``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105``` ```3^3 + 2^3 + 2^3 2^3 = 8 3^3 = 27 27 + 8 + 8 = 43 >>> math.pow(3,3) + math.pow(2,3) + math.pow(2,3) 43 Before last night, we had the sum of 3 cubes for every integer from 1-100 with the exception of 42. In 1992, Roger Heath-Brown conjectured that all even numbers would have a sum of 3 cubes, this was proven last night for at least 1-100 for the 42. Here is the famous equation:https://pad.yohdah.com/674/the-sum-of-3-cubes-solved-for-42/edit 42 = (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3 Or in python: >>> import math >>> math.pow(-80538738812075974,3) + math.pow(80435758145817515,3) + math.pow(12602123297335631,3) Dad, how do you even get a negative cube? Is it like a black hole??? So we learned the difference between conjecture and proofs. Conjecture is something one or many people think ought to be true, but do not have complete proof, While a Proof is something we have proven to be True! Most proofs in mathmatics start out as Conjecture first, so you should be a thoughtful guy or gal! 3 + 3 = x - 3 what does x equal? 3 + 3 + 3 = x - 3 + 3 3 + 3 + 3 = x - 0 3 + 3 + 3 = x 9 = x 3 + 2 = x + 1 what does x equal? 3 + 2 - 1 = x + 1 - 1 3 + 2 - 1 = x + 0 3 + 2 - 1 = x 5 - 1 = x 4 = x So lets test out our answer, by substituting 4 for x in our original equation. 3 + 2 = x + 1 3 + 2 = 4 + 1 5 = 5 does 5 equal 5, yes? then our answer of x = 4 is CORRECT! So that is algebra! All it means is shifting around an equation to make it easier to ... SOLVE!!! let us pretend we got the answer x = 5, plugging it into the original equation would give us: 3 + 2 = 5 + 1 or 5 = 6 which is absolutely, positively False. 5 cannot equal 6, ever in math. So then we would know out answer was ... WRONG kamahama big blackhole ballha!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! vijetu"ow" ```