[9up數學] 五次方程沒有解?

都睇得明嘅

利申：原本唔識

Lm

Ich habe dich auch am dem deutschen Post gesehen

呢個係最後最後講的野
但係我唔會講個proof, 淨係會講下點用, 有興趣睇proof可以睇書

電腦嘅出現已經唔需要解
代入百萬嘅值入去總會搵到最接近嘅解

有closed form最好求返closed form
無closed form(或者closed form太唔efficient)先會走去搞d numerical analysis同埋用理論的方法去睇properties (例如PDE)

想知唔同領域啲勁人嘅故事

1. 純睇圖，odd power function x-> +Infinity 同 x-> -Infinity 會相反，咁中間就會有個位穿過x-axis
2. integer 除完會有機會唔係integer
3. 唔識
4. Take p = 3
5. { a + bsqrt(3)}

3. polynomial 除 polynomial唔一定係polynomial
rational function的除法即係乘個reciprocal

咁都係老生常談

普遍黎講要搵電腦做野，你都係要識果堆野先得
你點解可以唔識條數都可以搵電腦解，係因為有好多野前人種樹做哂野先可以咁


同埋數學呢樣野有時電腦幫唔到手

劉明，得閒再仔細睇

polynomial 除 polynomial唔一定係polynomial
有無例子

(x+1)/x 已經唔係, C[X] 嘅定義係 finite linear combinations of non-negative powers of x, 一個Polynomial除以另一個我地一般叫佢做 rational function, notation係 C(X).

i see 明白

計體積面積點解會用到2，3次方?有冇例子?
中學到而家都唔明學黎有乜用

簡單講
(x-a)(x-b)(x-c)咁樣組成既體積

咁加番實用少少背景資料可以係生產成本/包裝體積等等


但老實講就咁cubic一條式又太簡單無乜實戰性
想apply real world problem都係要d calculus同non linear programming等等

諗起龜sir， 講緊佢最愛嘅Galois Theory

而家喺Mathematics 發展方面，數學家會唔會利用AI，deep learning，幫忙進行hypothesis proofing 同研究運算？

稍為離下題, Computer verification 係數學界而家開始多人發展, 最近有一單幾hit嘅topic, Peter Scholze 用 Lean proof assistant 成功 verify 咗一條出現係佢篇文上面好難嘅 lemma, 呢條 lemma 極之複雜, Scholze 寫完個證明都唔敢肯定係咪正確, computer verification 保證到佢個證明冇出錯

Scholze: I learnt that it can now be possible to take a research paper and just start to explain lemma after lemma to a proof assistant, until you’ve formalized it all! I think this is a landmark achievement.

詳情見： https://xenaproject.wordpress.com/2021/06/05/half-a-year-of-the-liquid-tensor-experiment-amazing-developments/amp/

利申: 唔識condensed math