2022's Biggest Breakthroughs in Math

Mathematicians made major progress in 2022, solving a centuries-old geometry question called the interpolation problem, proving the best way to minimize the surface area of clusters of three, four and five bubbles, and proving a sweeping statement about how structure emerges in random sets and graphs. Read more about these and other mathematical advances at Quanta Magazine: www.quantamaga...
You can read also about the biggest breakthroughs of 2022 in physics, biology, and computer science on our magazine website: www.quantamaga...
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Correction: An earlier version of this video incorrectly suggested that Vogt and Larson solved the Brill-Noether theorem and has been deleted. Instead, the couple solved the interpolation problem. This video more accurately reflects what they proved. We regret the error.

[@QuantaScienceChannel]

A note to viewers: We're taking a break from producing our "Biggest Breakthroughs in Physics" and "Biggest Breakthroughs in Biology" videos this year, but you can read our curated lists for these topics, plus a summary of computer science breakthroughs, at our magazine website: www.quantamagazine.org/tag/2022-in-review/ We’ll be back with more videos in 2023, including a full set of "Biggest Breakthroughs" videos. Correction: An earlier version of this video incorrectly suggested that Vogt and Larson solved the Brill-Noether theorem and has been deleted. Instead, the couple solved the interpolation problem. This video more accurately reflects what they proved. We regret the error.

[@primenumberbuster404]

Now it makes sense. It's awesome that you really deleted the earlier video. Some people don't do it. Massive respect for that.

[@aramesh428]

That's ok, sometimes Christmas presents get delayed until after the holidays 🙂

[@realdreray]

Ahh I see. Fantastic math video here. I applied for your Video Producer position I'd love to help bring those other videos to life!

[@sherlockmaverick]

Amazing! BTW, this is a reupload, right? I remember watching this more than a day ago!

[@jameschen2308]

I was about to say. I swear I saw this video uploaded yesterday

[@accipitridae2128]

I appreciate the efforts in trying to make these heavily technical subjects reachable to the general public. Kudos to y'all :⁠-⁠)

[@simonlinser8286]

i enjoy watching these subjects but if they didn't explain it this way i wouldn't know why it was important that these strides are being made.

[@soheil5710]

@@simonlinser8286 I honestly still don't know

[@jakublizon6375]

I'm happy for that math nerd couple. What a story it will be to their kids. "We met trying to solve the interpolation problem of advanced mathematics". Ahh, so sweet.

[@stefevr]

they actually named their kid Interpolation Problem

[@Somebodyherefornow]

@@stefevr " I hate you"

[@stefevr]

@@Somebodyherefornow "thanks"

[@slashtab]

The way she said "well! we got married.."

[@flyingspinners1]

@@stefevr atleast the child will get the big brain math genes

[@FirstnameLastname-fn6ik]

Thank god somebody likes math so I don't have to think about it and we can still advance as a society.

[@vaisakhkm783]

ikr

[@HilbertXVI]

If you don't like it you haven't been taught math right, unfortunately

[@ethanzheng1368]

@@HilbertXVI 🤓

[@hello-hb1ll]

@@ethanzheng1368 he's right. "Nerd" is just a compliment

[@Max-jm6md]

@@HilbertXVI what evidence suggests everyone is keen on learning math if "taught properly?" we're all unique and complicated individuals with different interests.

[@accipitridae2128]

I feel like a caveman compared to these smart guys. Keep up the good work!

[@akshatgupta8898]

right me tooo

[@resiliencewithin]

Thanks for sharing your feelings on the comment section.

[@CSTEnjoyer]

That is because we are. Mathematicians are a species of their own

[@Wabbelpaddel]

@@CSTEnjoyer Sure about that? The significant things that truly distinguish them are their imagination and building on abstraction moreso than mere language offers, via fully blown logic.

[@CSTEnjoyer]

@@Wabbelpaddel there's a reason why almost all mathmaticians are kinda "weird" people. What they lack in social skills, they have in IQ.

[@160p2GHz]

Was just telling my friend I don't even pay attention to who won the Nobel anymore, I just watch the Quanta biggest breakthroughs in X each year... feels more cutting edge, inclusive, and not just a friend of a friend... genuinely the new things that should excite me. And y'all do a great job making it understandable.

[@randomknowledgeperson2872]

are you guys gonna do a “2022 a year in physics” and “a year in biology” like you did for 2021? i really liked both videos and would love to see how we’ve improved this past year

[@artieschmidt3039]

They explained in the pinned comment that they will not do it

[@quantumbyte-studios]

Networks, bubbles, and curves.. never realized how technical and deep these can be.. kind of like chess, simple to grasp the basics but takes a lifetime to master

[@perseusgeorgiadis7821]

The most complex problems, often have very simple rules. Try proving that each even number bigger than 2 can be written as the sum of two primes…

[@neville132bbk]

I'm sure there are 13 *n possible opening plays in Bridge..... whenever I am on lead... the possibilities seem limitless :-) where n must be > 13.......

[@zitagus9207]

It's realy amazing seeing young mathematicians doing big discoveries 👏👏👏

[@DrRiq]

as well as big mathematicians doing young discoveries! 👏👏👏

[@Nat-oj2uc]

Not really would be more surprising if they were old

[@DrRiq]

@@Nat-oj2uc i was being dumb for the sake of the funny

[@kebman]

I probably got this video because I was interested in another video on splines by Freya Holmér. She has the most in-depth videos on the topic, and they are beautifully animated too!

[@vascomarques637]

we stan freya holmér

[@xylh5085]

Thanks for the recommendation. I've played with splines before and they are very strange and interesting at first blush

[@jayd2279]

@@vascomarques637 All the way!

[@themannyzaur]

Ayyyyy Freya appreciator in the wild! Les goooooooooooooooo My foundation in math is very weak but I managed to catch a few things in her video

[@chotai]

I just jumped here from that video

[@MAFiA303]

wheh the guy spoke, i didnt expect this to be his voice. amazing accomplishment regardless

[@Bhargav_Sarma]

Quanta Magazine should start a special category for Chemistry too!!!

[@EMC273]

I agree

[@zinzhao8231]

Hell no

[@DariusTheClairvoyant]

Fuck chemistry

[@astroid-ws4py]

Only if it is Computational Chemistry !

[@Fonsecaj89]

I’m ok thinking that chemistry is plain magic

[@Patashu]

I love hearing about the progress being made in math!

[@LolIGuess123]

The best part of these videos is hearing the struggles and challenges and how they were overcome. Please continue these types of inquiry!

[@IanGrams]

Dang, talk about relationship goals. It would be pretty cool to publish a paper with your partner, let alone one so substantial. Also cheers Quanta for reuploading to correct the error in the original. It was a small one but the commitment to accuracy is much appreciated.

[@thelocalsage]

i am nowhere near proficient enough in mathematics to understand these problems in depth, but i remember watching a couple lectures by jinyoung park earlier this year and being mystified by the subject matter and enjoying her lecture style! would love to understand all these questions more intimately

[@AlignedIT]

Beautifully presented and made these complex topics interesting and accessible.

[@Nat-oj2uc]

Math is the most fundamental and important science. The advancements in other fields often depend on how advanced we are in math. Respect to those people. Hypothesis is easy. Actually shutting up and proving it that's what is hard

[@RaffyEdris]

I have no idea on what I just watched, but it sounds like a really hard topic and to grasp. Kudos to all of the mathematician out there doing their best to solve a problem that could in turn help humanity. Your sacrifice will not be forgotten.

[@Ubsje]

3:21 at first it's just sus, but then it turns into something even more SUS

[@yotams6168]

LOL STOOOOOOOOOOP

[@swaree]

came to the comments to say just that

[@clawed_xo]

"They were able to get something simple enough that they can attack with their bare hands." Surely🗿

[@berliansuryani1401]

Certified sussy^2 baka moment

[@freydawg56]

I love these videos at the end of the year. I always look forward to all the different topics of science.

[@addisk22]

I love that these people have a chance to pursue their passions and solve these difficult problems.

[@hitarthk]

Thanks to the Simon Foundation for highlighting and maybe even fueling such fundamental discoveries!

[@elijahpharoah9807]

You have no idea how long I look forward to these videos

[@drewweber7874]

3:22 had me nervous for a second…

[@Jenny-tu9fc]

Fascinating stuff!!!! I admire and respect the individuals who tackle such beautiful problems. I wish I could be on that level.

[@veks374]

I love the video but Eric's voice caught me fully off-guard lmao

[@joshua1188]

Thank you for bringing attention to the people who are the least appreciated but most impactful.

[@ChrishBlake]

Please keep this series, and the series on breakthroughs in physics and biology, going forever.

[@sinesierra]

Amazed by the enthusiasm and determination of researchers. Great video, well presented

[@marcelcoetzee48]

Can anyone explain why solving the interpolation problem can improve data storage? Where can I read more on this?

[@hedgechasing]

I think the rough idea is that if you can capture all the points on a single curve, storing just the data you need to create the curve could allow you to recreate all the points. Like if I want to remember the numbers 5 6 7 8 9 I can just remember that there are 5 of them and they increase stepwise from 5 which is simpler than storing all five of them (especially as the number of points increases). I am not sure this is correct and I am not sure where you can find out more, but this seems like the intuitive reason it might be useful for that process.

[@marcelcoetzee48]

@@hedgechasing incredible. Thank you

[@leonmozambique533]

they can also be used for error correction. Look up “Reed Solomon codes”

[@maxmuller445]

@@leonmozambique533 Yes, compression and correction always walk hand in hand.

[@kindlin]

@Black Screen That's an approximation tho, this is dealing with exacts. I think hedge has a good handle on what's happening here.

[@jinpingxi6813]

The young couple Vogt and Larson : two nerds likely otakus who spent their leisure time studying together topology. Then they found more interesting curves and performed applied topology...

[@martinauld670]

I’m jealous of these people’s minds. So innovative

[@bijanajamlou5152]

Amazing video! Please do more of these.

[@badouceesay4468]

That first guy's voice caught me off guard 😭😭😭😭

[@GCKteamKrispy]

1:34 - They are real-life Sheldon and Amy "The big bang theory" 😂

[@yolanankaine6063]

Truly mind blown by the brilliance and determination of these people.

[@jaymayhoi]

love these videos every year - people are so damn smart!

[@lycantropos]

I see what you've done here at 3:23 😉

[@MatBat__]

Incredible! Thank you for this great video and thanks to the researchers for pushing humanity foward. Cheers

[@studypurposeonly69]

This video has way less views for its quality of content even though it's just a day old. Keep up your amazing work!

[@pressfinchat]

3:22 Woah Woah… WHAT exactly are you drawing?? 🤨

[@kaibuchan]

YES. SO AWESOME. Thank you mathematicians for everything. Humanity owes you everything.

[@scozember]

I have no clue what they' re talking about but I still watch to the end.

[@mikenator6682]

3:22 GET OUT OF MY HEAD GET OUT OF MY HEAD GET OUT OF MY HEAD GET OUT OF MY HEAD GET OUT OF MY HEAD GET OUT OF MY HEAD

[@TymexComputing]

Really, naturally interesting - thank you!

[@jedn1660]

This is the sort of maths stuff that had we known it back then would have made it more appealing to learn about and get good at in school

[@rujotheone]

Me: "They look like a couple, are we sure they are not dating? " 1:35 : "We got married" Me: "Oh😅"

[@ThumbsTup]

I hate myself for never being able to advance the world of maths

[@likhithjsw]

This is such detailed video making such complex topics understandable to the public! You guys are doing fantastic job! Thank you and kudos to all of you guys!

[@Zeggskoll]

I loved this video so much! Also, thank you Mr. And Mrs. Vogt! I absolutely want to learn more about their breakthrough! Heckin brilliant!

[@angel-ig]

Guys, read the description please lol. Edit: nevermind, now it's pinned also

[@WinterAliceLilac]

3:23 bottom left lol

[@justapassie]

the bubble thingy...it looks like shapes of hybridization lol

[@tcaDNAp]

I thought the same thing... that example seems to drive home the applications of the theorem!

[@thearchangel9835]

At 3:22 who is that bad student who can point out the dirty curve?! 😆🤣

[@ydcjydcj1724]

I was waiting for this!!

[@ConnoisseurOfExistence]

Nice! The graph solution of the last guys might combine nicely with the Wolfram physics model...

[@jrspringston]

I'll be honest, I clicked on this because my first thought was "there are breakthroughs in math??" And now I know. Pretty neat

[@Dr.Gamboa]

On a weekly basis, my friend.

[@johnleecooper8520]

clusters of Sullivan's shadow bubbles is definitely a dnd spell

[@STA-3]

Well, something I found out is that if you make a list of n to the power of 2 like this: (I'm not sure if someone has found this math easter-egg) 0² = 0 -> You subtract the results and get those numbers: 1, 3, 5, 7, 9... and if you subtract *again* you get a constant number: 2 1² = 1 2² = 4 3² = 9 4² = 16 5² = 25 ... Now what's interesting is that this also works in exponents bigger than 2. Like: 0³ = 0 -> You subtract like before and you get: 7, 19, 37, 61... and if you subtract *again* you get 12, 18, 24, 30, 36... if you subtract it again, you 1³ = 1 come up with 6 2³ = 8 3³ = 27 4³ = 64 5³ = 125 ... So far i did experimenting with the numbers and came up with a table like this: Exponent: 2 3 4 5 Constant: 2 6 24 120 Times subtracted: 2 3 4 5 So what we find that the exponent *matches* the amount of subtractions. But when i was looking at the constant, i immediately thought about the factorials, wich means that the constant *matches* the factorial of the exponent. Huh, thats very cool.

[@sarahtsakopulos76]

Broooo🤯

[@barakeel]

you rediscovered calculus (derivation in the discrete case)

[@STA-3]

@@barakeel Oh damn. Haha!

[@und3rcut535]

Wow the buble problem can lead to major improvments in Pharmacy and drug design

[@sypen1]

His voice was not what I expected.

[@accipitridae2128]

4:54 Having a surname like Neiman and dressing up like Magnus seems to be the new trend.

[@ImchautzuCHAUTZU]

6:42 the guy on the right looks like Hugh Jackman We got Wolverine solving math problems When we gonna get Darwin solving quantum problems....

[@abhinavchauhan4621]

In the morning I love to watch these kind of videos to boost my sleepy head, though I am only able to comprehend half of the content

[@takyc7883]

People don’t understand how huge a discovery this is

[@calebheet3758]

1. Ability to predict holes, degrees, and dimensions. 2. Ability to get largest volume in bubbles with least surface area 3. Ability to find thresholds in networks. khan-kalai conjectures

[@lasagnahog7695]

Hah, as soon as Vogt said "topological" I accepted this was beyond my lay understanding.

[@mygirl737g2]

this is so neat! Love Math!

[@maratmkhitaryan9723]

3:22 I see penus and amongus

[@10-AMPM-01]

3:20 - That's really cool. I was working on something similar as an analogue for chemical potential or quantum effects in a crystal (interior conditions vs boundary with electron, uv, x-ray, infra red subsurface scattering...) I was using groups of curves within a grid of connecting nodes/points. I assumed spline rules and tangency to fill each cell. I started coming across repeating patters that might equate to electron valences or the formation of atoms. Your friend looks like he can understand something valuable. I hope it was worth it. You got your 'break" around the time I posted. I recognize my own work... Free will isn't free if you control their perception. A blinded horse, for example...

[@kangaroo1q]

Which job you do?

[@matttzzz2]

@@kangaroo1q hand

[@johnvonachen1672]

I’m interested in how much these people depend on smaller simpler pieces of math/algorithms applied iteratively using computers. This is something hinted at in wolfram’s famous/infamous book.

[@ABHAY-hu9kw]

All of the mathematicians may not know other ones in this video but, There is a person in this video who now knows solutions of all three problems , The narrator: Thomas Hagena

[@spodeian]

Can the interpolation problem be used to solve the travelling salesman problem I wonder?

[@viewer9999]

can you do 2022's Biggest Breakthroughs neurology/ medicine. please and thank you

[@kangaroo1q]

Wow you read about neurology interesting

[@viewer9999]

it's not what you think .

[@bergrugu]

I did not expect his voice to sound like that

[@thesnazzmaster]

I can't wait until I get farther in college and can actually understand this

[@hrperformance]

It was really hard to get through the bubble bit because the images were just so gorgeous!!

[@igoromelchenko3482]

I will never look at my bath foam as I did before. My bubble innocence is gone.

[@weakw1ll]

These are the videos i really i appreciate come up in my algorithm

[@MrNihalusa]

thank for providing amazing knowledge and introducing the real heroes of human progress

[@anishkumaranjan]

Which tools have been used to create these animations??

[@matthewao]

Most likely AfterEffects

[@mathscraw3741]

Not to dismiss the fact that all the names mentioned are relatively young is quite impressive.

[@hypatiaishere]

These 2 young ppl are realy inspiring Love them

[@firdavszamirov]

It was very interesting. Thank you!

[@jurijaerts1086]

hahahaahhah the dude from the interpolation problem. his voice hahahahahah

[@danielhuhtala2773]

3:23 they knew what they were doing 😏

[@the_eternal_student]

Sullivan's bubble conjecture reminds me of Ptolemy's theorem.

[@adhamcomstock4409]

Woah went that dude with the headphones smiles I had to stop the video and make sure they wasn't fake prank teeth. Ahhh dude got me 🤣

[@fknGandalf]

Little did they know... the answer lies in the windows 2000 pipes screensaver

[@rikardhaugstad8575]

amazing work !!

[@snipersquanza1453]

3:22 ha pp *2 seconds later* _among us music intensifies_

[@Kaiwizz]

Levi was actually on to something when he said "Give up on your dreams and DIE!!!"

[@bungalowjuice7225]

I feel smart watching math videos that I don't understand.

[@benjiasner3919]

wait this is awesome. so at first i thought their theory was the same as knot theory but its actually got rules of knot theory but is more complex. so fascinating how structures build off of one another.

[@maxwellsequation4887]

These are some epic ones!

[@williamchamberlain2263]

This is amazing, in the best ways possible

[@siulapwa]

Fantastic work

[@behrad9712]

Exceptional chanel, great insights with wonderful animation and music... Happy Christmas! 🙏👌❤️

[@griseld]

I can swear i saw this video yesterday but it's published one hour ago, wtf?

[@zhinkunakur4751]

Reup

[@IanGrams]

There is a pinned comment explaining the original version had an error in it so they re-uploaded to correct that.

[@griseld]

@@IanGrams thanks!!

[@IanGrams]

@@griseld you're very welcome :]