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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 31mo ago
Replying to
1/6 This week for #MathsMonday I'm going do - again - a #mathematics order of operations proof, but the simple version. 🙂 Last time there were people who were claiming that + and - "can be a binary operator", and I was actually addressing that, but in the process proved that #Maths binary operators have to be solved before #Math unary operators, thus proving the order of operations rules, but this time an arithmetic approach, based on the operator definitions...
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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 4mo ago
Replying to
1/5 #MathsMonday #Maths #Math This week a commonly-forgotten rule of #Mathematics - because we usually skip these lines of working out and go straight to the solution - when we substitute a value for a pronumeral, the value goes in brackets. i.e. if a=3, then 2a=2(3), not 23, because 2a=6, not 23. We can see this explicitly demonstrated on page 36 of Modern Algebra https://archive.org/details/modernalgebrastr01dolc_2 If showing full working out (which Modern Algebra skips) then the next step is to apply...
archive.org

Modern Algebra: Structure and Method - Book 1, Teacher

v. 25 cm

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 4mo ago
Replying to
1/5 #MathsMonday I'm coming back to a point I've covered before, but this time adding #Mathematics textbooks for the sake of completeness, that being the history of what Division meant in #Maths, with emphasis on what it means now in #Math Up until at least the 17th Century everything that followed a division symbol was in the Divisor. We can see that in Teutsche Algebra (1659), on page 76, where 7÷GG+1 means 7÷(GG+1)....
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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 38mo ago
Replying to
1/7 #MathsMonday 1917 (ii) - Lennes' letter (Terms and operators) I've seen many refer to https://www.jstor.org/stable/2972726 as a change in #Mathematics precedence rules, and yet nothing at all actually changed! It does show that 100 years ago though, even then there were people #LoudlyNotUnderstandingThings #Math terms and rules! 😂 On page 93 he says "it is agreed that each symbol applies only to the term immediately following it" which shows he understands #Maths Terms and Left Associativity...
jstor.org

Client Challenge

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 38mo ago
Replying to
1/4 #MathsMonday 1917 (iii) - Terms included in denominator My investigation into (alleged) changes in #Mathematics rules in 1917 started with claims that the number of terms included in the denominator of a #Math expression was changed in 1917 (though I've yet to find any actual evidence of this - let me know if you have a reference for it). Some mentioned Lennes' letter, yet his letter says nothing at all about this! For now, let's assume it's true and see what that would mean for #Maths...
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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 38mo ago
Replying to
1/2 Postscript to Lennes' letter. My understanding of the alleged change to the #Mathematics rules was that /ab+cd was changed from meaning /(ab+cd) to /(ab)+cd. As I said, I could find no evidence of said change. Via another #Maths conversation today I came back to one of the sites which alleged this change to #Math as a result of Lennes' letter, and I suddenly realised what they ACTUALLY meant all along... though it STILL comes down to them not understanding Terms....
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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 38mo ago
Replying to
1/6 #MathsMonday I continue to see people who say that in #Mathematics ab=a*b, and thought of a good #Maths example to illustrate why ab is a single #Math Term (i.e. ab=(a*b))... Let's say I was 2 metres tall (just for the sake of using whole numbers in the example). We write that as 2m - in this case m is short for metres, but it also looks like an algebraic term, right? 🙂 So let's say m is a pronumeral, and in this case m is equal to 1 metre. In other words in both cases, m is the units...
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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 37mo ago
Replying to

1/9 #MathsMonday Today I'm going to talk about adding/removing brackets, for 2 reasons...

  • people prematurely remove them
  • people adding them incorrectly In #Mathematics we have many things which are the opposite of each other - add/subtract, multiply/divide, factorising/expanding - and so it is with brackets in #Math also. This is because if someone has put together an expression from a number, the rules of #Maths have to make sure we follow the exact opposite steps to get the same number...
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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 39mo ago
Replying to
1/7 This week for #MathsMonday we are going to debunk the "implicit multiplication" (IM) claims (and also look at the mnemonics). I say claims, because there is actually no such thing as IM in #Mathematics. I find invariably the people who say there is have forgotten The Distributive Law (TDL) and/or Terms, but most often both! As we have already seen, these are both rules of #Maths, taught in many #Math textbooks, so that right away debunks any claims that "there is no convention in Maths"...
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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 39mo ago
Thread index https://dotnet.social/@SmartmanApps/110897908266416158 Before I say what it is, I am NOT posting this as clickbait (which is how it's often used)! 😂 I'm posting this as a Maths teacher who knows this topic inside-out and wants to help people to understand it better. There are MANY mistakes that people make and get the wrong answer, and I'm going to cover them in bite-size chunks each week for a few weeks So 8÷2(1+3)=? What is the answer (bonus: and WHY is it the answer)? #Maths #Mathematics #MathsMonday
dotnet.social

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 (@SmartmanApps@dotnet.social)

1/4 #MathsMonday Order of operations thread index #Mathematics #Maths #Math Introduction https://dotnet.social/@SmartmanApps/110807192608472798 1 The Distributive Law #DontForgetDistribution https://dotnet.social/@SmartmanApps/110819283738912144 2 Terms #MathsIsNeverAmbiguous https://dotnet.social/@SmartmanApps/110846452267056791 3 Factorising<->The Distributive Law https://dotnet.social/@SmartmanApps/110886637077371439 4 implicit multiplication, mnemonics https://dotnet.social/@SmartmanApps/11

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 39mo ago
Replying to
I was going to start discussing this tonight, but was hoping for some more answers. I guess people don't want to risk a wrong answer in a #Maths teacher's post! 😂 Don't worry - I don't bite! 🙂 This is #Mastodon not the other place. This thread's here to help people learn, and there are MANY mistakes that can be made, and it helps to see some in action. You wanna learn where you might be going wrong with your #Mathematics ? Post here. 😉 I'll check in again tomorrow, and then start explaining
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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 39mo ago
Replying to
@DevWouter@s.poweredbydev.com @mattgoldman@mastodon.social both got the correct answer of 1 - well done! Let's look at the correct working out, then delve into where people go wrong with their #Maths #math 8/2(1+3) =8/(2*1+2*3) =8/(2+6) =8/8 =1 Also acceptable is... 8/2(1+3) =8/2(4) =8/(2*4) =8/8 =1 If you've seen someone say that it's ambiguous, it isn't - we shall see in coming weeks that #MathsIsNeverAmbiguous they have simply forgotten one or more #Mathematics rules First, #DontForgetDistribution the Distributive Law...
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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 37mo ago
Replying to
1/10 This week for #MathsMonday I'm going to talk about #calculators, in particular the current topic of #Mathematics order of operations (which I am nearly finished with now), and e-calculators (I'm looking at you #Developers #Programmers). It's important to know where brackets go in #Maths expressions, and after last week's topic I ran a follow-up poll https://dotnet.social/@SmartmanApps/111145907574869556 to see how many people could remember the #Math FOIL acronym from High School, because I sensed a deeper issue...
dotnet.social

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 (@SmartmanApps@dotnet.social)

#Mathematics #Maths #Math #Poll Do you remember the acronym FOIL from High School? i.e. what it stands for/how to use it Please boost for reach Thank you to those who voted. The result of this is discussed in https://dotnet.social/@SmartmanApps/111145907574869556 (also includes textbook screenshot of what FOIL is 🙂 - it's First, Outside, Inside, Last. i.e. multiply those terms in adjacent brackets in that order) [ ] Yes [ ] I'd forgotten about it... til I saw this poll! [ ] Sounds vaguely f

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 32mo ago
1/6 I have a #MathsMonday #FactFriday cross-over event post for you this week 🙂 The #fact is that #Mathematics is universal. We may use different notation in different countries, but the underlying #Maths is the same everywhere. i.e. there is nothing "arbitrary" about #Math I saw someone question if there might be "different" Maths somewhere else in the universe. No. If I have 1 thing, and I get another thing, I now have 2 things. i.e. 1+1=2 (or your country's notation)...
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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 39mo ago
Replying to
#MathsMonday week 2, Terms. Simply put, in #Mathematics Terms are separated by operators and joined by brackets. The most common example is 2a=(2*a). This makes it simpler to write fractions. e.g. 1/2a rather than 1/(2*a). That also means 1/2a isn't mistaken as half a, which would actually be written as a/2. Notice in the latter that the a is to the left of the division, which means it's in the numerator, and vice-versa for the former (more about this aspect of #Maths #Math later, but first)...
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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @SmartmanApps@dotnet.social
· 38mo ago
Replying to
1/6 #MathsMonday 1917 (part 1) - Left Associativity I have seen many people who argue about this #Mathematics issue that refer to changes in 1917, and I started to research it this week. The #Maths change I thought was made, I have not been able to find any reference for it, and that is about /2(1+3) vs. /2*(1+3). Apparently in pre-1917 #Math the latter was also considered to be a single term (in the denominator) but now is 2 terms. If anyone has a reference for that then please let me know...
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Scott Francis @darkuncle@infosec.exchange
· 4w ago
*sigh* rather than seriously considering the MathAndAI dot org declaration from 28 Fields Medal winners (including Terry Tao), OpenAI just plowed ahead full-steam and released another 372 major results in mathematics around unsolved problems (although the proofs are reportedly nearly impossible to independently understand—but verification via Lean appears to be included for many—and read like the author was stoned). I will tap the sign, once again, even though none of the AI companies are paying any attention. #maths #mathematics
scottaaronson.blog

The Mathocalypse

Updates (Oct. 9): To address some questions that keep coming up… No, I’m not aware of any direct practical implications of any of these results. I certainly don’t expect the O(n l…

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Scott Francis @darkuncle@infosec.exchange
· 4w ago
Replying to
this from Quanta on the topic is a good read: https://www.quantamagazine.org/is-ai-the-end-of-math-as-we-know-it-20261005/ #maths #mathematics
Is AI the End of Math As We Know It? | Quanta Magazine
quantamagazine.org

Is AI the End of Math As We Know It? | Quanta Magazine

Mathematicians are facing the sudden shift with grief, anger, and a desperate search for fresh ideas: “If we don’t adapt, there’s just no more math in 50 years.”

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Fedi.Garden @FediGarden@social.growyourown.services
· 1mo ago
Boosted by @fedicat@pc.cafe
Mathstodon.xyz is a Mastodon server for people who love maths. We have LaTeX rendering in the web interface! We hope there’ll be lots of maths chat, but any topic following the code of conduct is OK. This server has a post size of up to 1729 characters. :Fediverse: https://mathstodon.xyz You can find out more at https://mathstodon.xyz/about or contact the admin account @christianp@mathstodon.xyz#FeaturedServer #Mathematics #Maths #Math #LaTeX #Mastodon #Fediverse #FreeFediverse
Mathstodon
mathstodon.xyz

Mathstodon

A Mastodon instance for maths people. We have LaTeX rendering in the web interface!

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