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## discovering-new-math-concepts.md

      
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                new-math.md
              
          
    Discovering New Math Concepts Using LLMs: A Step-by-Step Guide

Step 1: Embrace AI's Potential for Innovation in Mathematics

Example Prompts:

"How has AI been previously used to enhance mathematical understanding or discovery?"
"What are the current limitations in our mathematical understanding that AI, especially LLMs, might help address?"

Step 2: Diversify Mathematical Inquiry

Example Prompts:

"Using LLMs, can we list down a variety of mathematical problems or areas that haven't been fully explored?"


## OpenAI_server.js
// Prompt:
// Write a node backend which accepts a .zip file from the JavaScript function in the following backticks:

// (the code in backticks ``` was here: https://gist.github.com/classmember/72ab335223722623af9ed5346e5ed6eb )

const express = require('express');
const multer = require('multer');
const fs = require('fs');

const app = express();

## OpenAI_client.js
// Prompt:
// Write a frontend JavaScript function to upload a .zip file from a chrome extension in a browser to a node backend using express. The code must publish to a POST endpoint over HTTPS.

// Response:
// Note: This code assumes the use of jQuery for the AJAX request

function uploadZipFile(file) {
  let formData = new FormData();
  formData.append('file', file);


## keys.html
<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta http-equiv="X-UA-Compatible" content="IE=edge">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Detecting Key Input</title>

    <!-- http://www.openjs.com/scripts/events/keyboard_shortcuts/shortcut.js -->
    <script src="shortcut.js"></script>

## split.cpp
vector<string> split(const string &str) {
    vector<string> tokens;

    string::size_type start = 0;
    string::size_type end = 0;

    while ((end = str.find(" ", start)) != string::npos) {
        tokens.push_back(str.substr(start, end - start));

        start = end + 1;

## phoneBook.cpp
/**
 * phoneBook.cpp:
 *   Hashmaps in C++ - Kolby Heacock
 *
 * build:
 *   clang++ -std=c++2a test.cpp -o phonebook
 *
 * run:
 *   ./phonebook < input
 *

## fraction.cpp
// fraction.cpp, Kolby Heacock
// Description: A simple fraction class.

#include <iostream>
#include <cmath>
using namespace std;


// Fraction
//   takes two integers as parameters during construction

## vue-markdown-editor.html
<!DOCTYPE html>
<html>
<head>
<script type="text/javascript" src="https://unpkg.com/vue@next"></script>
<script type="text/javascript" src="https://unpkg.com/marked@0.3.6"></script>
<script type="text/javascript" src="https://unpkg.com/lodash@4.16.0"></script>

<title> Markdown </title>
<style>
html,

## roll-20-sided-dice.clj
;; roll-20-sided-dice.clj

;; return a function that rolls a 20 sided dice
(def roll-20-sided-dice
  (fn [] (inc (int (rand 19)))))

;; call function to roll 20 sided dice
(roll-20-sided-dice)

## game.py
"""
Random number guessing game
"""

import sys
from random import randrange
from math import ceil, floor


class NumberGuessingGame:
	// Prompt:
	// Write a node backend which accepts a .zip file from the JavaScript function in the following backticks:

	// (the code in backticks ``` was here: https://gist.github.com/classmember/72ab335223722623af9ed5346e5ed6eb )

	const express = require('express');
	const multer = require('multer');
	const fs = require('fs');

	const app = express();
	// Prompt:
	// Write a frontend JavaScript function to upload a .zip file from a chrome extension in a browser to a node backend using express. The code must publish to a POST endpoint over HTTPS.

	// Response:
	// Note: This code assumes the use of jQuery for the AJAX request

	function uploadZipFile(file) {
	let formData = new FormData();
	formData.append('file', file);
	<!DOCTYPE html>
	<html lang="en">
	<head>
	<meta charset="UTF-8">
	<meta http-equiv="X-UA-Compatible" content="IE=edge">
	<meta name="viewport" content="width=device-width, initial-scale=1.0">
	<title>Detecting Key Input</title>

	<!-- http://www.openjs.com/scripts/events/keyboard_shortcuts/shortcut.js -->
	<script src="shortcut.js"></script>
	vector<string> split(const string &str) {
	vector<string> tokens;

	string::size_type start = 0;
	string::size_type end = 0;

	while ((end = str.find(" ", start)) != string::npos) {
	tokens.push_back(str.substr(start, end - start));

	start = end + 1;
	/**
	* phoneBook.cpp:
	* Hashmaps in C++ - Kolby Heacock
	*
	* build:
	* clang++ -std=c++2a test.cpp -o phonebook
	*
	* run:
	* ./phonebook < input
	*
	// fraction.cpp, Kolby Heacock
	// Description: A simple fraction class.

	#include <iostream>
	#include <cmath>
	using namespace std;


	// Fraction
	// takes two integers as parameters during construction
	<!DOCTYPE html>
	<html>
	<head>
	<script type="text/javascript" src="https://unpkg.com/vue@next"></script>
	<script type="text/javascript" src="https://unpkg.com/marked@0.3.6"></script>
	<script type="text/javascript" src="https://unpkg.com/lodash@4.16.0"></script>

	<title> Markdown </title>
	<style>
	html,
	;; roll-20-sided-dice.clj

	;; return a function that rolls a 20 sided dice
	(def roll-20-sided-dice
	(fn [] (inc (int (rand 19)))))

	;; call function to roll 20 sided dice
	(roll-20-sided-dice)
	"""
	Random number guessing game
	"""

	import sys
	from random import randrange
	from math import ceil, floor


	class NumberGuessingGame: