The Big X and Multiplication - Numberphile

[@forthrightgambitia1032]

I don't know if the author has seen this but this topic is actually mentioned in what is probably the nerdiest book every published, the 1928 two volume "History of Mathematical Notation" by Florian Cajori. It is available free on the Internet Archive. On pp. 254 and 264 he mentions Recorde and his method and on a later page he reproduces the cross you see in the book with the same multiplication, and notes that the same method had appeared in earlier works on the continent, for example in the French translation of Tartaglia. He traces the "cross" symbol originally back to Leonardo of Pisa aka Fibonacci in the Liber Abaci of 1202 who used it in a different method known as the "process of two false positions". He talks about this specifically in the context of the origins of the multiplication symbols and notes that this usage of the cross was one of several ways in which a cross like this was used in various arithmetic algorithms. He then procedes to enumerate and detail each usage. He comes to the conclusion that as symbols that bore a resemblence to the St Andrews cross were used in a wide variety of different methods - and that there were also competing notations that lost out - that we have no evidence to specifically trace Oughtred's innovation in 1633 to any previous use, except, perhaps tenatively, the use of the letter x by Napier in a 1618 book. As it currently stands the Wikipedia page actually uses this as a reference when stating that attempts to tie the notation to previous usages are unfounded in evidence. That said, perhaps, as you say Recorde's book was sufficiently well known that it has priority over other claims, especially in England. This is certainly plausible, especially as famously another book by Recorde, The Whetstone of Witte was most certainly the origin of the equals sign, which naturally suggests the degree to which it captured the public imagination. It is impossible to prove definitively though. The word cipher is directly from Arabic as other people here have mentioned, where it is zero. The term "cipher" to refer to someone as a nobody was still relatively common until the 19th century/early 20th century. See for example chapter XVII of Jane Austen's Mansfield Park. It came to associated with codes because a lot of early codes in the 16th and 17th century used substitutions between the Latin alphabet and Arabic numbers, obviously something encoded this was would be a collection of unintelligble of digits - ciphers - that needed to be reconverted into Latin letters, deciphered. In a strange way this does seem rather familiar to modern users of encryption algorithms like AES where the output may well be in hexadecimal digits! Also the verb 'to cipher', that is to reckon, to do arithmetic still existed in Victorian times, it is used in this sense in chapter VII of Great Expectations for example. Indeed at this time the term ciphers was still used to refer to what we would now call digits.

[@bernhardglitzner4985]

Thank you for this 😃

[@hugofontes5708]

Thank you for compiling this here As a bonus you made me realize something about the Matrix character Cipher

[@anyuru]

9:35 finally someone challenged Rob Eastaways conjecture!

[@davidneuway3412]

For a more lowbrow reference, the use of "ciphering" as slang for doing arithmetic can be found in the 1960s sitcom The Beverly Hillbillies. Specifically, in season 1, episode 2 Jethro does some ciphering for Mr. Drysdale -- "one and one is two, two and two is four, four and four is eight" before he runs out of fingers on which to count.

[@stephenbeck7222]

Surely he’s read Cajori. Cajori says that Oughtred himself probably is the author of the appendix in Napier’s book where the ‘x’ symbol is used. So Napier (if that is correct) gets no credit for the use of x.

[@ididagood4335]

“You’re like a 10 without the 1” harsh burn from Shakespeare once again

[@pyros6139]

By the way, the word "zero" actually comes from the same Arabic source as "cipher". According to Wiktionary: Arabic "sifr" --> Medieval Latin "zephirum" --> Italian "zero" --> French "zero" --> English "zero" Arabic "sifr" --> Medieval Latin "cifra" --> Old French "cyfre" --> English "cipher"

[@Oler-yx7xj]

I love how he used (1:43) X to stand for "ten" in "X. of Millions". Such a fun quirk of the language of the time

[@jasonwalter-tz4qz]

And C. of millions and M. of millions, or a billion

[@RFC3514]

@@jasonwalter-tz4qz - Thousands of millions was not "a billion" in English until Americans started using it. A billion was a million millions (still is, in most languages). In UK documents before 1974, 10^9 is "one thousand millions", and "one billion" means 10^12.

[@JacksonBockus]

Makes sense that he wouldn’t say “10s of Millions”.

[@frankmalenfant2828]

​@@RFC3514 In french, a billion is a "milliard", a trillion is a "billion", a quadrillion is a "milliard" and so on, usine the "ard" suffix doubling each prefixes use for 3 more orders of magnitude. Living in a bilingual country where people speak both french and english, I anticipate this will cause lots of confusion as these trillion figures pop up more and more in our lives.

[@dugferd2266]

I always wondered about a term like 'zip' in North America to mean zero or nothing. It was probably one of those mishearing or adaptations from other languages' version of 'ciph' for 0.

[@Tekay37]

Can't wait for all the youtube shorts showing this method and asking the question "why didn't we learn this in school??".

[@diamondsmasher]

@@justforplaylists I’m assuming OP is being facetious and making fun of KZbinrs as no one in their right mind would teach this nowadays

[@ElderEagle42]

It's a lot more work than just learning the full tables

[@Tekay37]

@@ElderEagle42 Yes, but making a video about is also content.

[@bobh6728]

But to multiple the 8x7, you have to multiply 2x3. So how do you do 2x3?

[@Tekay37]

@@bobh6728 use the big X method, of course. ;)

[@ke9tv]

Recorde introduced not only the multiplication symbol × with that big X, but also the equal sign =, which Recorde justified as 'no two thinges can be more equalle'

[@tonelemoan]

Robert Recorde, the noted inventor of writing stuff down.

[@shohamsen8986]

Like lord discoverye, the first man to have come up with the concept of discovering

[@deltalima6703]

You only get to see his writings if he is your uncle. Unless bobs your uncle, there is no recorde.

[@chriscreations8853]

You beat me to it. Just what I was about to say 😂

[@RFC3514]

Apparently he invented some kind of flute, too.

[@vytah]

The big X reminds of this method that uses fingers: show (a-5) fingers on one hand and (b-5) fingers on the other. Then, the tens digit is the sum of straight fingers, and the units digit is the product of numbers of bent fingers on each hand. In other words, a×b = 10×((a-5)+(b-5)) + (10-a)×(10-b)

[@thekaxmax]

'He's a cipher' is a saying that means 'he's an unknown' is the sense of 'we know zero about him'. Can also be used to call someone meaningless.

[@ObadaSaqqa]

Cipher sounds exactly as صفر which is zero in Arabic

[@ciaranhenderson9464]

Yeah that's where it comes from. The English, and assumingly many other European nations, got the word from French, which in turn got it through Arabic in colonial times. Many Arabic words make their way into European languages through the French. Really fascinating word etymologies if you dig into it a little

[@catakuri6678]

i'm Arabic, but i didn't realize that until i read this comment

[@calholli]

All of these numbers are Arabic

[@ciaranhenderson9464]

@calholli The symbols, yes, but not the names, they're all germanic (until you get to millions and higher, in which case they're latin)

[@maximkhan-magomedov431]

And Russian word "цифра" (cifra) for digit also has the same etymology.

[@johannesvanderhorst9778]

Interestingly, the proof here about why this cross method works, doesn't even use the fact that we are working in base 10. For example, when we do base 100, one can use it for multiplying 78 and 86. 78 * 86 = 100*(78 - (100 - 86)) + (100 - 78)*(100 - 86) = 100*(78-14) + 22*14 = 6400+308 = 6708

[@nicomal]

It's a pretty nifty trick when you multiply two numbers greater than or equal to 90. For instance: 92 x 95 (try and do it mentally) = 8740

[@smylesg]

11:52 That's ironic he called 1 a "crooked figure" because in baseball if a team has scored only one run in a number of innings, they hope to "put a crooked number up there"; that is, to score more than one run in an inning.

[@mikew6644]

Such a banger of an episode… classic numberphile!

[@mytube001]

It's worth noting that the Arabic word that here was used to indicate a zero, and now is just "cipher", became the main word for "digit" in the Scandinavian languages (Swe: siffra, Nor: siffer, Dan: ciffer).

[@Filipnalepa]

In Slavic (at least in Polish) too, the word for digit is "cyfra" (starting with ts, not k sound)

[@christopherellis2663]

Sifr الشفرة. Shifera

[@ShinySwalot]

Add to this "Cijfer" for Dutch! ("ij" is sort of similar to a "y" sound)

[@aceman0000099]

Multilingual W

[@vladyslavsmirnov1875]

Same in Ukrainian! We say "цифра" (cyfra) for digit and "шифр" (shyfr) for cypher Never occurred to me before that these two are related 🤯

[@TheMoroe1]

In german a "digit" is also knows as a "Ziffer"

[@jurjenbos228]

In Dutch: cijfer

[@bhatkrishnakishor]

Vedic maths cross (X) method for multiplication 2 digits (10a + b) x (10c + d) = 100ac + 10 x (ad + bc) + bd 3 digit multiplication (100a + 10b + c) x (100x + 10y + z) = 10000ax + 1000 (ay+bx) +100 (az+by+cx) + 10 (bz+cy) + cz

[@ZetaFuzzMachine]

You're the best, Brady! Please, never stop doing this

[@richardfarrer5616]

I like the Shakespeare links. The only one I disagree with is the wooden "O". I think that a clear reference to the circular Globe Theatre.

[@numberphile]

The roundness of either o or 0 is certainly riffing on the roundness of the theatre... Both are of course rather round symbols (and the Globe was not a perfect circle)... It is certainly debatable... But if it is pronounced "nought" or similarly, it may then create the logical rhyme with "Agincourt' in the next line...? And there is a reference to cipher within a few lines of it too...? It was certainly written at a time when Shakespeare seemed to be have been rather taken with the concept of zero... Who knows for sure?

[@forthrightgambitia1032]

​@@numberphile I actually think Shakespeare probably meant both things at once. Part of his genius was to layer very complex meanings on top of each other in metaphors that are sometimes strained to their limit (which was kind of in fashion back then) but sometimes quite inspired. The idea that the Globe Theatre was an theatrical O that was also in some ways a kind of nothing fits a lot with his reflections of human existence and life being a reflection of the stage and vice versa.

[@forthrightgambitia1032]

@@topherthe11th23 they mainly used cyphers that substituted non-Latin alphabet symbols for thosr of the Latin alphabet. One form of this was to replace letters by numbers - not in the order obviously - and thus the term cipher came associated with codes. There was no concept of statistical analysis of letter frequency at the time.

[@richardfarrer5616]

@@numberphile Not an argument I'd heard before but there are other internal rhymes with the ending of the next line in that speech so it is plausible. I've never heard it as anything except 'oh', however.

[@renerpho]

@@richardfarrer5616 If that's true then the reference is apparently lost to most stage directors, which is entirely plausible (and a bit funny, too).

[@KyleMaxwell]

The history of mathematics is, for me, one of the most fascinating fields of study. Thank you for sharing this!

[@darkpulcinella9690]

So basically Recorde is a 16th century Matt Parker (writing fun books about maths destined to general public)

[@42isEverywhere]

I'm starting a petition to rename the multiplication symbol to "the Parker X"

[@RFC3514]

@@42isEverywhere - The parker X is actually the _addition_ sign.

[@mati.benapezo]

Petition for the Parker Factor.

[@mytube001]

Also, a mid-height dot is more commonly used as a multiplication symbol today in some countries, like my own. Using an "x" is mostly for the first years in school, when basic arithmetic is taught. A dot is better once you start using "x" as a variable in algebra. Now, it's not supposed to be used together with a decimal dot, as they look identical except for the vertical position on the line, but I prefer the look of a decimal dot instead of comma, so I use both. Just have to write them clearly.

[@mihir2012]

I love the title and the flow of this video! Neither the title and the start of the video give away anything, but leads into "where did the multiplication symbol come from?"

[@smylesg]

4:12 It makes sense it was only designed for digits 6 through 9 because otherwise the second column would be (difference from ten). You'd just be starting over again.

[@martinwhitworth3989]

I enjoyed Rob’s talk on this at Cheltenham Science festival 2024. The reference to cypher is interesting, since I’ve long known the Henry V quote and thought I understood it but never really did. This makes sense and I’ll look up the other references.

[@StoryMode180]

How have you not plugged Objectivity before this Brady?! I just watched your intro video over there, and that channel looks absolutely AMAZING! I've been a Numberphile subscriber for years, and had absolutely cipher idea that you had that channel just, hiding in the wood work. Instantly subscribed, it looks like I have an enormous backlog to watch now.

[@Caa-Mjeed]

The word Cipher comes from the Arabic word Sifr (صفر ) which means Zero or empty. Also the Muslims and Arabs brought the Zero to Europe and not only this but they invented Al-Jabr ( Algebra ) by the great scholar Al-Kawarizmi.

[@DavidRoberts]

The equals sign guy! (Now I've watched the video, I see the invention of = is not discussed. .. 😢)

[@DavidRoberts]

"Cross-over"... groan

[@piepiedog1]

@@squidward5110 How do you mean? Are you saying the symbol itself should be replaced with a word, i.e. "a + b = c" replaced with "a + b is c" for English? In that case, it would defeat the purpose, given that the symbols are intended to replace words. Not to mention, there are other versions of equals that are not as easily replaced, like ≡, ≢, ⊨, ⊢, ≥, ≈, ≃, ≟, and ≔, among many others, and they are all based on = given some logical relationship to its meaning.

[@piepiedog1]

@@squidward5110 I didn't say that, I said they are intended to replace words. And in the past, a lot of math was stated only in terms of words which ended up making simple facts fairly cumbersome to write down. Plus, symbols are standardized for the most part, and thus you can read math regardless of what language you speak.

[@javen9693]

​@@squidward5110instead of speculating you can easily google that Recorde consciously designed the = sign as "a pair of parallels, or duplicate lines of one length, thus: =, because no two things can be more equal."

[@DavidRoberts]

@@squidward5110 Actually, no Robert Recorde gives the explanation for why he chose two "twin" lines in the text, because "no two things can be more equal". It's not a linguistic abbreviation, but an explicitly symbolic notation.

[@robertolson7304]

mean median mode range is what is generally considered your zero. So it's not what is or isn't with Zero. 1 over 0 is a function. 0 over 1 is your (M,M,M,R). You can also have 0 over 2 .. that is when you have 2 functions at once.

[@worldnotworld]

A small complication arises as soon as the multiplication of the left digits has a two-digit value: you have to "carry" the ten's digit calculated on the right and add it to the digit calculated on the left. For example, 6*7 gives us [6 over 7] on the left of the X, and [4 over 3] on the right multiplying 4 and 3 gives us 12. The one's digit stands; the ten's digit, here a 1, needs to be "carried" over the the diagonal difference of three, and added to it: 3+1. Then you get 42. So the notion of "carrying" digits appears here, as it inevitably will. It's a clever and possibly pedagogically useful trick -- but it doesn't get around the step of "carrying" digits that strikes fear into those who would make arithmetic painless... Is it better just to memorize "6*7=42," or to learn this technique to calculate it?

[@psmirage8584]

This is fascinating math history. Thank you. PS - I tried 7 x 3. That's why this trick isn't used for numbers less than 6.

[@phizc]

Still works, but you end up having to do 3×7 anyway in the second column. 😂 1×2 would be worse than useless.

[@olivier2553]

The big X, I knew it as the finger multiplication, possibly coming from Tunisia. Thumb is six, index is seven, middle is eight... Touch the two fingers that are multiplying, for example 6x8 is left thumb to right middle finger. Count the fingers under the touching fingers, including the touching fingers: 1 on left hand, 3 on right hand, that if 4 tens. Multiply the remaining fingers on both hands: 4 on left hand multiply by 2 on right hand is 8. Result is 48. I am pretty sure the demonstration is the same. I devised the demonstration to the finger multiplication years ago, but I forgot the details.

[@SirCumference31]

1:40 why is there a 9 in the middle of the "Six" row?

[@Kyle-nm1kh]

I think it was written by hand

[@SirCumference31]

@@Kyle-nm1kh You mean it's probably a typo?

[@Kyle-nm1kh]

@notnek12 yes. I'm wondering if it's stamped even

[@RFC3514]

That's actually a Parker 6.

[@Jimorian]

The lines may have been hand drawn, but if this was from a printing press, getting a 6 upside down in the type pieces would have been hard to catch in the tray.

[@ForOrAgainstUs]

Interesting that Cipher means 0. In the Matrix, Cipher was a bad guy, the zero, the Judas, the betrayer of Neo, the hero, who was the One (1). 01. Also the name of the AI-Robot city in the Animatrix short, The Second Renaissance, Zero One (01).

[@frankyboy1131]

That Big-X-trick is actually what is taught as 'vedic maths' in some YT videos for multiplying two two-digit numbers close to 100. To do that, just turn it clockwise for 90 degrees, and proceed basically in the same way. 86 × 93 | | -14 -7 ≈====== 79 79 (= 86-7 = 93-14) -14 × -7 = 98 Result is 79×100 + 98 = 7998 100-14)×(100-7) 7900=100×100 -14×100-7×100. 98 is 14×7. There are also other shortcuts to multiply two-digit numbers of a special pattern, such as 84×89 (same tens digit) 83×38 (same ciphers, switched) 47×47 (squares) 35×55 (unit digit=5) 54× 61 (tens close to 50), etc.

[@neilwoller]

Another fantastic video, Brady. You are a fantastic interviewer.

[@riadsouissi]

chiffre, cypher, zero, etc all originate from the same arabic word, صفر , or sifr, which means empty.

[@waddupbro]

Please have Domotro from Combo Class appear sometime 🙏

[@wyattstevens8574]

"Heeey, welcome to Combo Classss... *dives for a falling clock* I'm your teacher, Domotro..."

[@Kwauhn.]

I would love to see him just talking about math in a semi-casual setting without the chaotic character and set pieces. Not saying I don't like those, though, just that it'd be nice to see him under the Numberphile format.

[@YonDivi]

That'd be so fun

[@tomkandy]

Nottingham uni might take exception to him setting their offices on fire lol

[@ND62511]

I second this, he would make a great addition to the Numberphile cast!

[@robertolson7304]

The cipher is when you overlay the base numbers. Like 1/0 and 1/1. You can do amazing things with that. The 1/1 sets the rule it is always a whole number. 1/2 and 1/0 set the rule that its binary. The remainders are always half of 2. There's more, but it gets complex quickly.

[@diptasmathacademy]

I love this strategies wish I learn this multiplication strategies in elementary school. I love this stretegies

[@bigsarge2085]

Ten without the one, what an insult!

[@alpardal]

In portuguese we have the expression "zero à esquerda" ("a zero on the left"), which is an insult meaning you are useless

[@steveb1243]

"the multiplication sign" is such a mouthful when referring to the symbol. I might edit Wikipedia and note that Numberphile viewers have long referred to it as a "haran". It might catch on.

[@Dreamprism]

🤯 Very enlightening on the times sign notation. And I'm reading in the comments about the equals sign notation too.

[@cristianseres1353]

The multiplication symbol in Finland is an interpunct or a middle dot ( · ) and this probably applies to Germany as well. We use a non-breaking space as a thousand separator and a comma as a decimal separator so there is no risk of confusion. Apparently all this is according to the SI system. 1 000,45 · 123,45 ≈ 123 456

[@phizc]

We use the same in Norway.

[@Wolfram47]

“even if you’re a 10, you’re nothing without sum 1” - Shakespeare.

[@MichaelLoda]

Well that's the most fascinating I've watched this week

[@sarahgargani5836]

The book was published in 1542. Henry the 8th split with the catholic church in about 1530 (he started trying to leave Catherine of Aragon in 1527 and it took a couple of years for him to see the church as an enemy in this endeavor.). If England was significantly behind in Mathematics in 1542, the schism can only have been a small part.

[@unvergebeneid]

Oh so is this why the multiplication symbol is × in English-speaking countries whereas a centre dot is used in some other countries?

[@fphenix]

Who noticed the 9 in the 6s line?

[@YayComity]

Could that be very strange kind of historical typo? ...the printing press glyph for a 6 being laid out upside down and not caught until publication when it was too costly to reprint?

[@Kyle-nm1kh]

Stamp was upside down

[@RFC3514]

It's a Parker 6. It's the right way up if you're Australian.

[@jesusthroughmary]

It's called The Ground of Arts because arithmetic is the first of the four mathematical arts (the Quadrivium, which along with the Trivium make up the seven classical liberal arts).

[@deltalima6703]

Why not list the others?

[@peterk822]

@@deltalima6703 Wikipedia

[@jesusthroughmary]

@deltalima6703 why list them, but ok The Trivium is grammar, logic and rhetoric, and the Quadrivium is arithmetic, geometry, music and astronomy.

[@Peterseli3]

I'm Dutch and we use ''cijfer'' and it means digit or number.

[@macronencer]

When I saw the thumbnail, I assumed this would be about the trick for multiplying two 2-digit numbers :)

[@targetrbi]

This knowledge has been familiar to us in India for over a thousand years, and it's only now that the rest of the world is coming to appreciate it. This we can use for numbers which are close to 100,1000,10000 also.

[@chiquiramser9421]

Muchas bendiciones para usted y sus familias mucha hracias❤❤❤❤

[@fredg8328]

The common explanation is that the english "cypher", comes from the french "chiffre", which in turn comes from the arabic "sifr" which was thought to mean zero. Because we started to use indo-arabic numbers in Europe after translating arabic books.

[@whig01]

If Zero were a number, you would be able to divide by it. It has some but not all the properties of numbers. We treat it as a number, as with negative and complex values, but these are structures.

[@whig01]

If someone insists there are many kinds of numbers, then that is a terminology which needs refining to natural and unnatural.

[@mcmnky]

Is "being able to divide by it" part of the definition of a number?

[@whig01]

@@mcmnky As I said, you can insist there are many kinds of numbers, but then you have to still distinguish natural and unnatural. Yes, you can divide by a natural number. Always.

[@whig01]

On the other hand, I can also create extended matrices and call them numbers, as complex numbers are representable as a 2x2 matrix for instance. And division becomes problematic or impossible, but these are really structures, as I said.

[@oportbis]

People in the XVIth century: How to multiply two one-digit numbers? Robert Recorde: So start by multiplying two one-digit numbers

[@fahrenheit2101]

In fairness, memorizing wasnt a fun idea, and it still simplifies the problem, provided the 1 digit numbers are larger than 5...

[@timseguine2]

This prompted be to look up how to do arithmetic with roman numerals. It actually isn't as hard as I would have expected. And now I know how to do it if I ever have to go back in time to the early 16th century.

[@Frederic_Beatrix]

The arithmetic of fencing could be a reference to "Trattato di Scientia d'Arme, con un Dialogo di Filosofia" form Camillio Agrippa who describes a "mathematical " way of fencing. Later developed by Gerard Thibault d'Anvers in l'Académie de l'Epee that you presented on Objectivity channel.

[@danielbible3654]

I always thought that the multiplication x was the + from addition shifted, because multiplication is just repeated addition. Just like the division symbol is just the subtraction symbol with two dots, because division is just repeated subtraction. But that's just my opinion. I could be wrong, but it seems logical to me.

[@the_eternal_student]

I have not read the book about Shakespeare and numbers, but one thing you would want to include and speaking of King Lear is when the fool asks " Can nothing be made of nothing." And Lear says, no fool. nothing can be made of nothing. Most websites of favorite quotes from King Lear only include the quote from the exchange between Cordelia and Lear says something like, what will you speak?, and Cordelia says, nothing and be silent. And lear says, come now. nothing will come of nothing, speak again.

[@JohnDlugosz]

1:07 This book is introducing Indio-Aribic numerals, but note that it already uses page numbers! The table explaining numerals and positional notation is on page 23. What were Britons using before? I suppose Roman numerals from the Roman influence, but what did they use before that?

[@TomRocksMaths]

HI ROB!

[@boerhae]

26 x 11 left side 26 over 11 right side -16 over -1 -16 x -1 = 16 26 - -1 OR 11 - -16 = 27 27 tens = 270 + 16 ones = 16 = 286

[@justb4116]

10x26 + 26 And if insisting on the big X, maybe 20 instead of 10? 26 -6 =20 11 +9 =20 20(17) - 54= 340-40-14 =286

[@arpitkumargahlot]

This is one of the Sutras in Vedic Mathematics by Sri Bharti Krishna Tirtha Ji. While this work is more recent, this method can be traced back in ancient Indian arithmetic.

[@frederickbernet6689]

I love love love videos about maths history.

[@MattSeremet]

I'm loving hearing about these people who are famous for other things having a passion for math.

[@bhatkrishnakishor]

That 8x7 method is also applicable to any number. This method is from Vedic Maths.

[@ZaherHamiyah]

it came from france bcoz the origin was from Adalosiya where arabs pronounced it (seefer = صفر) and written by the french cipher not something myterious or code.

[@puyaa3000]

I believe, the word Cipher, is actually the Arabic word for zero "Sifr", and since the number entered by translation of Arabic literatures to Latin and then to English I think this is a more plausible origin. Please let the professor know about this.

[@CheeseAlarm]

More videos on the history of maths please! (But not, of course, less of everything else)

[@msolec2000]

Recorde also invented the equals sign, saying what could be more equal than two parallel lines of the same length.

[@schemen974]

This is so fascinating!

[@jaromir_kovar]

Of course I've checked the wiki page right away and although Oughtred is credited, the proposed origin of the symbol is not there (yet) 😊

[@Bouwentjes]

“Cijfer” is a Dutch synonym for “getal” which translates as “number” in English. Cijfer and number are basically the same. Pronunciation is even almost the same

[@muhammetboran8782]

Now I know why 0 (zero) is called "sıfır" in Turkish. (Because the Turkish pronunciation of the word "sifir" is very similar to the English word "cipher".)

[@noncompliant4316]

Robert Recorde also invented the = sign in another book, "The Whetstone of Witte" in 1557.

[@emilellenius]

The big X method is actually great for doing the ~12 to ~20 times tables in your head since most people know up to 10-12 by heart! I tried it on 19×19 for example

[@Kyle-nm1kh]

There are faster techniques. 19x19 for example is just 19x20-19=19x2x10-19=380-19=380-20+1=361

[@Kyle-nm1kh]

You can also go 9x9+10x10+9x10+10x9. Which is 81+100+90+90=361

[@emilellenius]

@@Kyle-nm1kh I think -9×-9+10×(19-(-9))=81+280=361 is quite fast too. And while there are faster techniques for each specific case, this method would be quite fast up to the 20 times table while still being general.

[@Kyle-nm1kh]

@emilellenius I don't think it's faster and I don't think it's simpler and I think it's harder to do in your head too. I don't see a practical use for it outside of teaching.

[@jb76489]

I’d be really interested to learn the history of orders of magnitude like million billion etc. Specifically when the average person on the street became familiar with the concept

[@criskity]

I wonder if "cipher" is where the word "zip" for zero came from.

[@Bacopa68]

Maybe, but then where'd "zilch" come from? For readers not from the US, "zilch" is a slang word for nothing. There is even the phrase "zip, zilch, nada" to mean "nothing". Of course, "nada" is from Spanish.

[@awandererfromys1680]

12:32 It's not in the movie because it's a stage line, it's exposition for the audience. You can't fit a lot of people on stage so the audience is regularly told here's a multitude of people just off-stage to the left, use your imagination. In a movie you can just show that multitude. A lot of text gets skipped when adapting a stage play to a movie because it's considered 'scene,' not 'dialogue.'

[@davidmilhouscarter8198]

0:47 I like the Early Modern English words and spelling.

[@ErikRyde]

More math history videos please

[@yabgu79]

I did not know this trick. Issue is I invented something similar to that to do multiplications. It really keeps things simpler,

[@f_vandenbroucke]

In Dutch numbers are called 'cijfers'

[@SG2048-meta]

Great video! (Not like I’ve watched it all the way through yet)

[@rudranil-c]

I am not an expert, but looks like techniques inspired by ancient Vedic math in India. Vedic math students may confirm if that's the case.

[@bhatkrishnakishor]

Yes

[@boerhae]

is there a reasonable way to do this for larger numbers? 603 x 367 left side: 603 over 367 right side: -593 over -357 multiply right side. i don't know how to do that in my head and getting a calculator seems to defeat the purpose. could i just do the process again? it just went in a loop when i tried. -593 x -357 left side: -593 x -357 right side: 603 x 367

[@alan2here]

(95 * 97) --> ((100 - 95, 100 - 97) = (5, 3), (5 * 3 = 15), (95 - 3) = 92) --> (92, 15) --> 9215

[@alan2here]

def multiply2(A : int, B : int, C : int): X = C - B return (A - X) * C + (C - A) * X # if C is a power of 2 then "(…) * C" # could instead be a bit-shift operation N, M = 58, 65 similar = 64 print("" + N + " times " + M + " = " + multiply2(N, M, similar))

I prefer the fingers multiplication. Assume you know your tables up to 5×5=25 You start with the closed fists. A closed fist means five. Six, one raised finger; seven, two raise fingers and so on. So, if you want to do 8 times 7 in one hand you raise 3 fingers and on the other one 2. And what is the result? Well, for the tens, you add the raised fingers: 3+2=5. For the units, you multiply the NON raised fingers: 2×3=6. So, 50+6=56. Let's try 8 times 9. 3 raised fingers and 4 raised fingers, ok? 3+4=7. 2×1=2. 70+2=72. What about 7 times 5? 2 raised fingers and NO raised one. 2+0=2. 3×5=15. 20+15=35. Demonstration is left as an exercise for the lector.

[@jimbobago]

Google Books has a version of "Ground of Arts" but this section is on page 102 in that version instead of 71 as in this video.

[@jansenart0]

The Bard had BARS!

[@MusicEngineeer]

In German, we have the word "Ziffer" which means "digit". I wonder, if there's some etymological connection to the "cipher". Maybe the rationale was like: "OK - we have the digits 1..9 but hey, here should be a digit in this position but there is none, so let's just use the general word for "digit" as placeholder for an "empty" digit" ...or something....wild speculation As someone who is interested in the intersection of math and art, I like the title of the book

[@calholli]

How am I just now hearing of your other channel?? WTF. I feel left out

[@numberphile]

Well get to work - kzbin.info - and tell your friends...

[@devttyUSB0]

This was fun! Thanks!

[@NealJennings]

10:00 "that's not like the official story on Wikipedia…" Three weeks into the future it appears that it now is, with this video cited as the reference! ❤

[@SolinoOruki]

It seems they don't know this, but the Arabic (& Turkish & Persian & Indian...) word for zero is Sifr, and that's probably why "Cipher" was the word used to describe it, as alp these number systems came from Arabic numerals and mathematics.

[@azrobbins01]

Brady, do you have a link to the clip with you and the King?

[@Taricus]

The one where it says: Brag.: A most fine Figure Boy: To prove you a Cypher The figure part is capitalized, because back then the numbers were called figures and all the ones except cypher were signifying figures. So, Brag. sets the metaphor up and the boy finishes it, by saying he wishes to prove he can aggrandize life for his love. It is the same as when the Foole talks to King Lear and says, "now thou art an O without a figure, I am better than thou art now, I am a foole, thou art nothing." A zero without any other number is nothing, so an O without a figure. It's even more biting, because he called him "thou," instead of using "you" for royalty. He was saying, "I am above you and I am common," using that personal pronoun and referencing an O with no other number.

[@robertfallows1054]

Pretty crazy. Gutenberg invents the printing press 1440 and 100 years later a handbook for arithmetic. Knowledge being spread - maybe not quickly but nevertheless. Question is - who could read it?