101 Mathematical Trivia

1. In 1988, Nicolas Slonimsky (1894-1995) invented a method of beating a different rhythm with each arm–created a new composition by identifying each note in Beethoven’s Fifth Symphony with a number, and then playing the square root of each note.

2. The symbol for infinity (∞) was used by the Romans to represent 1000.


3. All palindromes with even number of digits are divisible by 11.

4. The earliest evidence of a numerical recording device is a section of a fibula of a baboon, with 29 visible notches, dated to about 35000 BC, from a cave in the Lebombo mountains on the borders of Swaziland in Southern Africa.

5. The number 365 is equal to the sum of three consecutive squares and two consecutive squares in which the five squares are also consecutive.

365 = 102 + 112 + 122 = 132 + 142

6. £12 12 shillings 8 pence = 12128 farthings

7. Interesting number relationships:

12 + 42 + 62 + 72 = 22 + 32 + 52 + 82 = 102

1 + 4 + 6 + 7 = 2 + 3 + 5 + 8 = 18

8. Each fraction of the following equation contains all the digits 1 through 9 only once.


9. There are 293 ways to make change for a $1 using pennies, nickels, dimes quarters and half-dollars.


10. 13177388 = 71 + 73 + 71 + 77 + 77 + 73 + 78 + 78

11. 169 is equal to 132 and its reverse 961 is equal to 312.

12. 206156734 = 26824404 + 153656394 + 187967604. This is an integer solution for the equation w4 = x4 + y4 + z4 found by Noam Elkies.

20. 32768=\frac{(3-2+7)^6}{8}

21. A tablet from Susa, dating from the period 1900-1650 BC, uses the Pythagorean theorem to find the circumradius of a triangle whose sides are 50, 50, 60. Pythagoras himself lived in the sixth century BC.

22. 8114118 is a palindrome and the 8114118th prime, 143787341, is also a palindrome.

23. If you concatenate all the palindromes from 1 to 101, the number produced would be prime! In other words, the number 123456789112233445566778899101 is prime.

24. Perfect squares are the only numbers with an odd number of divisors.

perfect squares.png

Perfect Squares

25. From 0 to 1000, only the number “one thousand” has the letter “A”.

26. Saint Hubert is the patron saint of mathematicians.

27. e^\frac{1}{\sqrt 2}\approx 2

28. When the English mathematician Augustus de Morgan was asked for his age, he would reply, “I was x years of age in the year x²” (He was 43 in 1849)

augustus de morgan.jpg

Augustus de Morgan

29. 14641 = (1 + 4 + 6)4 × 1

30. There is only one long division extant in the entire corpus of Greek mathematics.

31. Newton is on record as speaking only once when a member of parliament, to ask that a window be opened.

32. Newton’s annotated copy of Barrow’s Euclid was sold at auction in 1920 for five shillings. Shortly thereafter, it appeared in a dealer’s catalog marked as £500.

isaac newton.jpg

Isaac Newton

33.  The square of 204 is equal to the sum of consecutive cubes 23, 24 and 25.

34. A knight’s tour order-8 magic square has been proven to not exist.

35. 1666666666661 is the smallest prime number which contains 11 6’s and it’s palindromic too!

36. 22273 is the largest prime in the Bible and it’s aptly in Number 3:43.

37. Except for 2 and 3, if you add and subtract 1 to any prime number, one of the results is always divisible by 6.

38. 19683=1\times(9-6)^8\times3

39. The Chinese were the first who used negative numbers around 2200 years ago or maybe even earlier.

40. Cardan (1501-1576) described negative numbers as “fictions” and their square roots as “sophistic”, and a complex root of a quadratic, which he had calculated, as being “as subtle that it is useless”.

41. If A+B+C=180^\circ, then \tan a+\tan b+\tan c=(\tan a)(\tan b)(\tan c).

42. -40 °C is equal to -40 °F.



43. Aside from 144 being the only square Fibonacci number. It is also the 12th Fibonacci number. Note that 12 is the square root of 144.


44. (9999998+0000001)2 = 99999980000001

45. In chess, there are 4897256 total possible positions after 5 moves by both players.

46. 165033 = 163 + 503 + 333

47. The probability that the thirteenth day of the month being Friday is the highest.

48. Richard Recorde is credited with inventing the equal sign (=) in 1557.

49. 3864 = 3 × (-8 + 64)

50. 26364=26^3\times \frac{6}{4}

51. There is a combination of 26,830 possible Tic-tac-toe games, excluding reflections and rotations.

tic tac to.png

52. 2646798=2^1+6^2+4^3+6^4+7^5+9^6+8^7

53. Every odd number contains the letter “e” in the English language.

54. 6455=(6^4-5)\times 5

55. There are 40320 minutes or 8! minutes in 4 weeks.

56. There are 3628800 seconds or 10! seconds in 6 weeks.

57. 3! × 5! × 7! = 6! × 7! = 10!

58. 15642=1+5^6+4^2

59. 28671=\left (\frac{2}{8} \right )^{-6}\times7-1

60. Given any four consecutive Fibonacci numbers w, x, y and z, yz – wx forms the hypotenuse, and 2xy and wz form the two other sides of the right triangle.

61. 40585 = 4! + 0! + 5! + 8! + 5!. This is the largest number in base 10 that is the sum of the factorials of its digits. the only others are 1, 2 and 145.

62. 48625=4^5+8^2+6^6+2^8+5^4

63. 343=(3+4)^3

64. The polar diameter of the Earth is approximately equal to half a billion inches, accurate to 0.1%.


65. 216 = 65536 might be the only power of 2 in base 10 that does not contain any digit that is a power of two, i.e., 1, 2, 4 or 8.

66. 241=\frac{(2^8 + 4^8 + 1^8)}{(2^4 + 4^4 + 1^4)}

67. Aside from 0 and 1, 82000 (in base 10) is the only number that can be expressed with 0’s and 1’s in bases 2, 3, 4 and 5.

820002 = 10100000001010000
820003 = 11011111001
820004 = 110001100
820005 = 10111000

68. 122 × 213 = 25986. Interestingly, if you reverse 122 and 213, their product would also be the reverse of 25986.

221 × 312 = 68952

69. While we use the base 10 number system (decimal), the Mayans counted by 20’s (vigesimal).

mayan numeral.png

Mayan Numeral

70. The product of two primes can never be a perfect square.

71. 63945 = 63 × (-9 + 45)

72. The sum of any 14 consecutive Fibonacci numbers is divisible by 29.

73. the difference between the time of a sundial and a standard clock is called “the equation of time”.

74. People back then believe that the number of grains of sand is limitless. However, Archimedes argued in The Sand Reckoner that the number of grains of sand is not infinite. He then gave a method for calculating the highest number of grains of sand that can fit into the universe, which was approximately 1063 grains of sand in his calculation.



75. Curiously, the number of nucleons in the observable universe of roughly the Hubble universe is approximately 1080 (this is also known as the Eddington number). Archimedes’ 1063 grains of sand is approximately equivalent to 1080 nucleons.

76. It is impossible to square the circle since the area of the circle is based on π, which is a transcendental number. Therefore, a person who obsessively insists on “squaring the circle” is said to be suffering from morbus cyclometricus.

77. The mathematician G. H. Hardy doesn’t like mirrors. He even covered the mirrors in any hotel rooms that he entered.

G. H. Hardy.jpg

G. H. Hardy

78. 999 is the largest number that can be formed by using three digits without the use of any other symbols. It consists of 369693100 digits!

79. 1285=(1+2^8)\times5

80. 27 × 594 = 16038. This is the only solution for a pandigital multiplication with a pattern of 2, 3 and 5 digits in this form. Also, notice that 27 is a factor of 594.

81. If you multiply all the divisors of 48 together, it would yield 484.

82. 34425 = 34 × 425

83. 1023 – 23 is the largest 23-digit prime. It is equal to 99999999999999999999977.

84. 45632=-4^5+6^{({3\times 2})}

85. 121 and 4 are the only squares that become cubes when increased by 4 (Discovered by Fermat).

121 + 4 = 53; 4 + 4 = 23

86. The first seven digits of the golden ratio (1618033) concatenated is prime!


87. \left (\frac{5}{8} \right )^2+\frac{3}{8}=\left (\frac{3}{8} \right )^2+\frac{5}{8}

88. 7 x 11 x 13 x 17 x 19 = 323323. The product of five consecutive primes yielding a palindrome.

89. Moreover, using the same five consecutive prime numbers, the sum of their squares is also a palindromic number!

 72 + 112 + 132 + 172 + 192 = 989

90. Some mathematical celebrations: March 14 – Pi Day; June 28 – Tau Day; October 10 – Metric Day.

91. If you stack one dollar bills equivalent to the approximate debt of the U.S. government, then the dollar bills would reach the moon five times over!



92. The symbol for division (÷) is called obelus.

93. On the other hand, the division slash (/) is called virgule.

94. When you multiply 21978 by 4, the product is the reversal of the number.

21978 × 4 = 87912

95. Negative numbers don’t have logarithms.

96. 987 × (9 + 8 + 7) + 1 and 987 × (9 + 8 + 7) – 1 are both primes. This is the only 3-digit number with consecutive descending digits that has this property.

97. 18 is the only number that is twice the sum of its digits. (18: 1 + 8 = 9: 9 × 2 = 18)

98. 11 is the only palindromic prime with an even number of digits.

99. The Babylonian mile is approximately equal to 11.3 km (about 7 miles).

100. 736=7+3^6

101. 9893941210243728=98939412^2+10243728^2

Posted by

My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. You can find me on Twitter` and Facebook. My email is edmarklaw@learnfunfacts.com

137 thoughts on “101 Mathematical Trivia

  1. I’ve always been fascinated by numbers. Came by to thank you for liking my review of an Irish singer’s concert and couldn’t resist this! I was born on 2/11/41 (in dd/mm/yy format), Married on 18/9/63 so my 18th wedding anniversary occurred on 18/9/81. All three dates reduce to 9 by adding digits. (As did my 9th, 27th and 36th anniversaries and all birthdays divisible by 9 during the 20th century.)

    Liked by 1 person

  2. Thanks Mark for sharing these important pieces of information. Upon these numbers our nation’s we’re built!

    Although Math wasn’t my strong suit, I can appreciate the time and delivery you bring to make the subject inviting.

    It also is proof that it is a subject that is needed to be taken seriously, and in fact, fun💕

    Liked by 1 person

  3. Fascinating, and exhausting! My working experience with math has centered on differential equations for simulating physical phenomena for engineering purposes. My personal interest was always to find an analytical, as opposed to numerical, solution to a problem. Not always possible, of course, but more often possible than most technical people have been willing to believe since the explosion of computer use (>~1970s).

    Liked by 1 person

  4. “32. Newton’s annotated copy of Barrow’s Euclid was sold at auction in 1920 for five shillings. Shortly thereafter, it appeared in a dealer’s catalog marked as £500.”

    Fascinating, but not so surprising when you consider that a “Cheeto shaped like slain gorilla Harambe sells for $99,900 on eBay”

    Imagine what we could get for Newton’s book today, on ebay?

    (Probably less the five bucks.)

    Liked by 2 people

  5. Reminds me of some of the stuff my 7th grade algebra teacher would throw at us:
    (a-x)(b-x)(c-x) … (z-x) = ?

    Here’s a cheap trick: Choose a three-digit number (abc) where every variable represents a single digit 0 through 9. Reverse the digits and subtract the smaller from the larger.
    abc-cba = def
    Reverse the digits and add them to the result:
    def+fed = ????
    The answer is always 1089.

    Liked by 3 people

      1. Heh. So did I. Occasionally when the neighbor hood kids were around, I’d do a bit of card manipulation, mostly forces and palming. Then I’d hand one some sidewalk chalk and run the number trick. Once they’d finished I’d take of my shoe and show them the 1089 on the bottom of my sock.

        Liked by 2 people

      2. Card manipulation? Do you mean stuff like multiple back palms and fan productions? I only did close up and occasionally parlor magic so I didn’t learn them that much. The only reason I learned back palming was to do Chad Long’s “The Wall”.

        For palming routines, I always got great reactions with Card to Wallet, Cards Across, and the Homing Card. Oh, the one from Expert at the Card Table called Card through Handkerchief is pretty good as Well.

        Liked by 2 people

      3. I couldn’t handle back palming with cards, so I used false and hidden cuts and shuffles with finger breaks. Adding different flourishes, I could do the same trick several times.

        I can vanish a quarter, show both hands empty and flip them over and back, but the move looks unnatural. I used it with a slide gaffe. “Mark up the quarter with this Sharpie, show it around and give it back.” Then you vanish it, dump it in the slide on your belt and produce the box in a box in a box gaffe as fast as you can and let them undo all the rubberbands to find the marked quarter.

        Liked by 2 people

      4. Harry Lorayne has stated many times that to do great card magic, all you need is aa good card control (this includes force and false shuffles), double lift and a good palming technique. Form there, you can build lots of routines. If you can do culling and the perfect faro as well, then you can do miracles with cards…

        That’s why I prefer “sleeving” the coin or using a pull for vanishing a coin. Spectators aren’t that stupid to not figure out that the coin is still in your hands. This is an issue many magicians don’t want to talk about. Though as David Roth said, a good vanish (personally, I prefer the retention vanish) together with a good routine can cover this issue.

        I also have that gimmick but I hadn’t used it that much professionally since I didn’t like to bring a lot of stuff during performances. Nonetheless, I like to do marked coin to impossible location routine. Sometimes, I would do a marked coin to spectator’s pocket, butyou need a lot of guts and misdirection when you do it. The first few times that I did it, I was caught many times. It took me several failures before I could do it without getting busted…

        Liked by 2 people

    1. I learned #42 from a teacher when he taught us the C to F and F to C conversion. Using this relationship, I was able to derive a simpler formula for the conversions. I’m not sure if the formula already exists since so far, I wasn’t able to find it in other references (all I could find is the standard formula), though I highly suspect that someone else has already thought of that first…

      For #91, I only heard it from the radio a few days ago and I think that the anology was quite amusing.

      Liked by 1 person

    1. Thanks!

      Your question piqued my curiosity so I did some calculations to see.

      It can be generalized. His age was was 43 in year 43^2 (or 1849). So he was born in 1806. The next is 44^2 – 44 = 1936 – 44 = 1892.

      The closest to our time is 45^2 – 45 = 2025 – 45 = 1980. So if you’re born in 1980, then you can use that statement. :)

      Liked by 2 people

  6. I had to work overtime studying algebra and trigonometry for 1 year to be inspired again. Books by James Stewart give people the opportunity to read mathematics to prepare to do proofs. Someday I want to work on writing proofs for problems in elementary geometry. Knowing the original thoughts that created the rational world is important to me. I fail to be creative without knowing the most basic ideas.

    Liked by 2 people

    1. Interesting. I mostly do number theory and combinatorics since those are my specializations. So my research projdcts center around them.

      I’m not that good at non-Euclidean geometries since I haven’t studied them that much though I’ve no problem with Euclidean.

      For me, the relevance of elementary geometry lies on the fact that it offers the introduction of mathematical proofs to most people (there are exception of cource, for example, I was introduced to proofs in Number Theory).

      While there are still many research opportunities and open problems in number theory and combinatorics, a lot of people consider that there is nothing more to prove in elementary Euclidean geometry and the focus should be pun in non-Euclidean geometry like hyperbolic geometry and Riemannian geometry. However, that’s what they said during the 20th century but tbere were still some new theorems in that period. So, who knows, if you get lucky, you might find some new theorems too in elem. geometry :)

      Anyway, are you familiar with real analysis and complex analysis? They are quite rigorous and proof-heavy subjects.

      Liked by 2 people

      1. I have heard of them and I have know students that studied them, but I have not studied them. I have used set theory. I was once a computer science student, so my interest was solving problems, my appreciation for mathematics is to have the knowledge and to know the facts that are required to solve engineering problems.

        Liked by 2 people

      2. Ah, ok.

        I’m not that good at programming. I only know Python, Matlab and a bit of Mathematica which I use for solving number theory problems. As for modeling and making simulations, I don’t have much knowledge about them…

        Liked by 1 person

      3. In particular, you will find the following excerpt from Wikipedia very illuminating:

        Mathematical set theory versus musical set theory[edit]
        Although musical set theory is often thought to involve the application of mathematical set theory to music, there are numerous differences between the methods and terminology of the two. For example, musicians use the terms transposition and inversion where mathematicians would use translation and reflection. Furthermore, where musical set theory refers to ordered sets, mathematics would normally refer to tuples or sequences (though mathematics does speak of ordered sets, and although these can be seen to include the musical kind in some sense, they are far more involved).
        Moreover, musical set theory is more closely related to group theory and combinatorics than to mathematical set theory, which concerns itself with such matters as, for example, various sizes of infinitely large sets. In combinatorics, an unordered subset of n objects, such as pitch classes, is called a combination, and an ordered subset a permutation. Musical set theory is best regarded as a field that is not so much related to mathematical set theory, as an application of combinatorics to music theory with its own vocabulary. The main connection to mathematical set theory is the use of the vocabulary of set theory to talk about finite sets.

        Liked by 1 person

    1. Hello Edmark, I agree with Daniella here about a job well done! Thank you very much for your effort indeed!
      As far as I can discern, trivia 25 is essentially the same as trivia 53 regarding every odd number in English containing the vowel e.
      As a result, either this post needs to be retitled as “100 Mathematical Trivia”, or one more trivia needs to be added to fit the title. :)

      Liked by 1 person

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