Is math natural or synthetic?

Primes are the same, no matter what the base. They would get expressed differently in writing. In Contact, they were expressed without needing a base: ** - *** - ***** - ******* - *********** - ...

I'm definitely in the finite universe camp, especially after taking advanced astronomy in college, the best class I took there.

Quote:

Maybe he will tell you there are no secrets to primes?

Could be. Somehow, I think there is a pattern to them that we just haven't figured out yet. Just the prime spiral I think argues they are not totally random in their placement.

Quote: Wizard

Somehow, I think there is a pattern to them that we just haven't figured out yet.

In the Math Olympiad question, there is clearly a patter to the Greatest Common Divisor, but it is still difficult to prove

Etop=a^2+b^2; Ebot=2*a*b+1, then prove Etop/Ebot is an integer if and only if
a=b^3 ( Etop/Ebot=a^2), or when b=a^3 ( Etop/Ebot=b^2).

a	b	Etop	Ebot	GCD		a	b	Etop	Ebot	GCD		a	b	Etop	Ebot	GCD		a	b	Etop	Ebot	GCD
1	1	2	2	2		2	1	5	3	1		3	1	10	4	2		4	1	17	5	1
1	2	5	3	1		2	2	8	5	1		3	2	13	7	1		4	2	20	9	1
1	3	10	4	2		2	3	13	7	1		3	3	18	10	2		4	3	25	13	1
1	4	17	5	1		2	4	20	9	1		3	4	25	13	1		4	4	32	17	1
1	5	26	6	2		2	5	29	11	1		3	5	34	16	2		4	5	41	21	1
1	6	37	7	1		2	6	40	13	1		3	6	45	19	1		4	6	52	25	1
1	7	50	8	2		2	7	53	15	1		3	7	58	22	2		4	7	65	29	1
1	8	65	9	1		2	8	68	17	17		3	8	73	25	1		4	8	80	33	1
1	9	82	10	2		2	9	85	19	1		3	9	90	28	2		4	9	97	37	1
1	10	101	11	1		2	10	104	21	1		3	10	109	31	1		4	10	116	41	1
1	11	122	12	2		2	11	125	23	1		3	11	130	34	2		4	11	137	45	1
1	12	145	13	1		2	12	148	25	1		3	12	153	37	1		4	12	160	49	1
1	13	170	14	2		2	13	173	27	1		3	13	178	40	2		4	13	185	53	1
1	14	197	15	1		2	14	200	29	1		3	14	205	43	1		4	14	212	57	1
1	15	226	16	2		2	15	229	31	1		3	15	234	46	2		4	15	241	61	1
1	16	257	17	1		2	16	260	33	1		3	16	265	49	1		4	16	272	65	1
1	17	290	18	2		2	17	293	35	1		3	17	298	52	2		4	17	305	69	1
1	18	325	19	1		2	18	328	37	1		3	18	333	55	1		4	18	340	73	1
1	19	362	20	2		2	19	365	39	1		3	19	370	58	2		4	19	377	77	1
1	20	401	21	1		2	20	404	41	1		3	20	409	61	1		4	20	416	81	1
1	21	442	22	2		2	21	445	43	1		3	21	450	64	2		4	21	457	85	1
1	22	485	23	1		2	22	488	45	1		3	22	493	67	1		4	22	500	89	1
1	23	530	24	2		2	23	533	47	1		3	23	538	70	2		4	23	545	93	1
1	24	577	25	1		2	24	580	49	1		3	24	585	73	1		4	24	592	97	1
1	25	626	26	2		2	25	629	51	17		3	25	634	76	2		4	25	641	101	1
1	26	677	27	1		2	26	680	53	1		3	26	685	79	1		4	26	692	105	1
1	27	730	28	2		2	27	733	55	1		3	27	738	82	82		4	27	745	109	1
1	28	785	29	1		2	28	788	57	1		3	28	793	85	1		4	28	800	113	1
1	29	842	30	2		2	29	845	59	1		3	29	850	88	2		4	29	857	117	1
1	30	901	31	1		2	30	904	61	1		3	30	909	91	1		4	30	916	121	1
1	31	962	32	2		2	31	965	63	1		3	31	970	94	2		4	31	977	125	1
1	32	1,025	33	1		2	32	1,028	65	1		3	32	1,033	97	1		4	32	1,040	129	1
1	33	1,090	34	2		2	33	1,093	67	1		3	33	1,098	100	2		4	33	1,105	133	1
1	34	1,157	35	1		2	34	1,160	69	1		3	34	1,165	103	1		4	34	1,172	137	1
1	35	1,226	36	2		2	35	1,229	71	1		3	35	1,234	106	2		4	35	1,241	141	1
1	36	1,297	37	1		2	36	1,300	73	1		3	36	1,305	109	1		4	36	1,312	145	1
1	37	1,370	38	2		2	37	1,373	75	1		3	37	1,378	112	2		4	37	1,385	149	1
1	38	1,445	39	1		2	38	1,448	77	1		3	38	1,453	115	1		4	38	1,460	153	1
1	39	1,522	40	2		2	39	1,525	79	1		3	39	1,530	118	2		4	39	1,537	157	1
1	40	1,601	41	1		2	40	1,604	81	1		3	40	1,609	121	1		4	40	1,616	161	1
1	41	1,682	42	2		2	41	1,685	83	1		3	41	1,690	124	2		4	41	1,697	165	1
1	42	1,765	43	1		2	42	1,768	85	17		3	42	1,773	127	1		4	42	1,780	169	1
1	43	1,850	44	2		2	43	1,853	87	1		3	43	1,858	130	2		4	43	1,865	173	1
1	44	1,937	45	1		2	44	1,940	89	1		3	44	1,945	133	1		4	44	1,952	177	1
1	45	2,026	46	2		2	45	2,029	91	1		3	45	2,034	136	2		4	45	2,041	181	1
1	46	2,117	47	1		2	46	2,120	93	1		3	46	2,125	139	1		4	46	2,132	185	1
1	47	2,210	48	2		2	47	2,213	95	1		3	47	2,218	142	2		4	47	2,225	189	1
1	48	2,305	49	1		2	48	2,308	97	1		3	48	2,313	145	1		4	48	2,320	193	1
1	49	2,402	50	2		2	49	2,405	99	1		3	49	2,410	148	2		4	49	2,417	197	1
1	50	2,501	51	1		2	50	2,504	101	1		3	50	2,509	151	1		4	50	2,516	201	1
1	51	2,602	52	2		2	51	2,605	103	1		3	51	2,610	154	2		4	51	2,617	205	1
1	52	2,705	53	1		2	52	2,708	105	1		3	52	2,713	157	1		4	52	2,720	209	1
1	53	2,810	54	2		2	53	2,813	107	1		3	53	2,818	160	2		4	53	2,825	213	1
1	54	2,917	55	1		2	54	2,920	109	1		3	54	2,925	163	1		4	54	2,932	217	1
1	55	3,026	56	2		2	55	3,029	111	1		3	55	3,034	166	2		4	55	3,041	221	1
1	56	3,137	57	1		2	56	3,140	113	1		3	56	3,145	169	1		4	56	3,152	225	1
1	57	3,250	58	2		2	57	3,253	115	1		3	57	3,258	172	2		4	57	3,265	229	1
1	58	3,365	59	1		2	58	3,368	117	1		3	58	3,373	175	1		4	58	3,380	233	1
1	59	3,482	60	2		2	59	3,485	119	17		3	59	3,490	178	2		4	59	3,497	237	1
1	60	3,601	61	1		2	60	3,604	121	1		3	60	3,609	181	1		4	60	3,616	241	1
1	61	3,722	62	2		2	61	3,725	123	1		3	61	3,730	184	2		4	61	3,737	245	1
1	62	3,845	63	1		2	62	3,848	125	1		3	62	3,853	187	1		4	62	3,860	249	1
1	63	3,970	64	2		2	63	3,973	127	1		3	63	3,978	190	2		4	63	3,985	253	1
1	64	4,097	65	1		2	64	4,100	129	1		3	64	4,105	193	1		4	64	4,112	257	257

Quote: Wizard

Primes are the same, no matter what the base. They would get expressed differently in writing. In Contact, they were expressed without needing a base: ** - *** - ***** - ******* - *********** - ...

You can explain that over a few beers at Bugsy's Bar one day. I'll buy first round.

Quote:

Could be. Somehow, I think there is a pattern to them that we just haven't figured out yet.

Don't look at me there, I am still working on the pattern for "0" Roulette.

Quote: AZDuffman

Don't look at me there, I am still working on the pattern for "0" Roulette.

Touche!

I love math, especially when you get to the point where numbers almost disappear. It becomes more like logic to figure out the answer.

I think that any material thing like the universe has to be finite. While we can have the concept of mathematical infinite, there is no such thing as an actual infinite. Without a absolute starting point there could be no present.

Quote: FrGamble

I love math, especially when you get to the point where numbers almost disappear. It becomes more like logic to figure out the answer.

I think that any material thing like the universe has to be finite. While we can have the concept of mathematical infinite, there is no such thing as an actual infinite. Without a absolute starting point there could be no present.

You are correct that infinity is a concept that has no basis in reality. This math question is very interesting to me in that I've been putting together an argument for creation or intelligent design vs naturalism which I define as the view that only matter and energy exist (energy alone actually but an individual would be hard pressed to even define what energy is). My contention is that there are other things that exist that aren't matter and energy, mathematics for one thing, consciousness for another. Love, morality, beauty and art defy quantification (science) therefore cannot be constrained by the space time continuum.

Quote: pew

You are correct that infinity is a concept that has no basis in reality. .

How would you know, when the people
trained in this stuff don't know. There's
so much to learn, we only know the
tiniest part. Don't be like the Church and
just blurt things out as settled science
when none of it is settled at all.

Quote: Evenbob

How would you know, when the people
trained in this stuff don't know. There's
so much to learn, we only know the
tiniest part. Don't be like the Church and
just blurt things out as settled science
when none of it is settled at all.

Who is trained in infinity? One things for sure, you're right about the fact they (whoever "they" are) don't know. That's the point.

Infinity is not part of science by the way.

Quote: pew

Infinity is not part of science by the way.

Uh Huh.

Infinity (symbol: ∞) is a concept describing something without any bounds or larger than any natural number. ... Modern mathematics uses the general concept of infinity in the solution of many practical and theoretical problems, such as in calculus and set theory, and the idea is also used in physics and the other sciences.