friend's backyard, taking a break from tutoring his friend kid for calculus.

36:11 — practically every time I hear Tao's name come up, it's a story of him being both a mathematical genius and just a really nice guy

32:57 I'd actually argue the opposite: the fact that Yitang Zhang had to spend 7 years outside of academia after his PhD, and even longer as a lecturer (i.e. not paid to do research), is a weakness in the academic system. It is a tougher issue to fix now with more people wanting to get PhDs and academic funding becoming more scarce due to the current political environment, but it should be regarded as an institutional failure (rather than a personal triumph) that Zhang was essentially cast aside after his PhD and had to make a generational breakthrough in order to be taken seriously again.

The Zhang's story is unreal. Not because he made a breakthrough, that happens. But mathematicians that positively verified a paper IN A WEEK? That's crazy. I'm a coauthor of several papers and always waited for a review at least few months (except situations where the journal didn't even send it to reviewers). One of the journals has specifically written on their website "please don't bother us if you send your paper less than 6 months ago". I've heard from my colleague that he waited for a review for 3.5 years.

this video has been through 4 title changes in the span of this 3 days

So.... You're telling me the title was misleading. You mean a university professor who once did the accounts for a Subway.

3:20 Hardy and Littlewood is a crazy combo

Dude, Yitang (Tom) was my pre-calculus and calculus professor at UNH. He couldn't attend our final exam because he had to leave to present his proof. I failed and had to retake both classes cuz I suck at math. He was a very nice and funny guy when i knew him. Amazing I'm seeing this now 😅

One of the smartest people I've ever met basically "lived" in our university library. You could go there on any day, find him, and basically ask him any question on any topic and he could immediately give a breakdown of it. He did not have the use of one arm since birth. It turned out he had a doctorate in Probability Theory and was well on his way to becoming a professor in Germany in the early 90s. However, he said in the end he was not able to publish papers fast enough to become a professor. Thus, he gave up his dream and just decided to spend the next 20 or so years walking around in the library.

2:28 "huh, 2 trillion isn't that large—OH."

The craziest detail in Zhang's proof is how much of it relies on just reorganizing error terms so they mostly cancel each other out. He didn't invent some wild new branch of math or break the universe open. He literally just grouped the errors differently. Everyone at the 2005 meeting was trying to smash through the wall with brute force and Zhang walked around it because he didn't know the wall was even there. That's the most Zhang thing ever.

It is also worth noting that Zhang was 58 years old when he announced his discovery, showing that he successfully made a mathematical breakthrough in his 50s. There is a lot of skepticism around old people being capable but this guy proves everyone wrong in more than one way.

Oh so it wasn't "A guy actively working at subway solved the impossible math problem." it was "A mathematician who used to work at subway solved the impossible math problem"

I love how Derek only appears in beginning of videos now to hook us in until the new guys take it from there.

Happy he appeared more often in this video though

Head to brilliant.org/veritasium to try Brilliant's tutor for free + 20% off an annual Premium subscription