Click on the link for my website Crow's Math Class where I have organized the videos. I am currently in the process of organizing the videos. Hope to have it completed soon. Check out what I have so far.
Suprise suprise, a language model is bad at math. Its not built to have logical thinking capabilities, its built to have a conversation and to emulate language. Thats why it can talk about étale cohomology with ease but fails to correctly solve its own algebra test. Thats just not what its built to do. (Which is why the models that are great at math are not language models).
Not really though… wolfram alpha does a great job of displaying answers in many formats and showing the work/rational and while Chat GPT is getting better by the month, it wasn’t to long ago that it thought 9.11 > 9.9
They aren't even the same thing,one is a highly glorified probabilistic search engine and the other is an engine to parse mathematical expressions into computable problems, completely different things. They'll probably integrate an engine like wolfram to chatgpt(its highly probable that such a project already exists),as wolfram is good at computation while gpt is good at parsing the problem(hopefully).
@@tfg601 I mean yes? Chat gpt is getting better but my point was that wolfram alpha already is better. Trying to get chat gpt to solve certain integrals (ex. 1 to inf of ln(x) / (1 + x^2) just fails miserably and there are still more basic problems (though less common) that it can’t solve.
Can you give an example (doesn't have to be practical) where this conversion is necessary? By that I mean: Is there an example where the general form "pops up" naturally (and the standard form does not)?
This is just babysteps, even calculus 1-3 or more advanced maths is baby steps for chatgpt or most LLMs really. I strongly recommend you try math specialized GPTs, if you are surprised by this then youll be mindblown. I like to think about it this way, if there is a book about that topic online, chatgpt has already studied it thousands of times.
@@user-cn6lu7pi3m I am Bangladeshi. But in admission,we,the engeneering aspirant, solve indian writer book's math+ our engeneering question bank. That's why,we can solve hard and tricky question:3
Hi Prof. Crow, I am a fan and a subscriber, so I offer the following with the greatest of respect -- I am so glad that you mentioned signs of grouping symbols, because here is the real issue with these order of operations problems on RU-vid: they are using the symbol for division (the line with the two dots) instead of the actual operator for division. That's right, they are not the same thing. Division is one of the few math operations that has both a symbol and an operator. There are two, and only two operators for division: the venculum (like the line between a numerator and denominator) and the long division box. By definition, these operators function as grouping symbols also. As signs of grouping, any ambiguity as to order of multiplying or dividing is generally removed. I am guessing that the use of the symbol as an operator comes from grade school when we are first learning how to divide - and that works as long as it is understood that only the number in front of the symbol and the number immediately after the symbol are the only operands to be considered. As to the problem here, the answer is definitely 1, as malcolmtaylor pointed out. This is verified by Casio and how they treat the notation. For example, when I enter the problem exactly as written, my Casio fx-991EX Classwiz calculator will automatically put parentheses around the factor 3(2) so that it looks like this: (3(2)). This is the juxtaposition that malcolm is talking about. Here's a quote: "Latest models of EDUCATION APPROVED SCIENTIFIC CALCULATORS Like CASIO, SHARP & CANON used in board exams give higher priority to implicit multiplication or multiplication by juxtaposition." Now, if you enter the problem on the calculator using 3*(2) or 3*2, you will get the answer of 4. Even so, forget about the juxtaposition for a moment and look at the order of operations. Parentheses must be cleared before exponentiation, and both of those before doing multiplication, division, addition, and subtraction. You are absolutely correct in saying that multiplication and division are done in the order they are encountered going from left to right, but what is the first operation that you see in the problem? By order of operations rule, you have to multiply the 3 times the 2 to clear the parentheses, then you must do the exponentiation. This leaves you with 36 divided by 6 divided by 6, which results in an answer of 1. The real problem here is not the math or the order of operations; it is the syntax used in writing the problem. The syntax being used here must generate 1 as the answer because of the precedence given by implicit multiplication . Change the syntax by using explicit multiplication and it must generate the answer of 4. If anyone is interested, just enter "juxtaposition in multiplication" in a search box and you will find any number of entries that talk about and explain the idea and its precedence.
I just did a little investigation. I entered the expression in google, wolfram alpha, and on ti 30x II calculator and all of them gave me an answer of 4. I also found 2 videos with very similar problems. Links are provided below. www.google.com/gasearch?q=6%5E2/3(2)/6&source=sh/x/gs/m2/5#fpstate=ive&vld=cid:4f73abd2,vid:tvjJppmx9Hk,st:0 www.google.com/gasearch?q=6%5E2/3(2)/6&source=sh/x/gs/m2/5#fpstate=ive&vld=cid:fdd744f0,vid:gBd-qYaEWq8,st:0
@@crowsmathclass Yes, I get the same answer of 4 on my TI. Only Casio and the others that are mentioned in my quote seem to pay any attention to the change. By the way, I very much enjoyed your series of videos on applied calculus - you're a great teacher!
This video is a waste of time. It doesn't address the source of the controversy and declares an answer (because I say so). The source of the controversy is that different people use different conventions. The SOLUTION is to understand that it may be ambiguous and write the question more clearly. Personally I feel that the answer is 1, and I think that most people who do a graduate level degree in math/physics/engineering would agree. Here are three videos that actually teach you something rather than just spreading more confusion. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-lLCDca6dYpA.htmlsi=EiaMkC92SJYZEhOD ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-4x-BcYCiKCk.htmlsi=2S8YyB2c0GPftMve ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Q0przEtP19s.htmlsi=ioZYUHrSgI5HleyX
