To create an extensible platform, we’ll start with the most simple mathematics and geometry and slowly build up to the most complex.

Towards a Unified Theory of Mathematics

An index for an in depth study of each of the 202 notations: A work-in-progress

.
200201202
190191192193194195196197198199 ∞
180181182183184185186187188189
170171172173174175176177178179
160161162163164165166167168169
150151152153154155156157158159
140141142143144145146147148149
130131132133134135136137138139 ∞
120121122123124125126127128129
110111112113114115116117118119
100101102103104105106107108109
90919293949596979899
80818283848586878889
70717273747576777879
60616263646566676869
50515253545556575859
40414243444546474849
30313233343536373839 ∞
20212223242526272829
10111213141516171819
..0....1....2....3....4....5....6....7....8....9.. ∞

Highly-integrated, Mathematical UniverseView

Infinity:  Of course, this page layout is two dimensional. Imagine if you will that it is three dimensional and that infinity touches every cell both above and below it so three face of infinity — continuity, symmetry and harmony — have a direct finite relation.  

Primes: Priority will be given to those notations that are prime numbers. Each prime number has been boxed.  #2 is the first prime.  0, the transformation number, is reserved for the Planck units.  It is postulated that each prime represents a new mathematical system yet each still builds successively on the all the other notations preceding it.

From 1-to-202 there are 45 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 197, and 199.

1 and 9:   2, 3, 5 and 7
10 to 19:  11, 13, 17 and 19
20 to 29:  23 and 29
30 to 39: 31 and 37
40 to 49: 41, 43, and 47,
50 to 59: 53 and 59
60 to 69: 61 and 67   

From 0-to-67 there are 19 primes.

70 to 79:  71, 73 and 79
80 to 89: 83 and 89
90 to 99:  97
100 to 109:   101, 103, 107, 109
110 to 119:  113
120 to 129:  127
130 to 139:  131, 137, 139

From 68 to 134 there are 13 primes.

140 to 149:  149
150 to 159: 151 and 157
160 to 169: 163 and 167
170 to 179:  173 and 179
180 to 189: 181
190 to 199: 191, 197 and 199
200, 201, 202: None

From 134 to 202 there are 13 primes.

From 1-to-202 there are 45 primes. The postulation is that each prime supports a new mathematical system that initiates even more diversity and complexity.

FYI
Primes: 200 to 1000 are 211 223 227 229
233 239 241 251 257 263 269 271 277 281
283 293 307 311 313 317 331 337 347 349
353 359 367 373 379 383 389 397 401 409
419 421 431 433 439 443 449 457 461 463
467 479 487 491 499 503 509 521 523 541
547 557 563 569 571 577 587 593 599 601
607 613 617 619 631 641 643 647 653 659
661 673 677 683 691 701 709 719 727 733
739 743 751 757 761 769 773 787 797 809
811 821 823 827 829 839 853 857 859 863
877 881 883 887 907 911 919 929 937 941
947 953 967 971 977 983 991 997 1009

Please note: There are some HTML coding issues that need to be resolved. so each of the prime cells can have unique borders and background color.

color

Animation showing how the sine function (in red) y = sin ⁡ ( θ ) {\displaystyle y=\sin(\theta )}

y=\sin(\theta )

is graphed from the y-coordinate (red dot) of a point on the unit circle (in green) at an angle of θ. https://en.wikipedia.org/wiki/Sine