A Mathematician's Apology

No video

A Mathematician's Apology

Рет қаралды 293,560

Күн бұрын

Some thoughts on the value and beauty of mathematics.
A Mathematician's Apology by G H Hardy (Free PDF) archive.org/de...
Physical copy: amzn.to/39eC1bs
Irrationality of root 2 proof: archive.org/de...
Subscribe to my channel to see more videos like this: / tibees
Support me with a monthly donation on Patreon and receive a gift from me and access to my podcast: / tibees
Buy me a coffee (one-off donation): ko-fi.com/tibees
Website: tobyhendy.com/
TikTok: / tibees
Twitter: / tobyhendy
The pen I use amzn.to/338otuw
Music: Reconcile - Peter Sandberg

Пікірлер: 1 000

@Hailfire08 4 жыл бұрын

"I have never done anything useful. No discovery of mine has made, or is likely to make, directly or indirectly, the least difference to the amenity of the world" Very relatable.

@Aengrod 4 жыл бұрын

At least he understands that the mathematics that he engaged in, was useless. He should have gone to engineering instead.

@mgame8082 4 жыл бұрын

@@Aengrod Hahahahahaha

@BGBTech 4 жыл бұрын

Ironically, this makes me feel a little better about my "useless" personal projects, which while not necessarily making any money, might at least potentially be useful, eventually. I am also in the minority of people who have their own custom processor architecture and similar. With an FPGA implementation, associated C compiler, a sort of terrible OS of sorts, ... While it is unlikely to ever really "compete" against x86 or ARM for "market share" or similar, this is not why it exists... ( Some of us might want to do things that seem interesting, even if one could do the same basic thing with an off-the-shelf microcontroller, or not bother making anything at all. )

@vk2ig 4 жыл бұрын

@@BGBTech I have done likewise with radio equipment - designed and built my own. I get comments like "Why bother? You can't build something as good as what you can buy nowadays." I agree - but I learn an awful lot in through the design-and-build process. And then there is the satisfaction of using the equipment to make contact with someone on the other side of the planet - no internet required!

@BGBTech 4 жыл бұрын

@@vk2ig This project is mostly writing code, kind of a lot of code (in total, currently around 2 million lines of code, mostly C, with some amount of Verilog). The CPU runs on an FPGA (essentially, programmable logic gates). In theory, could have an ASIC version made (conventional microchips), but this part (getting a chip fab to make them) requires a mountain of money... Have built some physical stuff as well (such as a few CNC machines). Once tried to make my own electric motor (via machining it), but this was unsuccessful (despite having plenty of turns of copper, its magnetic fields were very weak, so it didn't have enough torque to be able to turn on its own; possibly due to the rotor and stator being milled out of solid chunks of carbon steel rather than silicon steel, or the fairly large rotor/stator gap, or ...). Have a few times wondered about (but not tested) how the magnetic permeability of iron oxide+epoxy compares with steel...

@TheQuantumCore 4 жыл бұрын

There's something about reading books with faded yellow paper. It gives the feeling that you are reading an ancient scripture or scroll and trying to decipher it meaning. The feeling is priceless.

@Saturnia2014 4 жыл бұрын

The smell of the old paper is great, too.

@stephenpowstinger733 4 жыл бұрын

Yes. I have a small book on philosophy sort of like that.

@4thesakeofitname 4 жыл бұрын

True

@SpartanFunnyProyect 4 жыл бұрын

I use the sepia setting when reading Kindles, so yeah, I know exactly what you mean.

@theasianguy9812 3 жыл бұрын

Reading modern textbooks gives me the feeling of trying to decipher its meaning too.

@Orosdeo 4 жыл бұрын

I recall reading Hardy's apology when I was finishing a bachelors in Mathematics. I specially enjoyed the line "Beauty is the first test: there is no permanent place in the world for ugly mathematics." and have always thought it true.

@randomCoolGuy 4 жыл бұрын

I wish my math was handsome. Instead of horrible approximations, rounding to some decimal place and handwaved limits to infinity. Cs student btw.

@jdmccue9722 4 жыл бұрын

Tell that to modern architecture

@nicktarantino7188 4 жыл бұрын

I remember reading this line in the book.

@zeldamage001 4 жыл бұрын

I think it's something all mathematicians wish to be true. However, wishing something to be true and it actually being true is not the same. I wouldn't be surprised if there are recorded arguments for this 'wish', or hypothesis, though.

@Ockerlord 4 жыл бұрын

I fucking hate this argument. No, a mathematical conjecture should not be judged by its perceived beauty nor should any model of the world in physics.

@Skibbityboo0580 4 жыл бұрын

Your channel calms me down during panic attacks. I just wanted to let you know!

@ninepuchar1 4 жыл бұрын

Her soothing and tranquil voice,makes us feel calm and at ease. I feel she could even calm down the rage of a man simply with her mannerism and voice.

@borisbadenov651 4 жыл бұрын

@@ninepuchar1 And neither can her natural beauty be ignored !

@Bunny_Aoife 4 жыл бұрын

while i find her voice as well as her subject matter very soothing, the pen in the book gives me a bit of anxiety.

@ronanstephens1597 4 жыл бұрын

Mathematical ASMR when?!

@robdee81 3 жыл бұрын

when youre having a panic attack and believing youre about to die you boot up your computer and load up a maths video?

@gregsimpson9391 4 жыл бұрын

I remember a time many years ago when I simply could not grasp mathematics - by that I mean algebra etc etc. My brain simply could not adapt to thinking in these "abstract"ways. I was bottom of the class and simply felt I was outside the group. It was very frustrating. Then I had a change in teacher and some help from a friend. For some reason I started to "get it". I then simply progressed and eventually studied engineering and became successful in that field and others. So what has mathematics done for me? It has not made me into a mathematician but it has shaped my thinking. I became very good at problem definition (not justr in engineering but in life) - many others became better at problem solving but my persistence in following subjects in which I was interested was underpinned by my eventual understanding of mathematics all the way to partial differential calculus and equations - and their applications in our world and the universe. I am so grateful to have achieved a level of mathematics that enabled my thinking to expand. That is the message I want to send to you and your readers and their children. I know this and I have been there!!

@lai8544 4 жыл бұрын

Wow thats so cool! Im glad for you! I´ve always been bad at math and thats really inspiring to read

@EdWhiteSpyHI 4 жыл бұрын

This has been my journey as well! I actually went to university later in life and by the time I got there, I had forgotten what the syntax for absolute numbers was! But CS is a math degree (at my school at least) and I’m persistent, and I noticed that advanced math was like a programmer’s super-power, so driven by interest and application I started learning more and more math on my own, just to use it in my programming. It was what made math fun and understandable for me.

@Shaolin-Jesus Жыл бұрын

we should question if it is wise to think in terms of 'becoming a mathematician' when we look at the evidence, the evidence suggests that to some extent, is it short-sighted to see one's self as a mathematician rather, the evidence suggests that we are the embodiment of mathematics we are all mathematics in motion .

@PapaFlammy69 4 жыл бұрын

Sry.

@otiswong2091 4 жыл бұрын

hello lol

@helmiazizm 4 жыл бұрын

No u make bad meme

@doctorpanigrahi9975 4 жыл бұрын

I forgive you :)

@PapaFlammy69 3 жыл бұрын

@@doctorpanigrahi9975

@Abstractor21 3 жыл бұрын

i need a "Ft. Flammable Maths" in this channel

@kevinbaird7277 4 жыл бұрын

I think Hardy is too hard on himself, sad that a great intellectual has feelings of no self worth, I admire his great honesty, a few less notable individuals could learn a thing or two from this great man.

@Mephanderos 4 жыл бұрын

But it's true. His own work really had no value. The only thing that actually mattered in his life, is his collaborations with Ramanjuan and so.

@yuiosway 4 жыл бұрын

"I am the wisest man alive, for I know one thing, and that is that I know nothing." -Socrates

@NTNscrub 4 жыл бұрын

Dettlaff Van Der Eretein It had value in the inspiration it brought to aspiring mathematicians. Just look at the comment by a math professor left on this video about how his apology had a profound effect on his thought.

@Mephanderos 4 жыл бұрын

@@NTNscrub Maybe so, but with all due respect, the inspiration it brought isn't actually gonna have an effect on the world, as a whole. Specific individuals do not count.

@NTNscrub 4 жыл бұрын

Dettlaff Van Der Eretein Who’s to say how widespread that inspiration is? I absolutely agree that in tangible contributions for the progression of mathematics, Hardy was lacking. However, to say his work is of no value at all is an overreach. Surely, some value can be found when approached from a perspective of education, inspiration, or entertainment.

@epajarjestys9981 4 жыл бұрын

"First rule of mathematics: You don't talk about mathematics." _G.H. Hardy_

@jiwoongjang2764 3 жыл бұрын

Yeah. Moreover, we need to think and create something new and that is what math is.

@jorgealbertoguizaralfaro9047 4 жыл бұрын

Tibees, I got accepted in a PhD at University of Canterbury, NZ, I have read that it is your Alma Mater...

@priscilaguimaraes2732 4 жыл бұрын

What’s an alma Mater? Thanks

@thearchibaldtuttle 4 жыл бұрын

Priscila Guimarães where you’re money goes

@vk2ig 4 жыл бұрын

@Pete is never wrong Higher education (up to and including undergraduate level) used to be fee-free in Australia from when the Labor government abolished fees in the early/mid 70s until another Labor government introduced the Higher Education Contribution charges in the mid/late 80s. (The Coalition (conservative) government in between didn't touch fees.) Sure, there were people who rorted the system by swapping courses every few years and remaining permanent students, but our country mostly benefitted from the fee-free arrangement.

@vk2ig 4 жыл бұрын

@Pete is never wrong The HECS fees are a debt burden which can follow someone around for quite a while ... it's not quite as bad as a mortgage, but it's getting there. And given how little a science graduate gets paid here, I really wonder how some people are able ever to service that debt, especially when later "normal life" elements like family and home ownership are factored in. Many of the "permanent students" I saw didn't actually finish any one course - they just swapped to stay in the education system. Quite a few were almost permanent fixtures on student union councils ... politicians-in-the-making, maybe? These were not the same as the people who would do an undergraduate course with Honours, then a Masters, then a Ph.D, and then stay in academia lecturing and conducting research.

@ajitsen6927 4 жыл бұрын

Not a NZ'er or Tibees but who cares lol - Congratulations Dude .

@holden.a 4 жыл бұрын

As I become older and older the more I love mathematics. It has timeless beauty.

@EG-cs3wv 4 жыл бұрын

There is always value in any expression of humanity. Mathematics are a great representation of what we are, its a part of our core. So maths are always useful. I think we confuse utility with tangible things or results. Utility is everywere, but some paradigsm does't allow us to see it. And sometimes something is useful not for what it causes but for its causes Great video, voice and inspiration... As always.

@Nono-hk3is 4 жыл бұрын

Hell yeah

@michaeljames4904 4 жыл бұрын

_apology_ ≠ “sorry” As in apologia, or apologetics: defending your own tenets from critique.

@bettercallmepol3493 4 жыл бұрын

Απολογία είναι η υπεράσπιση του αληθούς....its definitely not deflecting as such

@alexpotts6520 4 жыл бұрын

Moreover, it has quite a negative connotation, one of defending the indefensible. One would describe a person supporting creationism, or eugenics, or North Korea, as an apologist.

@michaeljames4904 4 жыл бұрын

Alex Potts Many words not only have separate meanings, they sometimes have little used ones in the contemporary sense, or completely differing original definitions. If I describe Tibees as having _catholic_ interests, most would think I meant religious ones, rather than “varied and separate.” Should a contemporary have described St Paul’s Cathedral as _awful,_ to Sir Christopher Wren, he wouldn’t have felt insulted but complemented that the person was “filled with awe” by the construction. If a Victorian had told a friend that they’d had an _accident_ the other day, her friend would be interested rather than concerned, as before the much later ubiquity of the motor car it meant a curious incident of chance, rather than anything injurious or mistaken. Similarly, _Hello!_ was originally a cordial exclamation of surprise, then refashioned in the search for an appropriately novel greeting, when using the newfangled telephone; almost as a throat-clearer to check the line was working okay. Now it’s used in any context rather than just telephonic. (It narrowly beat out the competitor candidate, _”Ahoy-hoy!”_ which in a cheeky hat-tip to the blaggard’s extreme age, Mr Burns still uses on answering the ‘phone, in _The Simpsons.)_

@michaeljames4904 4 жыл бұрын

rice eater G.H. Hardy was a Cambridge man, born in 1847, and until the later explosion of the natural sciences it was a centre of learning dominated by three disciplines: divinity, law and mathematics. Theology as a field still has, just like you say, a rich and continuing use of the derivatives of _apologia_ in its once more dominant sense. You’ll, though rarely, still hear its contemporary collocation with the verb that suits that use, “I wish to *make* an apology,” rather than ‘give.’ If you think of the aforementioned fields of study, and keep in mind the request, “permit me to humbly explain my position,” you can likely appreciate not merely how the word ‘apology’ would have been understood by Hardy’s academic contemporaries, but also how its meaning in common parlance today branched off from the original.

@GODandGODDESS 4 жыл бұрын

The Greek word apologia (Strong’s G 627) is a verbal defense.

@tufanbanerjee4571 4 жыл бұрын

It's now 3.20 am here And I got the notification Tibees ❤️❤️

@namenotavailable9989 4 жыл бұрын

Same

@tibees 4 жыл бұрын

Thank you for your dedication 😅

@shuklaviswesh 4 жыл бұрын

Here too

@auravstomar7629 4 жыл бұрын

thats why ive turned off notifications

@kivuosark2088 4 жыл бұрын

You must be an engineering student

@TheQuantumCore 4 жыл бұрын

Pure Science is an art in itself. It is to express oneself. Not everything requires immediate application. Sometimes it takes centuries for it to be applied. Othertimes it just lays foundations for future inventions. Its value is not immediately or directly perceivable or measurable. Nevertheless Hardly was a genius. Often it takes a genius to identify another. If not for Hardy there would be no Ramanujan. He personifies "Ars gratia artis". A true artist.

@eroche12 4 жыл бұрын

Even in his old days being in his 80's my late dad used his Sundays to solve old math problems and had to create some new formulae for aerodynamics and add quantum physics (was amazed of what he called the "fat" electron :-). I wish he was still alive and watch your videos. He would have enjoyed them. Keep up the great work Tibees!!

@chemomatik8276 4 жыл бұрын

Yay, a new video from Tibees! Hi Tibees. You just inspired me to a silly joke: Q:"What does the doctor tell the mathematician?" A: "Your days are numbered"

@peterbrough2461 4 жыл бұрын

I'm reminded of that every time I see a calendar😳

@greywolfwalking6359 4 жыл бұрын

Muckan ???? Ooooohhhh!! Got it!!!✌the third estate!

@vk2ig 4 жыл бұрын

@Muckan Or ... There are 10 types of people in this world - those who understand binary numbers, and those who don't.

@vk2ig 4 жыл бұрын

@@peterbrough2461 That's why calendars get the chop at the end of their useful lives.

@ifrazali3052 4 жыл бұрын

@@greywolfwalking6359 I didn't get it

@idjles 4 жыл бұрын

Hardy, you gave us Ramanujan, so all is forgiven. (But you could have kept him warmer in winter!!)

@Jerry113 4 жыл бұрын

We forgive you king

@sahilbaori9052 4 жыл бұрын

Who?

@TheSummerLab1 4 жыл бұрын

Hardy didn't train Ramanujan 😑 He just gave him value regardless of race.

@aniketsaha1601 4 жыл бұрын

u r pretenging as if he created ramanujan...he just gave him an opportunity that's it and ramanujan was way better and leagues above other mathematicians so he came and rocked the world✌️

@vae3716 4 жыл бұрын

@@aniketsaha1601 why do people keep comparing mathematicians? Like I know ramanujan undoubtedly was a great mathematician but assuming that certain mathematician is greater than other is ridiculous or doesn't make sense. Take hardy for example he acknowledged that his work would be "useless" because of no real life applications of it but does it make him or his mathematical legacy any less greater than any other mathematicians? Not at all

@hebrewwolf6540 4 жыл бұрын

Your videos have such beautiful aesthetics. I love the fact that you just randomly insert your cat scenes. 😍

@zubin8010 4 жыл бұрын

I highly recommend the book "An Introduction to the Theory of Numbers" by Hardy (the same Hardy from this video) and Wright.

@thearchive26788 4 жыл бұрын

I'm definitely interested in gobbling up more books he has written!

@nachisuper 4 жыл бұрын

What did you like about it?

@thearchive26788 4 жыл бұрын

@@nachisuper I haven't read all of it yet. I stated that in a previous comment. As mentioned I was just a kid and in my early teens. I remember how I felt reading it. I don't remember the details, even vaguely. I just purchased it now on kindle. I will definitely share my opinion, that is if this comment was intended for me. If not, then I apologize. But, I will share it anyway when I'm done. Thank you so much for making me type something out. I am always and ever in dire need to express my thoughts in a written form. Thanks to all of you including and especially, the uploader of this video.

@kasterborouskitten 3 жыл бұрын

I'm so happy I just found your channel! Your videos are so calming and insightful and lovely, it's so inspiring to see someone who looks like me (a blonde gal!) talking about maths and actually being taken seriously and supported by people for it! Thank you 💖💖

@xshortguy 4 жыл бұрын

"Hardy was well past his prime" - right after talking about infinite number of primes. :P

4 жыл бұрын

I read this as a teen and it taught me to find beauty in everything. Also maths

@fernandolovato3979 4 жыл бұрын

In my opinion this is one of the best videos you've ever made, congrats!

@humilulo 3 жыл бұрын

Tibees, you have the truest math i've ever seen in my life. you are such an inspiration. What you shared in your Mathemation's Lament is so true about true math. thank you for 'sharing this truth from a housetop' or 'sharing this truth in the concourses'. You have done this well from your KZfaq channel, in such elegance & beauty! thanks so much for sharing a piece of your brilliant, beautiful mind that just lights up from the beauty of true math! You are the greatest mathematician i've ever found or heard of. Thanks for inspiring me to continue learning true math! it is so beautiful! you have relit my love for math!

@user-oy2vx9xw8t 3 жыл бұрын

I could literally listen to you whole day nonstop.

@leezhao 4 жыл бұрын

7:50 Charles Percy Snow was a physicist by training and best known for being a novelist. But anyway, Hardy's Apology greatly influenced my thinking when I first read it as a graduate student (wish I had read it much earlier). Though it probably didn't present new ideas to me, the best writings sometimes are precisely those that articulate the reader's own thoughts so well that they are brought to a full and sharper relief. I am a math professor now and I've tried to have my students read it. I can only hope that they can benefit as much as I did.

@neonskie7008 4 жыл бұрын

If u don't mind me asking Did u anytime lose motivation to study? This is random but I just wanted to know.

@leezhao 4 жыл бұрын

@@neonskie7008 Well, there of course have been moments of doubt, prompted by external factors like job prospects, etc. But I suppose that's not the same as losing motivation. The subject of mathematics itself never lost its appeal, I don't think.

@neonskie7008 4 жыл бұрын

@@leezhao ahh Well did u ever fail in maths?

@leezhao 4 жыл бұрын

@@neonskie7008 Ha, I fail all the time, failing to prove a theorem that I want, failing to come up with the correct statement to prove, failing come up with interesting problems to work on... This is not to say that I don't ever succeed. Scientific research works at the boarder of knowledge and the unknown. Failures come way more frequently than successes.

@neonskie7008 4 жыл бұрын

@@leezhao awh Well, thank you for telling me :)

@e.l.2734 8 ай бұрын

Toby, you've always seemed like a solid role model with your smarts, hard work, sweetness, joy, and just general virtues and passion. Please never leave the internet, because so many generations can benefit from watching you and being inspired by you.

@runneypo 4 жыл бұрын

i dont have the mind to do mathematics but i can appreciate the writings and thoughts of those brighter than me. good video

@SIGSEGV1337 4 жыл бұрын

maybe you do, maybe you just don't like the way others do mathematics

@runneypo 4 жыл бұрын

@@SIGSEGV1337 could you elaborate please? what are the alternative ways to do mathematics?

@SIGSEGV1337 4 жыл бұрын

@@runneypo I don't know, maybe you just need to carve your own path like Ramanujan did

@runneypo 4 жыл бұрын

@@SIGSEGV1337 ah but ramanujan had an exeptional mind for mathematics, i have only average intellect

@SIGSEGV1337 4 жыл бұрын

@@runneypo Maybe you just haven't tried.

@troycooper7180 3 жыл бұрын

I am no "Mathlete," but an artist, and as an artist I find you intoxicating to view and to hear... even as I have no desire to ponder great mathematical questions or equations. I am fascinated by Ramanujan's life and his passion, and I find myself "enduring" your topics and being fascinated by you for your beauty - which is oddly as potent externally as it is internally. *Prettiest Kiwi ever... thank you for your wonderful distractions! You're as sweet as cherry Pi.

@benheideveld4617 4 жыл бұрын

Lovely! If you are a second rate mathematician, you are still way more intelligent than me, a lowly physicist. Yes, theoretical physicists are the masters of our Universe, but let me remind you that Mathematicians are the grandmasters of all universes, existing or not...

@borisbadenov651 4 жыл бұрын

And God's existence has been proven through mathematics. See the video entitled: "Mathematical Challenges to Darwin’s Theory of Evolution."

@cygil1 4 жыл бұрын

Her website says she only has an undergraduate degree, albeit with first class honors. I wouldn't be too quick to draw that conclusion.

@jordanjacobson6046 4 жыл бұрын

@@borisbadenov651 math cant "prove" anything about the world, in fact, the only things that can be definitively proven are mathematical truths. Worldly things can be empirically tested but still have, even if only infinitesimally, a chance of having been coincidence. God, spirituality, or other metaphysical concerns are not even empirically testable let alone mathematically provable.

@costakeith9048 4 жыл бұрын

@@jordanjacobson6046 No, you can't prove anything empirically with mathematics, but mathematics does allow us to directly interact with the world of forms, which is obviously more real than anything made of matter and observable by the senses. I wouldn't go so far as to say that one can 'prove' God's existence with mathematics, but certain mathematical proofs have added to the weight of evidence, such as Godel effectively proving that truth exists even outside of any conceivable axiomatic system, that is to say that the world of forms, that the real world, both exists and is infinitely vast.

@vincemarenger7122 3 жыл бұрын

Boris Badenov Darwin’s theory doesn’t even disprove god, in the first place. I know people that believe in evolution, big bang etc. And still believe that god created the universe. “God doesn’t play dice with the universe” - Albert Einstein, criticizing quantum mechanics “God not only plays dice, he also somtimes throws them where they cannot be seen”. - Hawking, later contradicting Einstein

@lockqspur Жыл бұрын

Your videos are amazing! I watch them for study breaks and they’re so nice 🙃

@slaasavic5044 3 жыл бұрын

Tobby, I don't think I ever commented on any of your videos before, but now I have to say it- you are just awesome and everything you post is just fascinating. Thank you for quality content :) .

@hrperformance 4 жыл бұрын

I rather be a happy but average physicist than great and unhappy. That's the lesson I'm taking from this 😁👍🏽

@s7d788 4 жыл бұрын

Same, as a fellow physicist. I am quite young but truth be told I don't think there's this spark of historical genius in me. However, as long as I am able to I will put great effort on studies which fulfill me and that I find interesting

@stargazer137 10 ай бұрын

@@s7d788 How are you doing now brother?

@turicaederynmab5343 4 жыл бұрын

When we getting a room tour homie? Background looks like the set of Downton Abbey. And honestly this Hardy guy sounds like he was going through it, hope the dude found a way to appreciate himself before he passed.

@Nono-hk3is 4 жыл бұрын

Word

@standowner6979 3 жыл бұрын

@@Nono-hk3is Sentence

@anoopnayak9751 4 жыл бұрын

Thank you for sharing. I have not read it yet but based on your words, he surely was a person with big heart.

@TheOne-um7rp 3 жыл бұрын

Her voice, so soothing, brings me peace. I have been watching videos lately on vibrational frequencies, and when I wrote a comment that it was not working for me, one guy suggested that I had not found the right frequency. I have found it now.

@Kaynos 4 жыл бұрын

Value is in the eye of the beholders.

@JoeCMath 4 жыл бұрын

Started sweating nervously when reading the title... great video! That whole not feeling "useful" seems to be pervasive among those who achieve quite a lot.

@friedrichn7767 4 жыл бұрын

Everytime I hear your voice I feel happy 😃 So thx for all of your GREAT videos. It's midnight, I am sleepy but I got the notification then I'm I'm watching the video. I'm exhausted and sleepy but I can't help it. Thx

@Red-Brick-Dream 4 жыл бұрын

Since leaving university, I've struggled to find purpose. I never pursued a graduate degree, as I was in poor mental health and did not feel I could bear the commitment. But play - play never lost its joy. To play with numbers, play with equations, and shapes, and sets, and to try and share that joy and wonder with others as an educator... Here, I have found something close to catharsis; as close, I suspect, as I will ever get. And these readings from Hardy's book have helped brighten my day a bit, as I prepare to apply for teacher's college ASAP. Thank you for this! ❤ from Canada.

@jacquesrabie4599 4 жыл бұрын

"There is no permanent place in the world for ugly mathematics." *Stares in Algebraic Geometry*

@mayabartolabac 3 жыл бұрын

can you explain the joke?

@StewartMcGinnis 3 жыл бұрын

Them's fightin' words

@anupamdebnath1884 3 жыл бұрын

Well, ugliness has it's own beauty.

@Zeer0042 4 жыл бұрын

I watched this video called "Beautiful Trigonometry" or something from the channel Numberphile and in the video there's a line which is like "Mathematicians do maths because it's beautiful. Maths is beautiful. Then they realise 'ohhhh this can be applied somewhere'".

@2bsirius 4 жыл бұрын

I am lucky enough to live close to G H Hardy's grave. I can and have bicycled from where I live in Cambridgeshire. I think as soon as Covid-19 is just a bad memory, I return to his grave and leave a copy of _A Mathematician's Apology_ in a weather proof box on Hardy's forgotten grave with the hope that it will be found by a fellow lover of the beauty of mathematics Among the many passages I love within the book are, _The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics_ and _Chess problems are the hymn-tunes of mathematics._ I hope your readers will be prompted by your video to read the book and find their own gems within its pages. Thanks for this video.

@cicad2007 4 жыл бұрын

Dear heart, i'm sure Hardy would view you efforts as well worthy of praise. You are a teacher to many more students than he could ever conceive of! Myself included. 😊

@AeroCraftAviation 4 жыл бұрын

6:06 Well he was only three years past his last prime.

@tibees 4 жыл бұрын

haha, 61 is prime so he had just passed it but his last prime was really at 67

@AeroCraftAviation 4 жыл бұрын

@@tibees Oh shoot this is the second time in a week that I've forgotten about 61 being prime. 🤣 But yeah I suppose it was.

@vk2ig 4 жыл бұрын

@@tibees I was wondering if that line "[Hardy] thought he was well past his prime" was a pun intended.

@jeffreyengel 4 жыл бұрын

@@AeroCraftAviation Well, I hadn't thought of it at all this week until now, so effectively I've forgotten it umpteen times.

@AeroCraftAviation 4 жыл бұрын

@@jeffreyengel Haha fair enough. I suppose by that logic there are infinitely many primes that we've all forgotten infinitely many times, assuming we forget once per instant. 😆

@nuclearwinter6231 4 жыл бұрын

she's undoubtedly stunning, she carries herself with an air of calmness, intelligence and confidence. throughly enjoyed this video (even tho my mathematical knowledge is severely limited lol)

@jcbguy4099 4 жыл бұрын

Your voice and your English makes me feel meditative.

@ari-cowan 4 жыл бұрын

With respect to the idea that talking about mathematics is something for second-rate minds, it's clear that you've demonstrated that this is not the case. I'm an ontological theorist (the nature of reality and being with a focus on compassion, conflict, and human development) and I've not truly appreciated mathematics nor fully considered the role it plays in the development of the human mind and the impact on humanity. Watching your videos (brief presentions by a young woman thousands of miles away from me, rendered in two dimensions on my computer screen) is something of an unexpected revelation. For this, I'm quite moved and deeply thankful. You're something of a gift. Do press on.

@harjeck9518 4 жыл бұрын

There is a brilliant TED talk to this topic by Grant Sanderson from channel 3Blue1Brown, definitely worth watching.. :) As well as Toby's videos, of course! :D

@xenontesla122 4 жыл бұрын

6:04 Sure he was a year past his prime, but couldn't he just wait 'til he was 67? :)

@baruchbelmont5821 4 жыл бұрын

Always a pleasure to see a new video by you Toby.

@larrysherk 4 жыл бұрын

I am a retired educator, mathematician, and physicist, and I do like your work !

@ReeceyPeecey87 4 жыл бұрын

What my favorite KZfaqr makes a video in my birthday awesome

@tibees 4 жыл бұрын

Happy birthday!

@ReeceyPeecey87 4 жыл бұрын

Tibees thank you soooooooo much this means a lot to me 😭

@souravroy3988 4 жыл бұрын

Wow today is also my birthday

@ReeceyPeecey87 4 жыл бұрын

Sourav Roy awesome happy birthday

@souravroy3988 4 жыл бұрын

Thanks, you too happy birthday

@timeless_realm 4 жыл бұрын

How do you find someone you trust to start a foundation for math? If one starts to learn from someone who pretends to know and really doesn’t it is very discouraging.

@Felipe_Ribeir0 4 жыл бұрын

It depends on your level. You are talking about college level? You can research for the better math course that you can do (by price, location) and go there. I guarantee that the people there will be enough.

@Noahakavalkrie 4 жыл бұрын

I could listen to you read or talk about pretty much anything. I’m always so relaxed afterwards, and end up learning something interesting.

@nunosoares2329 4 жыл бұрын

Hi Toby. Hope you're doing well. It's always a pleasure seeing and listening to you. I'm sure Mr. Hardy would think the same. All the best to you :-)

@vk2ig 4 жыл бұрын

Great video Toby, I had never heard of this work. 7:39 "I'd hate to know what he thinks of me talking about him talking about mathematics" - Hardy would probably think in terms of powers, so someone talking about him talking about mathematics would be a 4th rate mind, and us talking about you talking about him talking about mathematics makes us all 16th rate minds? It's funny how many mathematicians investigated subjects which, in their day, had very little application, but nowadays their work underpins the very technology that makes our society possible. Fourier is another who comes to mind.

@MrAlRats 4 жыл бұрын

@James Herndon Hardy didn't derive his feeling of self-worth by declaring his superiority to others. He was simply stating that mathematicians who talk about mathematics as opposed to doing mathematics is the reserve of second-rate mathematicians. This is a reasonable point of view since very good mathematicians don't have the luxury of time to engage in such things. His depression was a consequence of his view that he cannot be as productive as he once used to be and as a result he now has enough time to contemplate about and write about mathematics. Hardy was among the most accomplished mathematicians of his time and it would be delusional for him to not realise that he was a superior mathematician to a lot of his peers.

@vk2ig 4 жыл бұрын

@@MrAlRats Agreed. I didn't see or hear anything stating that Hardy's sense of self-worth derived from considering himself superior to others. Instead, per what you indicated, his self-worth in later life was gauged against his own ability in his early life.

@swastikdey7498 4 жыл бұрын

Oh boy.... Imma sending all your videos to playlists....... JEE ADVANCED is just near the corner.... Just lemme crack it and then Imgonna watch all your videos.

@pedro.zoppiski 4 жыл бұрын

your voice is soooo calm, sooo charming, soooo elegant

@jordanrenaud-pq7rx 3 жыл бұрын

YOU are the treasure dear. So sad to feel what Hardy felt...my journey is nearly over and I feel I have made no difference, thus depression looms.

@tedskins 4 жыл бұрын

These videos are great. It's like educational ASMR

@luca_magna7753 4 жыл бұрын

I'm taking a Mathematics A level this year!

@Hailfire08 4 жыл бұрын

Good luck

@GeorgeSPAMTindle 4 жыл бұрын

Enjoy it, and do well.

@luca_magna7753 4 жыл бұрын

Thank you both

@ForAllEpsilon 4 жыл бұрын

Having read Hardy's Apology during my senior year of my undergrad studying Math, I couldn't help but be overwhelmed with sadness, but above all ambivalence. It was during my senior year of undergrad that I started feeling a diminishing passion for Math, which was my main obsession in all the previous years. The fact that Hardy was able to articulate so elegantly what I was feeling so deeply left an ever lasting impact on me.

@HypothesisI 4 жыл бұрын

Thank you for producing your work. I am neither a first, second or third rate mind but I love the window into mathematics and physics which you provide. Thank you Tibees!

@janani_jade 4 жыл бұрын

"There is no permanent place in the world for ugly mathematics." - I always enjoy mathematics classes because of this. There has never been a math class where I hated/got bored of the topic that was being taught. Great video! My September reading list now has a new addition.

@luiszamudio1572 4 жыл бұрын

You must have always had very good teachers, I envy you

@janani_jade 4 жыл бұрын

@@luiszamudio1572 I've had my fair share of bad teachers too. That's why the back benches exist.😂

@Hi_Brien 4 жыл бұрын

@@luiszamudio1572 not nessisarily, I never had a good math teacher, but I isolated myself from their lessons and taught me everything I know using the resources at my disposal. I have then found that there is no boring topic except for the one you don't delve into.

@luiszamudio1572 4 жыл бұрын

@@Hi_Brien Makes sense, you said the topic of the class, no the class itself. But I have personally disliked some math classes so much that I take it upon the subject. I know, its not fair

@luiszamudio1572 4 жыл бұрын

@@janani_jade Then how do you enjoy the class?

@bangersareforever480 4 жыл бұрын

Hardy promoting the idea that mathematics is a “young mans game” is one of the worst things to happen to mathematics

@vector8310 4 жыл бұрын

I took to mathematics in my late 30's. I am an amateur mathematician at 60 now, and I hold it as my most prized endeavor.

@Felipe_Ribeir0 4 жыл бұрын

But this is the truth, according with our historical data. Most of the brilliant jobs were done when the mathematician had 15-30 years of life.

@bangersareforever480 4 жыл бұрын

@@Felipe_Ribeir0 this is just not true, there are multiple papers and essays disproving this myth, google “A Young Man’s Game”: Youth, gender, play, and power in the personae of mid- twentieth century global mathematics by Michael J. Barany

@thetntsheep4075 3 жыл бұрын

I didn't expect this video to give me an existential crisis

@1325cmith 4 жыл бұрын

I dont know how i got here but im not complaining. I watched a couple of your videos just because of how relaxing they are.

@Notofsoundmind 4 жыл бұрын

I tip my hat to an incredibly charming, intelligent, and lovely mathematics enthusiast.

@ln5321 4 жыл бұрын

When you're making a video about a guy's writing and come across a burn on yourself being essentially called a third rate mind.

@atc35012 4 жыл бұрын

I like to believe that effort is worth something given the right amount of time. I love to journal. I recently found out that a series of journals in time are valuable to collectors, important as historically personal accounts of how people lived during a specific period that those in the future will never see or experience, and can be sold for more money than single accounts of a person's life lasting only a few months or a year. I always feared that someday my journals would be burned or destroyed at the end of my life and by then I should have enough to fill a bookcase. I started journaling at just 8 years old. I've been journaling for 27 years and have only kept the journals from 2009 to the present and I named them Bernardo. Effort is valued with time. One of the cool things about Bernardo is that it is hand-written so it will be readable in ten or twenty years unlike a computer program and it won't crash and vanish forever.

@emanna7868 4 жыл бұрын

I studied Arts, I'm 35, I don't have friends or a job. To hear his words saying that somehow he sees worthy the work of a painter or a poet, but judges so harshly to himself. One that never saw through mathematics but loves to hear about it... I know, that he defines his kind of beauty to make a work valuable or not, but still... Love your videos ;) Gracias

@gemanimates 4 жыл бұрын

i forgot why i subscribed.

@bluebite01 4 жыл бұрын

A ti te perdonamos todo, mi amor, ojos bellos

@lacanian1500 4 жыл бұрын

che cálmate, cheatur

@rosadovelascojosuedavid1894 4 жыл бұрын

Lol

@oatmealbro6977 4 жыл бұрын

Thumbnail game was sneaky good! Excellent content as usual, Tib! :)

@TCt83067695 3 жыл бұрын

Such a soothing voice for a quite profound subject matter about life accomplishments

@danicifu6031 4 жыл бұрын

This has depressed me ahaha🥴🥴

@Ezrik2006 4 жыл бұрын

I love the fact that you included the pen you use. Literally my favorite person on KZfaq!

@sc6155 4 жыл бұрын

I truly love you. I'm pursuing my master's degree in astrophysics and your videos are among the things that inspire me and remind me how beautiful science is. ❤️Love from Egypt.

@mrknarf4438 4 жыл бұрын

I've stopped studying maths. In my bachelor's I couldn't see the beauty behind it, I loved (and still do!) the subject but hated the way it was taught and how much more emphasis was put on remembering formulas than on understanding them and seeing what was behind. Sometimes I regret it, but I just couldn't force myself to do it.

@Shaolin-Jesus Жыл бұрын

You seem more inclined towards the philosophy of mathematics. this is a very organic way to approach such an abstract subject remain true, one should not do mathematics without regard for its origin.

@stkyriakoulisdr 4 жыл бұрын

I have heard somewhere an interesting point on Hardy's and others' view of the usefulness of their work (or rather, the lack thereof): They lived at a very difficult time of history. They had been shaped by WW1, the Spanish flu (which I suppose we will start noticing now), the great depression and (by the time the book was written) the beginning of WW2. They had observed great suffering and pain. They also saw fellow scientists making advancements that (perhaps unintentionally) led to this suffering: Chemists developed poisonous gases, engineers designed deadlier weapons and just a stone throw away, in the same university, physicists split the atom to pave the way for the strongest bomb ever to be made. Amidst all this violence and place for usefulness, they were able to take pride in their work for being simply beautiful and only that. Because creating beauty is for a time of peace and prosperity. And when your creation has no practical use, no one can make a weapon out of it. And to me, that's inspiring and that's beautiful. I would imagine the world would be a profoundly better place if we had more people with Hardy's mindset. P.S. It is ironic that number theory, hardy's field has since found a very useful and, in some sense, warlike application in cryptography. P.P.S: I heard a thought along those lines from a KZfaqr but I cannot remember who it was. If anyone has any link, it would be helpful.

@mrtubeyou77 4 жыл бұрын

I love mathematics. I am a candle. You are a lighthouse. I wish I could comprehend and remember as much as you do! Have a great day!

@MrPablitoKs 4 жыл бұрын

Your pronunciation OMG It's so satisfying... Holly. I don't know much about math, pretty much just what I learned from your videos, Wich I can't stop watching

@onwarmermusic 4 жыл бұрын

I'm working through "Mathematics for Computer Science" on MIT's Open Courseware, and Hardy is mentioned briefly at the outset of one of the chapters. It's noted that he hoped number theory would not be used in warfare... and the chapter then goes on to discuss that very thing, by talking about Turing's work. I hadn't heard about Hardy until reading about him in that textbook, and this was a lovely companion to that. Really gave his character some extra depth. Thanks for making such a neat video.

@btwineu2me Жыл бұрын

We all have passions/hobbies for sure and we must try not to be influenced away from them. Hardy, Littlewood, Ramanujan all have motivations for their unending interests and activity.🌹

@jjkthebest 3 жыл бұрын

I'll show this video to my parents next time they ask me what my master project is supposed to accomplish.

@Ashish-gobal 4 жыл бұрын

Mathematics has a vital role in our life. We can't imagine the world without it.👩‍🏫👩‍🏫

@mainakbiswas2584 4 жыл бұрын

Although I knew all these things about Hardy, I never knew he loved cricket so much😍.... do you like cricket too? Are you excited for the Ashes, and india vs Australia coming up later this year. I often find the beauty of physics and maths in cricket. (Swinging of balls, the DRS system and also the duckward Lewis method)

@emilyscloset2648 4 жыл бұрын

I don't remember why I first came to read a number of sections from a mathematician's apology but it is something that has fleetingly stuck with me these past few years. When reminded explicitly about the book (such as done excellently by this video), those feelings from when I first "discovered" it emerge to the surface, like they never left

@emilyscloset2648 2 жыл бұрын

well said past me, well said

@themax2848 4 жыл бұрын

So beautiful how articulate Hardy was

@waderivers3304 4 жыл бұрын

I watch primarily just to listen to her voice....and her exquisite face. The song by Sam And Dave comes to mind, Wonderful World.

@ericmichelsen3233 2 жыл бұрын

I can't say what Harding would think of you talking about Harding talking about math, but there is no doubt that you bring the joy of discovery to many people. What could be more worthwhile than that?

@dabouras 4 жыл бұрын

the shear intellectual accomplishments needed to construct mathematics are under appreciated.

@Columba_Kos 4 жыл бұрын

Nine minutes and thirty two seconds well spent. Thank you.

@shrikantprajapati9150 4 жыл бұрын

idk why but your voice is literally solid content for asmr video

@eathannvdb 3 жыл бұрын

I'm not sure why this was in my recommended videos, but for *some reason* I'm glad it was.

@lematindesmagiciens8764 4 жыл бұрын

Than you Tibees for this wonderful video ! This touched a nerve with me. I think a lot of us are wondering if we are contributing something positive to the world. Not as a matter of vanity, but simply to add a tiny, little, minuscule something that makes the world a better place.

@nicolasforerocalderon1626 4 жыл бұрын

Thanks for sharing this apology Toby! And for you there's nothing to apologize. Your videos make me happy every time : )

@phillair3813 Жыл бұрын

As a science and math teacher, I take the position that teaching these proofs creates critical minds, so there is at the same time revelation of truth and beauty. Truth to be used in some cases and beauty in others.