14. ‘all mathematics is beautiful, yet
some is more beautiful than the
other’
paraphrasing George Orwell
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15. What is the most beautiful formula?
How and Why is it Most Beautiful?
How and why something is Beautiful?
A Few Remarks on Mathematics, Mathematicians,
and Formula…
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16. The moving power of mathematical invention is
not reasoning but imagination.
Augustus de Morgan
Imagination is more important than knowledge.
Albert Einstein
How can it be that mathematics, being after all a
product of human thought independent of experience,
is so admirably adapted to the objects of reality?
Albert Einstein 1612/28/2018
17. There is no branch of mathematics,
however abstract, which may not some
day be applied to phenomena of the real
world.
Nikolai Lobatchevsky.
A mathematician is a blind man in a
dark room looking for a black cat which
isn’t there.
Charles Darwin.
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18. Lt y →xU = 1 ; Buddhahood (enlightened)
y → x is “Human Revolution”,
“Casting off the transient and Revealing the True”.
LIFE
A philosophical Version of the Mathematical Identity
U = x/y y = Bodhisattva, x = true identity
“Yui Butsu, Yo Butsu”
1812/28/2018
20. Does an infinite series necessarily have a finite Answer?
Convergence
S = ?
S = 1+x +x2 +x3+ . . .+xn-1 + xn
S.x= x+ x2 +x3 +. . . + xn +xn+1
S.(1-x) = 1 - xn+1
S = (1 – xn+1)/(1-x)
S => 1/(1-x) [since xn+1 =0 for large n]
Check it using calculator and see the convergence
2012/28/2018
26. ½ ¼ 8
1
16
1
The hare quickly reaches the turtle’s
starting point – but in that same time
The turtle moves ¼ mile ahead.
2612/28/2018
27. ½ ¼ 8
1
16
1
By the time the rabbit reaches the
turtle’s new position, the turtle
has had time to move ahead.
2712/28/2018
28. ½ ¼ 8
1
16
1
No matter how quickly the hare
covers the distance between himself
and the turtle, the turtle uses that
time to move ahead.
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46. Kanser and J. Newman, in Mathematics and the
Imagination.
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47. A discovery of the
remarkable connection
between the
exponential and the
trigonometric functions,
by all time great
Mathematician,
Euler.
Euler was a great
experimental
mathematician.
He played with
formulas like a
child playing
with toys.
4712/28/2018
49. Can I expand an arbitrary function f(x) around x=a
as an infinite series?
f(x) =c0 + c1(x-a) +c2(x-a)2 + c3(x-a)3+ . . .+cn (x-a)n ;
But how to get all those {ci}?
4912/28/2018
55. Replacing x by iy is like playing with meaningless
symbols, but Euler had enough faith in his formula to
make it meaningful. Thus we get,
eiy = 1 + iy - y2/2! - iy3/3! + y4/4! + iy5/5! - y6/6! – iy7/7! + …
5512/28/2018
58. It involves three most important mathematical operations,
namely
addition,
multiplication and
exponentiation.
It connects the five most important constants in
mathematics:
e, π, i, 0 and 1.
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59. It includes four major branches of classical
mathematics:
arithmetic (through 0 and 1 ),
algebra (by i),
geometry (by π), and
analysis (by e).
5912/28/2018
