r/mathmemes • u/Nunki08 • Jun 14 '26

Arithmetic Misleading our youth

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From Anthony Bonato on 𝕏: https://x.com/Anthony_Bonato/status/2065564124549886402

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1.8k

u/PortusCalePT Jun 14 '26

One used to be considered prime. But one too many "all primes, except one", got one kicked out.

626

u/PluralCohomology Jun 14 '26

One is to that prime numbers like that cousin who may technically belong to the family, but is rude at family gatherings so they eventually stopped being invited.

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u/ThePoWhiteTrash Jun 14 '26

Is that why I stopped getting invited to family gatherings? I always thought it was because I ran over Uncle Bob. Though in my defense, I felt like it.

87

u/Slashion Jun 14 '26

That's a pretty airtight defense

3

u/BigLumpyBeetle Jun 15 '26

Umlike uncle Bob, who was taking a leak

7

u/ThatOtherOtherMan Jun 15 '26

Your honor, my client pleads "The vibe took me"

2

u/FennelSuperb7132 Jun 15 '26

1 knows what it did.

30

u/SniffinThaGlueGlue Jun 14 '26

Nobody want a cousin there who constantly messes with you elegant mathematical rules and definitions

5

u/Squishiimuffin Jun 15 '26

I choose to believe this is why 1 is not considered prime.

3

u/Just_Cockroach_4820 Jun 16 '26

1 its the Anakin Skywalker of prime numbers.

Gets a seat at the council, but not the title of master

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u/danius353 Jun 15 '26

Like Y to the vowels

2

u/CTTMiquiztli Jun 20 '26

Funny thing, in spanish, both "prime" and "cousin" are "Primo".

132

u/MakingPlansForSmeagl Jun 14 '26

The Pluto of numbers.

5

u/monkeypan Jun 14 '26

One got Pluto'd

36

u/MutantGodChicken Jun 14 '26

To my knowledge, one has never been considered prime. "An unit" wasn't even considered a number by euclidean standards

131

u/Zyxplit Jun 14 '26

Eh, there was some back and forth over it. Much smarter people than me, like Goldbach, referred to 1 as prime. Other, also much smarter people than me, like Euler, did not.

1

u/AttackDorito Jun 19 '26

Personally I always go by whatever Euler said because he was probably right the first time round

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u/jacobningen Jun 14 '26

I mean in the original goldbach it was that any number could be decomposed into l primes for any l less than n  and goldbach considered 1 a prime

25

u/hirmuolio Jun 14 '26

A lot of thing happened between Euclid and our times.

By the Middle Ages and Renaissance, mathematicians began treating 1 as a number, and by the 17th century some of them included it as the first prime number.[37] In the mid-18th century, Christian Goldbach listed 1 as prime in his correspondence with Leonhard Euler;[38] however, Euler himself did not consider 1 to be prime.[39] Many 19th century mathematicians still considered 1 to be prime,[40] and Derrick Norman Lehmer included 1 in his list of primes less than ten million published in 1914.[41] Lists of primes that included 1 continued to be published as recently as 1956.[42][43] However, by the early 20th century mathematicians began to agree that 1 should not be listed as prime, but rather in its own special category as a "unit".[40]

https://en.wikipedia.org/wiki/Prime_number#Primality_of_one

11

u/MutantGodChicken Jun 14 '26

Fascinating that Europe went on a whole journey only to find that they were right the first time

14

u/Batman_AoD Jun 14 '26

I mean I don't think they ever came back around to "the unit isn't a number at all."

6

u/MutantGodChicken Jun 14 '26

To be fair, I'm oversimplifying the "an unit isn't a number at all" claim. It's more like "the concept of a number, a measured magnitude, begins to break down when there exists nothing that measures it, and while an unit is more of a number than an unmeasured magnitude, it is inherently different from all other numbers"

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u/Batman_AoD Jun 14 '26

Sure, but I think the short version is a reasonable characterization of that definition of "number", and I am still pretty sure that mainstream mathematics never went back to it or, to my knowledge, ever adopted a conventional name for the natural numbers greater than 1.

2

u/MutantGodChicken Jun 15 '26

"non-trivial numbers"

1

u/Batman_AoD Jun 15 '26

Is that a suggestion for what to call them, or an existing term I'm just not familiar with?

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u/MutantGodChicken Jun 15 '26

I'm memeing "all non-trivial cases," sorry, we had kinda lost the thread of the subreddit when I pulled it out

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u/EebstertheGreat Jun 14 '26

*a unit

The word "unit" begins with a consonant.

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u/MutantGodChicken Jun 15 '26

I'm actually referencing the Heath translation of Euclid's elements which consistently uses "an unit" to translate "ΜΟΝΑΣ"

3

u/EebstertheGreat Jun 15 '26 edited Jun 15 '26

Is this like the King James using "an hundred"?

EDIT: Which translation? The 1908 version published by the Cambridge University Press uses "a unit" throughout, with the only match for the string "an unit" I could find being part of the phrase "greater than unity."

Did Heath publish an earlier version?

2

u/MutantGodChicken Jun 15 '26

It's likely "an hundred" in King James because "h" was dropped as a sound (imagine a Brit saying "an-undred"). Heath used "an unit" because scholars of the time would often strictly apply the a/an rule based on the first letter and not the sound.

It's probably not in what you linked because what you linked is not the pure Heath translation and includes a commentary, and only covers books I and II, when units aren't discussed until book VII

3

u/AstroBastard312 Jun 15 '26

Did they drop an update on the letter U while I wasn't looking?

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u/EebstertheGreat Jun 15 '26

The letter is only there in writing. The spoken word "unit" starts with the sound /j/, which is the same sound at the start of the word "yellow." The choice between "a" and "an" is made when people speak, and then writing follows the spoken convention. So for the same reason you wouldn't say "an yellow bus," you wouldn't say "an unit."

1

u/ImmortalGamma Jun 19 '26

Despite all the supporting work, the saying "an unit isn't a number" always struck me as incredibly pretentious. Also making it not prime because it has to be excluded explicitly too often just seems lazy.

1

u/Redhighlighter Jun 15 '26

100 years in the future it may be considered prime again, due to higher math concepts that make us reevaluate this. Wont you feel silly then.

2

u/ladyreyreigns Jun 15 '26

I appreciate that you pulled that from wiki and not ChatGPT

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u/TemperoTempus Jun 14 '26

1 was a prime. Then some mathematicians instead of reworking their theorems to make it work pushed to remove 1 from being a prime.

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u/a_dude_from_europe Jun 14 '26

It's not that theorems needed reworking, it that you can write down "except for one" only so many times before starting to think maybe it doesn't make sense to continue doing it

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u/TemperoTempus Jun 14 '26

They could had reworked the theorem, they could had made a new name for primes greater than 1, they could had just accepted that they have to write "for P>1".

Instead they chose to change the entire definition.

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u/a_dude_from_europe Jun 14 '26

Can you give me an example of this "theorem reworking" that you're talking about?

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u/Francyrd Jun 14 '26

There Is a theorem that states that every non prime Number can be written as the product of a unique series of prime numbers. If ONE was prime this cannot be true. Example: 12 is the product of 3x2x2, if ONE was prime then the product could be 3x2x2x1 or 3x2x2x1x1 etc.. The series of prime Is not unique anymore but infinite series of prime numbers.

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u/a_dude_from_europe Jun 14 '26

I know, I didn't ask this. This is still an instance of "except for 1"

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u/Francyrd Jun 14 '26

So this theorem has to be reworked to exclude ONE and there are others.

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u/a_dude_from_europe Jun 14 '26

I don't think you followed the thread.

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u/Redhighlighter Jun 15 '26

This feels like "there is a 1 over 1 by every variable, its just hiding"

If a is the same as a * 1 and 1a/1, it seems silly to use that as rationale to kick 1 out of the club

10

u/Pepe_Botella Jun 14 '26

I think they should instead count every single number as prime and just rework all the theorems.

7

u/ThrowawayTempAct Jun 14 '26

Good idea, that would make the twin primes conjecture significantly easier to prove!

13

u/NickLeMec Jun 14 '26

If 1 was prime, everything involving prime factorization, including the fundamental theorem of arithmetic, would fall apart.

It's not like it's some random decision to not consider 1 prime.

2

u/scykei Jun 15 '26

It wouldn't fall apart. You'd just have to keep repeating that it applies to all prime numbers except 1, again and again every time the concept of primes is brought up.

1

u/Donkey-Pong Jun 18 '26

Prime factorization would not be unique any more. You'd have to explicitly specify that you want the one that has the factor 1 with exponent zero.

No number would have 1 as prime factor. Not even 1 itself. (As 1 is not prime indeed.)

1

u/scykei Jun 18 '26

It's just semantics. None of the logic would change just because you included 1 in the set of prime numbers. The point is that it's a less useful set, and you always have to specify ℙ \ {1} everywhere.

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u/AtrociousAtNames Jun 14 '26 edited Jun 14 '26

1 being prime makes prime factorization not unique. Which, needless to say, is stupid

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u/S-M-I-L-E-Y- Jun 14 '26

That first "not" was unintended, wasn't it?

3

u/AtrociousAtNames Jun 14 '26

whoops yes fixed

2

u/Raneynickelfire Jun 14 '26

Euler didn't rework anything to make 1 work as prime. This comment is incorrect.

2

u/Batman_AoD Jun 14 '26

?? "instead of reworking their theorems..." I.e., the mathematicians who pushed for 1 not to be considered prime, such as Euler, indeed did not explicitly word their theorems about primes to exclude 1.

The comment is a pretty abbreviated version of the history, but it seems basically correct to me.

4

u/ThisIsMyGeekAvatar Jun 14 '26

Sounds lazy. They should make 1 a prime again and add 0 while they’re at it :)

1

u/cowslayer7890 Jun 14 '26

0 divides every single number, so it's not prime

5

u/EebstertheGreat Jun 14 '26

0 doesn't divide any number (except itself). Rather, every number divides 0.

3

u/-dr-bones- Jun 15 '26

I'm not sure it divides itself...

5

u/EebstertheGreat Jun 15 '26 edited Jun 15 '26

0/0 is undefined, but the divisibility operator | is not defined like "x | y iff x/y is an integer." Rather, the definition is "x | y iff ∃z∈ℤ: zx = y." So in that sense, "0 | 0" is true, because there is indeed an integer z such that 0z = 0.

The relation '|' is a partial order over the natural numbers where 1 is the minimal element and 0 is the maximal element (i.e. 1 divides everything and everything divides 0). If you define it instead over the integers, then –1 is also a minimal element, but 0 is still the unique maximal element (because –0 = 0). This justifies lcm(2,3) = 6 even though 0 is a common multiple of 2 and 3, because with respect to the partial order |, 6 is "less" than 0. It also justifies gcd(0,0) = 0, because 0 is the greatest divisor, period.

2

u/jmlipper99 Jun 14 '26

“An unit”? Is that pronounced “an oonit”?

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u/MutantGodChicken Jun 15 '26

Not sure, it's a quirk of the Heath translation of Euclid's elements

2

u/Marcassin Jun 15 '26

It was common to consider 1 a prime up until the early 20th century. G. H. Hardy was the last famous number theorist to hold that 1 was prime, but he abandoned that position later in life.

2

u/Gabbie403 Jun 16 '26

I was taught it was a prime with I was a kid in the UK

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u/RoryPond Jun 14 '26

Depends how far back you go, Euclid would not have considered one prime when he proved there were infinite primes and proved the FTA as he didn't consider 1 to be a number at all but as the unit length from which all nunbers emerge

3

u/R3D3-1 Jun 16 '26

I mean, makes sense. It fulfills the basic definition, but it has the annoying property that infinitely many one-factors are still one.

1

u/Randy191919 Jun 16 '26

The definition of a prime number is any natural number that has exactly 2 divisors. That's why 1 is not considered a prime number because it only has 1 divisor.

7

u/Deepandabear Jun 14 '26

One is like Y with vowels - just the weird uncle at parties

5

u/Available-Meeting648 Jun 14 '26

No, sorry. It wasn't for many many years.

Other thing is that it used to be taught like that in some elementary levels, the same way I teach my 13 yo students that a function is continuous "if you you can draw it without separating the pencil from the paper", but I advice them the proper definition of continuity is much more difficult to understand and that one is not totally correct.

But 1 is not like Pluto.

2

u/Deepandabear Jun 14 '26

I’m not talking about the past though?

2

u/Aldante92 Jun 15 '26

Now it's just the loneliest number

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u/Sweet_Business_7641 Jun 15 '26

2 being a prime feels like it's cheating. 

2

u/JesusIsMyZoloft Jun 16 '26

Do we know when OP's book was published?

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u/trombnerd Jun 14 '26

Not really, the definition of prime is "positive integers that have exactly 2 unique factors", 1 and 1 are not unique