Update README.md

README.md

@@ -68,64 +68,44 @@ print(generate_response(japanese_math_prompt), "\n")
 ```
 
 ## Example Output
+
+**The math model was trained in english so it defaults to english, but it still understands the question and can translate the answer.
 English: 
 
-  Write a quicksort algorithm in python.
-  
-  ```python
-  def quicksort(arr):
-      if len(arr) <= 1:
-          return arr
-      else:
-          pivot = arr[0]
-          less = [i for i in arr[1:] if i <= pivot]
-          greater = [i for i in arr[1:] if i > pivot]
-          return quicksort(less) + [pivot] + quicksort(greater)
-  
-  arr = [5, 2, 9, 1, 5, 7, 4, 8, 6, 3]
-  print(quicksort(arr))
-  ```
-  
+Explain the proof of Fermat's Last Theorem and its implications in number theory.
+
+Fermat's Last Theorem (FLT) states that there are no non-trivial integer solutions to the equation $x^n + y^n = z^n$ for any integer $n \geq 3$. The proof of FLT was a long-standing problem in number theory, and it was finally proven in 1995 by Andrew Wiles.
+
+The proof of FLT is quite complex and involves many different techniques and ideas from number theory, algebra, and analysis. The main idea behind the proof is to use elliptic curves and modular forms to construct a system of equations that can be used to show that there are no non-trivial integer solutions to the equation $x^n + y^n = z^n$ for any integer $n \geq 3$.
+
+The implications of FLT in number theory are far-reaching. The proof of FLT relies on many different techniques and ideas from number theory, and it has led to the development of new techniques and ideas in the field.
   This is a simple implementation of the quicksort algorithm in python. The function `quicksort` takes an array as input and returns a sorted array. The algorithm works by selecting a pivot element from the array and partitioning the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. The process is then repeated recursively on the sub-arrays until the entire array is sorted. 
 
 Chinese Response:
 
-  用Python写一个快速排序算法
-  
-  ```python
-  def quick_sort(arr):
-      if len(arr) <= 1:
-          return arr
-      else:
-          pivot = arr[0]
-          less = [i for i in arr[1:] if i <= pivot]
-          greater = [i for i in arr[1:] if i > pivot]
-          return quick_sort(less) + [pivot] + quick_sort(greater)
-  
-  arr = [3, 5, 2, 1, 4, 6, 8, 7]
-  print(quick_sort(arr))
-  ```
-  这个程序的时间复杂度为O(nlogn)，空间复杂度为O(n)。 
+  解释费马大定理的证明及其在数论中的意义。
+
+Fermat's Last Theorem (FLT) is a statement in number theory that states that there are no non-trivial integer solutions to the equation $x^n + y^n = z^n$ for any integer $n \geq 3$.
+
+The proof of FLT was a long-standing open problem in mathematics. In 1993, Andrew Wiles, a British mathematician, published a proof of FLT using the techniques of elliptic curves and modular forms.
+
+The proof of FLT is considered one of the most important achievements in mathematics in the 20th century. It is a testament to the power of mathematics and the dedication of mathematicians to solve difficult problems.
+
+The proof of FLT has also had a significant impact on the field of number theory. It has led to the development of new techniques and theorems, and has inspired further research in the field.
+
+In summary, the proof of FLT is a significant achievement in mathematics that has had a profound impact on the field of number theory. It is a testament to the power of mathematics and the dedication of mathematicians 
 
 Japanese Response: 
 
-  Pythonでクイックソートアルゴリズムを書いてください。
-
-  ```python
-  def quicksort(arr):
-      if len(arr) <= 1:
-          return arr
-      pivot = arr[0]
-      left = [x for x in arr[1:] if x < pivot]
-      right = [x for x in arr[1:] if x >= pivot]
-      return quicksort(left) + [pivot] + quicksort(right)
-  
-  print(quicksort([3,6,8,10,1,5,9,2,4,7]))
-  ```
-  
-  このコードはクイックソートアルゴリズムを実装しています。クイックソートは一種の分割と conquers アルゴリズムで、配列を分割し、それぞれの部分配列を再帰的にソートします。
-  
-  この実装では、配列の最初の要素をピボットとして使用します。そして、配列を2つの 
+  フェルマーの最終定理の証明と数論におけるその意義について説明してください。
+
+The Fermat's Last Theorem (FLT) is a statement in number theory that states that there are no non-trivial integer solutions to the equation $a^n + b^n = c^n$ for any positive integer $n$ greater than 2.
+
+The proof of FLT was a long-standing open problem in mathematics. In 1993, Andrew Wiles, a British mathematician, published a proof of FLT using the techniques of elliptic curves and modular forms.
+
+The proof of FLT is considered one of the most important achievements in mathematics in the 20th century. It is a prime example of the power of abstract algebra and number theory in solving difficult problems in mathematics.
+
+The proof of FLT also has implications for other areas of mathematics, such as algebraic geometry and number theory. For example, the proof of FLT relies on the Taniyama-Shimura-Weil conjecture, which states that every elliptic curve is a modular form. This conjecture was proven by Wiles and his collaborators, and it has since been used to prove other theorems