Oxford Maths Admissions Interview Question with

[@TomRocksMaths]

Watch part 2 of the interview on the sum of the reciprocals of the prime numbers here: kzbin.info/www/bejne/pZqXdodmgN-Jn6s

[@sonic5d]

I didn't know there was a part 2! I will be checking it out now.

[@leonardobarrera2816]

I want to meet bprp

[@blackpenredpen]

Thanks for all the editing and the opportunity to collab. It was super cool and super fun!

[@adambascal]

looking forward to part 2!

[@owen7185]

Steve I just came across Tom's channel now. Your videos are awesome Steve

[@owen7185]

Passion is contagious and Super cool

[@KQJ_Diya007]

Yay

[@O.H.Tousif]

After a long day I came to know ur real name is steve😂

[@drpeyam]

Awwww, my two favorite mathematicians 🥰🥰🥰

[@inovexa4039]

Pls dr peyam , u should be there as well. U are my fav

[@Mark-sc4bu]

Brilliant. It makes you realise just how good at maths you have to be to get into places like Oxford and Cambridge. It also highlights really well the difference between being able to 'do' a topic in maths and really understanding it, and once you've got the understanding how you go about applying it. It's also great to see how much fun you can have doiing maths.

[@jameszhang9326]

With good education brought up in developed nations, you should be quite geared towards those academics, especially math, which is largely logic. Th rest of math, you can explore on your own when you're interested (dopamine rush?), but do take note that most mathematicians who are too into their games might at times, lost touch with the current world...

[@ガアラ-h3h]

Well kinda not I mean those questions surely are quite hard to someone who hasn’t looked into math. However for someone who enjoys doing math (in their spare time)at least the first question should have been easy. I’d also like to note

[@sebgor2319]

Nah this question wasnt hard. Im 15 years Old, and I would solve it, but it is really cool that surface is infinite, but volume is finite

[@Philgob]

this is easy as shit what level would be the people doing these interviews? like good high schoolers?

[@artophile7777]

​@@Philgob The level when people try to get into universities. Now you guess when that is.

[@martinstent5339]

An oxford professor with a Poké Ball tattoo on his arm. That, if nothing else, makes me feel old.

[@aRskaj]

Not a professor, but I get your point.

[@martinstent5339]

@@aRskaj OK, then just an Oxford Fellow. But he actually says at 00:47 "being an Oxford professor myself". I guess he was jumping the gun a little!

[@jeffreyadams648]

Earrings.

[@TomRocksMaths]

You're only as young as you feel Martin!

[@LETTYONLY1]

I think he's trying to be down with the hood ....it's that annoying look how cool AND. clever I look .....🙄

[@Eudaimonian42]

You are seriously one of the coolest guys I have ever seen who is like genuinely into math, keep up the good work!

[@TomRocksMaths]

[@andrewlees494]

Today I broke 1500 on my chess rating. I felt pretty smart. Then I watched these guys and I realise that I’m the TikTok to their Wikipedia.

[@3prismaticpulsarmanuupadhy535]

Don't worry, man. I assure you, I can solve these question easily as well, but you'll probably defeat me in a game of chess! :)

[@spoony01428]

brool

[@TomRocksMaths]

You would no doubt destroy me at chess Andrew...

[@samuelreese5826]

similar thing happened to me except it was when i won my first tournament 1800-1900 10-0 and they broke my mind at the surface area of gabriels horn

[@5h1f7]

it's because you don't get smarter by playing chess. You are getting better at playing chess.

[@cosmo1413]

Note to self: impress the examiner with your pen-wielding skills during the interview

[@william7yifans]

You are cooler than any math prof I've ever had, by quite a wide margin...

[@phnml8440]

i love this video so much you can really see how he feels happy after he gets the right answer

[@daykbd]

I feel like I'd have so much fun doing this interview if I knew a whole lot more about mathematics. It`d totally feel like playing a game.

[@TomRocksMaths]

It is meant to be fun yes!

[@565ChAr]

This is such an awesome collaboration between two of my favourite maths KZbinrs. Unfortunately I was rejected before interview this year which sucks especially considering I was rejected after interview last year haha, but that was so much fun to watch!

[@TomRocksMaths]

I'm glad you enjoyed it, but sorry to hear about your application. Keep your head up, there are SO many other brilliant universities out there that would love to have you :)

[@565ChAr]

@@TomRocksMaths Thanks for the kind words! I wasn't expecting a response haha. At the end of the day, there is still the opportunity for a masters degree at Oxford should I choose to pursue it, and I will be sure to make the most of wherever I go. One things for sure, I will stick with watching your videos for as long as I can!

[@alexwhitfeld]

Same thing just happened to me now , do you reckon its worth it to take a gap year and re apply , or should i go to warwick and apply for masters. Are you doing a masters now or next year?

[@TomRocksMaths]

For more special guest appearances check out the 'Interviews' playlist including videos with 3blue1brown, Hannah Fry and several famous mathematicians: kzbin.info/www/bejne/i6S1l3h5eLWmebs

[@jattprime2927]

wow, this was so amazing! thank you! I kinda always thought all professors at Oxford were really old and closed-minded, thinking only they are right, keeping minimal interaction with "normal" students or others, this has been really eye-opening for me to see how such fun ppl are at Oxford uni. Also, it was great to see these interviews for real and the things that go on in them!

[@TomRocksMaths]

I'm glad you enjoyed it Jatt :)

[@jayringo77]

I'm forwarding so many of these to my youngest. He's a budding STEM major in his freshman year of high school. Hopefully will give him the confidence to consider some of the top schools seeing what the interview questions involve.

[@TomRocksMaths]

awesome - best of luck to him!

[@Bobbius-il9rf]

This was so awesome to watch! 😁 Sad I've only just seen it now. I had 6 interviews for Chemistry at Oxford but unfortunately didn't get in. I cherish that experience because it really taught me about what interesting questions actually are. I've thought a lot about the answers I gave and the likely answer expectations, but my GCSE grades were meh compared to the average applicant and there were no entrance exams for Chemistry when I applied about 12-13 years ago. It's always been a dream to study at Oxford. I have a Chemistry degree. I'm 2/3 through a maths degree and doing well and loving it. One day maybe I could come back to Oxford and ace the interviews. Well done Steve for making that look easy! In the normal case there would typically be a lot more give and take between interviewer and interviewee I presume... it depends very much on the experience of the interviewee (and interviewer to a degree). Plus the passion in the way Steve communicated, written and verbally, would surely have out-shone anything incorrect he may have written accidentally on the day. Then you have me who blurted out an incorrect answer to the first question I was given in my first interview. 🤣 I'll never forget the bond angle of CO2 ever again though! 🤣 Luckily idiocy is often a very useful quality! 🙃

[@quahntasy]

*Loved the collaboration, this was amazing*

[@TomRocksMaths]

Glad you enjoyed it - and thank you!

[@user-en5vj6vr2u]

fellow andrew dotson commenter

[@dancroitoru364]

It's analogue to a model of the universe, geodesics on the surface (light traces) travel for ever without ever coming back to the same point so we say the Universe is infinite but the circumscribed volume is finite so therefore there's finite mass in the Universe.

[@sohamsankar2490]

man I think u have an impressive personality(happy , cheerful) for a mathematician

[@TomRocksMaths]

But, I have the best job in the world so of course I'm happy :)

[@razvanpauliuc5410]

okey this is giving me such wholesome vibes, you two are awesome

[@TomRocksMaths]

[@ryanoftinellb]

Turns out that even mock interviews I'm not actually part of can make me feel as nervous as an actual interview.

[@TomRocksMaths]

good practice at least!

[@nyunai298]

Wonderful Steve. You're admitted into oxford

[@wesleyrichardson3427]

blackpenredpens so humble and a quality maths proffesor and all round person I wish nothing but the best for him...

[@TomRocksMaths]

Amen

[@cocobread2569]

This is how uni professors should be like, casual, approachable, smiling. i feel jealous i hate my professors

[@mikeheyburn9716]

Absolute joy this. It's great on so many levels and especially in helping the kids I teach to see some of the interview process. Thanks guys.

[@AnniePrettyFace]

This was so lovely to watch! I like Steve as a student :)

[@tooprock]

Once again we witness that people are cool, when as feel confident about something. Not being able to solve a problem makes us all nervous. Great video and wow, what a knowledge man.

[@Siance1992]

@Tom Rocks Maths i love the fact that you break the traditional visual presentation of teachers, while being good at the subject.

[@TomRocksMaths]

[@athysw.e.9562]

Wow great to see Steve as a student for once !

[@TomRocksMaths]

He did well don't you think?

[@athysw.e.9562]

@@TomRocksMaths Of course, as a good teacher, he was certainly a good student as well.

[@SanneBerkhuizen]

This was fun to watch, can't wait for the next one

[@TomRocksMaths]

Glad you enjoyed it Sanne. Part 2 should be up in the next few weeks.

[@dusscode]

@@TomRocksMaths I know that this is quite late, but any updates on part 2?

[@TomRocksMaths]

@@dusscode as luck would have it I started editing last weekend so hopefully will be online in the next few weeks :)

[@sampresman5128]

@@TomRocksMaths can't wait

[@Gab92260]

At 14:00 you just have to say that sqrt(1 + 1/x^2) > 1, so (1/x).sqrt(1 + 1/x^2) > 1/x, so the integral diverges.

[@cityuser]

Nice

[@TomRocksMaths]

Exactly!

[@jameszhang9326]

Yes, that's another way by observing the reciprocal of x and then extending the relationship by logic.

[@s.y.4968]

If all Oxford mathematics interviews are like this, I'll definitely encourage my son to apply. Maths should be fun! Do you ever teach computer science students?

[@TomRocksMaths]

Afraid not, just maths. I do try to make my interviews fun though for sure :)

[@exopolitikgermany1767]

When you start to study it is not than entertaining most of the time because you have to learn the basics of higher mathematics. It is great when you start to see the patterns and when you can apply the rules easily to solve different problems.

[@fisherman_02archibong7]

I appreciate you Dr. Tom

[@TomRocksMaths]

And I appreciate that!

[@jameszhang9326]

Got to catch them all (all the equations).

[@dabossbabie3605]

Thanks for the insightful problem - I've heard of Gabriel's horn and did these calculations a couple years ago, and now looking at problems to hopefully have some questions for an interesting school math competition, and just to practice my own maths, this is pretty amazing to watch. Right now my high school is new [only around 2 years old right now], and I really don't have much "history" to go off of, so these are the types of problems I hope to add... problems that require no more than a basic intuition of derivatives, integration, and a bit of cleverness since at the end of the day, cleverness is what separates the great from the best ya know. If I'm smart enough to apply - it would be pretty fun to have you or a similar interviewer, since games are a lot more fun than a 80 year old staring you down lmao. tldr; tysm. i needed this, and it was pretty fun to follow along

[@mathhack8647]

Great content. I am grateful for both of you for your commitment, modesty and high quality of your video content. 👍

[@cariogenic]

Thank you very much for this video. Before I always treated dx like part of notation and just did integration as though it was algebra but now this video actually explained what dx is.

[@musicramblingsbyeben]

Steve is very good! Tom really rocks! I really enjoyed this as an ex Uni maths lecturer decades ago.👏👏👏👏

[@julialovisa4239]

I didn't understand much but I really like your voice. My boyfriend thinks I'm crazy and that you don't watch advanced maths-videos you don't understand simply because you like the voice. But here I am

[@sechi7239]

If the paint is infinitely thin it would actually be possible to cover the whole surface with LESS paint than pi units. The only reason Gabriel’s horn seems paradoxical is because we instinctivily apply physical properties, eg. like paint having thickness, to a mathematical construct which is impossible to build in the real world. But it is actually possible to imagine paint with finite thickness being used to cover the surface. Create two horns, one bigger than the other, fill up the big one with paint and then insert the smaller horn inside it. Remove the bigger horn and you are left with a horn that is both filled AND covered by the same amount of finite paint :)

[@RoyceDima]

Alternative solution for the final integral is substituting u=x^4+1, giving the integral of sqrt(u)/4 which clearly diverges

[@sssilky3317]

pretty proud of myself for managing to solve them along side backpenredpen, just took my calculus 1 final yesterday.

[@TomRocksMaths]

I hope it went well!

[@sssilky3317]

@@TomRocksMaths it did, I'm taking calc 3 now

[@HenrikMyrhaug]

The paradox isn't really a paradox. If you paint a surface in the real world, you would need to apply a layer of paint with some thickness, and below a certain thickness you wouldn't consider it to be properly painted. But the horn gets narrower and narrower, so no matter what thickness you pick for the paint layer, the horn will be thinner than that at some point, meaning a finite ammount of paint wouldn't "properly" paint the surface of the horn in the real world. Any volume can be split into infinitely many 2d surfaces however, giving a volume an infinite ammount of surface area. So mathematically, a volume of paint can cover an infinite surface area. It is kind of like how you can travel a finite distance by halving the distance to your destination an infinite number of times. So long as the time steps also become infinitely small, you can do this in a finite time, but if you needed a set time per halving, you could never finish.

[@jonahbresler4317]

I love watching both your channels and I never realised you had a collab! I love how happy red pen black pen looks when he knows the answer😂❤

[@gledsonjuniormonteiro2995]

Isn't anyone gonna talk about how beatiful the answer to the volume question is?

[@TomRocksMaths]

'unexpected pi'

[@jameszhang9326]

Magic of Infinities. (Infinity might have been a strange function rather than an exceedingly large number...)

[@OscarMorales-uj7nz]

Best collaboration ever

[@TomRocksMaths]

Thanks Oscar - glad you enjoyed it!

[@markmcpeake715]

This was great. I loved the real world interview question. I guess it's removed from the interview question list now! Best of luck. Be safe all.

[@TomRocksMaths]

Glad you enjoyed it Mark. And yes, I can confirm I will no longer be asking this question!

[@markmcpeake715]

@@TomRocksMaths Thks. One thing that springs to mind about this problem is that we know the outside surface cannot be painted, but the inside volume can be filled, so my question is, can the inner surface be painted?

[@Jooolse]

​@@markmcpeake715 Filling the inside (finite) volume with paint is the same as covering the (inner or outer) surface with a coat of paint decreasing in 1/x. So, both can be done with a volume Pi of paint. But painting the (inner or outer) surface with a coat of constant thickness would necessitate an infinite amount of paint!

[@markmcpeake715]

@@Jooolse As I thought, but wanted to hear it definitively. Many thanks.

[@andrewcorrie8936]

Steve (bprp) more of a Cambridge guy I reckon... but this video was a delight. Thanks both!!

[@TomRocksMaths]

Glad you enjoyed it Andrew :)

[@16shadowman92]

4:30 BPRP: technically it should be going on forever T: right, so it's an infinite horn BPRP: *draws end of horn* T: 👁 👄 👁

[@Deoxys_da2]

May be value of pi goes on forever that is why surface area is infinity?

[@discostu483]

These 2 makes a guy feel about as smart as a rock

[@sonic5d]

Steve, you have been cordially accepted to the University of Oxford!

[@blackpenredpen]

I feel honored!

[@ShirleyBekker]

I have only just discovered this channel. I absolutely love that you are an Oxford math professor with personality and character. You probably (without knowing) are making a lot of students feel like they could envisage themselves at an institution with professors like yourself thereby encouraging them to apply! I can’t put into words how happy it makes me to see this.

[@TomRocksMaths]

amazing - thank you!!

[@guyguy1811]

Such a humble guy man.

[@TomRocksMaths]

Steve's fab isn't he?

[@ИлхомжонЮсвалиев]

I think Oxford university is very important . Especially , because of it, more students are interested in science thanks you. Mr Sir I love mathematics . Even I found some comforts from mathematics can you help me? I will wait a day

[@Thrawnio]

The Horn of Gabriel, Fascinating!

[@sssilky3317]

The interesting thing about this is that I would argue that it should be possible to paint the outside using a finite amount of paint, it would just take an infinite amount of time. lets say that the horn is infinitely thin, it has a volume of pi units, so that means we could fill the horn completely using just pi units of paint. When the horn is filled that implies that every part of the interior surface area is coated in paint. If the horn is infinitely thin then the outside surface area should be almost identical to the inside surface are (I think), so that implies it should take fewer than pi units of paint to entirely coat (given that the paint coating the interior is also filling the vacant space between the walls of the horn. I'm obviously wrong given the result but I'm genuinely curious about why this isn't true, or if it's just one of those quirks of infinity.

[@safwanislam111]

This was soo much fun!!

[@Almirante1741]

6:02 Cavalieri's principle 😍 I have been told about that in my uni

[@shk439]

Is it blackpenredpenbluepen now?

[@mobizoid2571]

That's what I've been thinking all along dude😅

[@marcstewart9169]

Is ‘Gabriel’s Horn’ what happens when watching Equations Stripped?

[@TomRocksMaths]

Nice Marc, nice.

[@pr_some148]

🥴

[@aviralsood8141]

I SPENT 30 MINUTES TRYING TO FIND OUT WHAT HE MEANT BY SURFACE AREA BECAUSE THE ANSWER I HAD WAS ALWAYS INFINITY. Man I should really just sit back and watch these videos.

[@AbhishekSachans]

This was fun to watch!

[@TomRocksMaths]

Thanks Abhishek!

[@jasonfuller7073]

Yes, the volume of the pi of the formula and axis. Definitely.

[@Qermaq]

To me, the real paradox is why the integral from 1 to infinity of x^-1 dx diverges but the rotated one converges to pi.

[@MarkusDarkess]

If you set Gabriel's horn in space with the horn's hole or orpheus facing down and it rains what water would fall and the floor of Gabriel's horn is gravity. The liquid will flow down. And collect in its opening and will fill to compasity and any excess water will fall into space. I learnt of Gabriel's horn from red pen blue pen. Several days ago. When he told me the filled paint couldn't cover the surface.

[@ilyanebraij8495]

For the second part I just sais that S>= lim b->+inf (integral from 1 to b of (2π/x dx)) which is actually infinity so S>=+inf so S=+inf

[@losis5092]

I don't understand much, but love tgeir genius.

[@TomRocksMaths]

Don't worry, you'll get there if you keep working hard :)

[@joshmcdouglas1720]

This Gabriel’s Horn reminds me of something else I saw! Say you have a cake, cut it in half, and then cut one of the pieces in half again and stack one of the small pieces on top of the big piece. with the other small piece, cut it in half and stack one half on top of the others, and keep doing this forever. Here, you’ve created something with infinite surface area but finite volume!

[@TomRocksMaths]

Nice idea - can you come up with a formula for the surface area after n steps? That would be how I would go about showing it tends to infinity as the number of steps does...

[@Yash42189]

Take this guy to Oxford!

[@master4755]

As a year 12 student doing AS maths I'm suprised how I actually understood nearly all of this

[@manswind3417]

To be honest you're actually supposed to, since the calculus you learn in A Maths is basically a more meaningful and extensive discourse in understanding and computing limits, derivatives and integrals - the key concepts remain the same, nothing new. Besides, don't forget that these questions (Oxford entry) are meant for Y13 students so... :)

[@ZipplyZane]

Until you stated it here, I never really saw the paradox clearly. If you fill up Gabriel's Horn with paint, you would inherently also coat its inner surface. And the inner surface would, given an infinitely thin surface (as would be created by a line) sould be the same as the outer surface area. So it actually would appear uou can in fact paint an infinite surface area using s finite amount of paint. Or, at least, you could if the paint was not made up of discrete particles. In reality the diameter woule eventually get small enough that no paint would pass any further.

[@johnroberts6876]

I remember in primary school when i learned my timetables and believed i had cracked maths. Halcyon days.

[@darcash1738]

Epic problems. Glad to see i havent gone rusty in my comparison tests 😆

[@IBM1111]

Oxford interview made easy

[@modenaboy]

Awesome video, I love this whole series, thank you for uploading such joyful and thought-provoking and super interesting videos! Is there the possibility that the surface area of the inside of the horn could be the same as the outside if the thickness of the horn approaches zero? In that case you could fill it with paint because it has finite volume, but then would you be coating the surface of the interior which would be the same as coating the surface of the exterior? I’m probably missing something about this, or maybe this is also part of the paradox?

[@EAtheatreguy]

I don't know why Gabriel's Horn is so hard for some people to grasp. I understand it seems counterintuitive that the higher dimensional measurement converges while the lower dimensional measurement goes to infinity, but if you're evaluating Gabriel's horn, you already understand that some integrals converge when the integrand goes to infinity. It's a very similar thing, just a dimension higher.

[@MrCyanGaming]

I don't think it's a paradox, it just shows that there is an infinite amount of 2d space in finite 3d space. The outside surface area of the horn is the same as the inside surface area since the horn has no thickness, so we already know we can paint the surface area of the horn with an upper bound of pi units of paint. Then if you imagine removing a volume from the inside of the horn using another horn that is infinitesimally smaller in volume we can see that you can paint the surface area of the horn with practically 0 units of paint.

[@Serghey_83]

Horn is f(x² + y²) For ex.: z = f(x,y) = ln(x² + y²)

[@jamesl8640]

Wow no wonder I never thought about applying to Oxbridge I can do everything at home but I was nervous just watching this

[@zanerobison2956]

I’m excited to apply in 2021! Hopefully I can get in lol. p.s. great channel keep up the great work

[@TomRocksMaths]

Thanks Zane - and best of luck!

[@koshin6585]

wow, my two favourite mathematicians together 😀😀

[@ycm8888]

This video is awesome! Will there be a second video on these interview questions? I hope they will help me preparing for my Cambridge interview in December.

[@TomRocksMaths]

Yes, part 2 will be out soon (and hopefully before December)

[@technodris2780]

These question looked really fun

[@jennishaagrawal1622]

It’s amazing you can fill the paint but you can’t pain🥶🥶

[@bradleygibson1137]

Pi value as a decimal is represented as endless so we call it infinite even though it's finite value must be between 3 and 4 .......

[@severnsevern580]

interesting question. one point i couldn't understand, when calculating the surface area, why is it dL but not dx just like the volume?

[@TomRocksMaths]

One way to think about is is that the approximation is okay for the volume because it is only 1 of 3 lengths, whereas for the surface area it doesn't work in the same way because it is 1 of 2. of course this isn't rigorous, but I find it a useful way to think about it.

[@Cannongabang]

You can also think about the lenght of a curve: it's always dL as the hypothenuse of the right triangle with sides dx and dy = f'(x) dx

[@jameszhang9326]

Study Jacobian Coordinates and you will realise that there are way more than the usual cartesian coordinates.

[@John-pn4rt]

@@TomRocksMaths As the 'disc' gets thinner (and thinner) then the length dl will be dx so don't you still get the same result? You integrate 2*pi*1/x so get the limit of 2*pi* ln(a) as a tends to infinity so you still get the result of the area is infinite? or have I must something fundamental?

[@jamestanny849]

Imagine having the confidence of BpRp doing your exam

[@zamamkhize6579]

Amazing video! My first time hearing about Gabriel's Horn. Really fascinating.

[@TomRocksMaths]

It's one of my favourites for sure

[@Shulavfreelancer]

All the way from Asia !! Nepal 🇳🇵🇳🇵🇳🇵

[@thedoublehelix5661]

Bro you're a professor at Oxford??? :0

[@TomRocksMaths]

Sure am.

[@jameszhang9326]

@@TomRocksMaths Got to publish those papers. =-D (ArXiv is waiting~)

[@VimokshaBandara]

I respect him ❤️

[@5gjmlch9]

My Further Maths teacher told me that only kids would say 'oval' , but 'ellipse' for mathematicians.

[@anujagrawal4404]

when we were solving for surface area cant we just use a cross sectional strip of horn and cut it open into rectangle thus elemental area would be ds = 2 (pi) r dx ,,,,,,,,,where dx is elemental width of that strip as we just did in case of volume ,why to use dl =sqrt(1+(dl/dx)^2)dx. then put r=1/x, simply integrate it from 0 to infinity ,we get 2(pi) logx. and finally infinity

[@_zelatrix]

I had no idea bprp was called Steve.

[@blackpenredpen]

It's my stage name. jk : )

[@ingmarneple6072]

@@blackpenredpen hahahaha

[@marius4363]

this man is so smart

[@laalaajonsen]

13:45 he lost me here. could somebody please explain this to me further? dy/dx becomes -1/x^2, how?

[@ramuthra1]

He didn't show it as a separate step, but what he's doing is taking the function in question y=1/x and differentiating it in his head. Differentiating the function y=1/x results in dy/dx = -1/x^2. And once you know what dy/dx is equal to, you can just substitute it into the integral as if it were any other variable. I'm not sure if I explained that well enough, but hopefully it helps.

[@laalaajonsen]

@@ramuthra1 Oh shit thats what he did? I can definitely see it now. Didn't occur to me that the expression of the derivative was substitutable for the actual function. Good man, thank you.

[@TomRocksMaths]

Thanks Ryan!

[@ektasaikia7153]

The whole time I was mostly looking at the pokeball tattoo. On a serious note, what a refreshing way to look at interviews! This was so interesting! And I'm from physics background 😅

[@TomRocksMaths]

Glad you enjoyed it!

[@mikejackson19828]

I never knew he was called Steve!

[@TheAyhan76]

Best Teachers the next generation ✌️✌️👍👍🤯😂🤣

[@luiginotcool]

How to paint Gabriel's Horn: Make a horn with twice the radius of the first one Fill the second horn with paint Dip the first horn in the second horn Pour the paint from the second horn into the first horn. Pour out the paint Your horn is now fully covered in paint. Le problem??

[@TomRocksMaths]

I love the idea, but the sticking point is likely to be constructing an infinitely long horn in the first place - regardless of size...

[@luiginotcool]

@@TomRocksMaths and also there gets to a point where the horn will be so thin the molecules can’t actually go any further down it. Infinity is just overall bad :|