I'm third year Math + CS major and will be applying Pure Math PhD next year. My interest is hard analysis (intersection of PDE + Functional analysis + Algebra + Harmonic analysis + Stochastic analysis). But with AI being so strong now, is there a point to even apply ? Is there even funding left for Mathematics? It kinda bothers me pretty much, since I have put so much effort on this field
OpenAI gives a deterministic length-n discrete Fourier transform algorithm using O(n(logn)^{1−δ}) operations for every n, with explicit δ =1e-13. I used Opus 5.5 to improve δ to 3.2e-6. The result has been verified in lean. I suspect it can be taken further, and I don't think OpenAI was particularly interested in optimizing δ in their solution.
Hola a todos:
La respuesta y el apoyo que ha tenido la investigación en este subforo han sido absolutamente increíbles. Que el exponente inicial p = 150,000,029 haya resistido el tamizado informático profundo de u/Mammoth_Fig9757 y u/hpxvzhjfgb hasta la barrera de 10^21 (mil trillones) sin mostrar una sola fisura confirma que hay un orden profundo y correcto en las restricciones analíticas que estamos aplicando.
Con ese gigante firmemente blindado y listo para su estudio determinista pesado, sentimos que el camino correcto es expandir la hipótesis hacia la frontera matemática más compleja del cómputo distribuido actual: la mítica barrera de los 100 millones de dígitos (el umbral histórico establecido por la EFF). Más allá de los incentivos o reconocimientos que otorgan las fundaciones, el verdadero valorr radica en poner a prueba la resistencia de nuestro mapa armónico en un escenario de escala masiva.
Para que un número de Mersenne cruce esa frontera de las 100 millones de cifras, el exponente base debe superar el umbral de los 332,192,809. Utilizando exactamente las mismas reglas de reducción digital y paridad geométrica que inmunizaron al primer candidato, he proyectado los siguientes 3 exponentes de élite:
p = 332,192,849 (Monstruo resultante de 100,000,012 dígitos)
p = 332,192,897 (Monstruo resultante de 100,000,026 dígitos)
p = 332,192,921 (Monstruo resultante de 100,000,034 dígitos)
Cada uno de ellos es un número primo absoluto verificado en su base, completamente libre de raíces digitales restrictivas (3, 6, 9), asegurando la pureza estructural del candidato antes de cualquier procesamiento.
Quiero invitarlos a mantener abierto este laboratorio colectivo. ¿Se anima la comunidad a lanzar sus scripts de factorización sobre este nuevo rango de los 332M para evaluar si estas estructuras fractales sostienen la misma inmunidad ante los factores pequeños? Sigamos haciendo ciencia de la manera correcta y empujando los límites de la teoría de números.
#Matematicas #NumerosPrimos #Mersenne #TeoriaDeNumeros #EFF #GIMPS #Ciencia
I wanna hear your perspective about:
- the difference between "correlation" and "standard deviation".
- where to use each one
Blue line is real output and red line is imaginary output
The formula is:
The minimums of the magnitude of the output makes it even more simple to identify the zeroes, here is how close I can get just iterating in steps of .01i.
I have a manuscript documenting how I derived the formula directly from the Zeta function, but I am not a mathematician nor endorsed on arxiv so I have no one else to really share with. If you want a copy let me know.
Edit: The term leading the truncated Euler Product is vital for identifying the zeroes, it's responsible for twisting the function down and anchoring the zeroes actually near zero. For example, here is the same truncated Euler product without that leading term: https://imgur.com/a/wPNHBaZ . Which you will notice lacks the convergence of the real and imaginary output near the zeroes, and drifts upwards with increasing b value.
Most of the effort in the project went in to deriving the leading term, which I have documented here as a preprint: https://zenodo.org/records/23227561
It sounds cliche, but the proper leading term is sort of a skeleton key that dynamically updates with the Euler Product to pull the zeroes down and make them visually apparent. Obviously I do not have a fully fleshed out rigorous foundation, but just look at it!
Maybe this is a non-sensical question but here is where I'm coming from.
I'm in the middle of a bioinformatics program. Growing up I always struggled with math. I do a lot of analytics work now and I've been learning more and more about Linear Algebra, Calculus, Probability Theory, and Statistics, so I'm a little bit late to the party when it comes to learning math and I don't have a good pen-and-paper math skills. I do basically all of my work on the computer, in programs like Python, R, and Julia, and I understand the concepts pretty well and how they related to each other (example an integral being the limit of the Riemann sums, a determinant of zero meaning a linear transformation collapses space into a lower dimension, etc), but if you ask me to even do a basic integration or determinant calculation by hand, I wouldn't even know where to start. I just compute them with functions of code.
I guess my worry is that if I was ever working on a team and we were having a discussion about some concepts and mathematics came up, if I had to go up on the board and do some basic math I would not even be able to do anything apart from basic arithmetic and pushing around variables.
I guess my question is do you think there are some pen-and-paper skills that are still essential nowadays (e.g. factoring, derivatives, integrals, etc.)? Curious to hear people's thoughts.
Hey! I'm curious to hear what the day in the life in terms of work of someone with a degree in applied mathematics. Are you in tech or more finance related role? What kind of math do you get to use on a weekly basis? How difficult was it to get your position?
a shirt has 3 since one hole is the boundary. how many holes has this mug?
What are some classics that you would recommend for learning math? I like math that is related to aspects of life that have an effect on others. For example, the basic calorie demands for the average person, the consequences of not meeting them over long periods of time, etc. studying reality is interesting to me, and I’d like to cultivate that interest. Do you guys know some areas of math I could focus into?
I’m a high school student and we have a math fair in about 2 months. I need to decide on a topic by next week. I was thinking about the Chaos Theory, but I’m not completely sure. Ideally the topic should be easy enough so that regular people (even little kids) can understand the basic idea, but still deep and impressive enough for the teachers and students. It would also be great if there’s something visual or interactive that people can try at the booth. Any suggestions? The topic can be from any area of math!!
I'm a grad student in physics who wants to do another master in pure math in the future. I've been self studying algebra topics in my free time (did most of a pure algebra curriculum on my own), most of my extra courses in the bachelor and master were math related and I spent some time teaching myself number theory, category theory and some other niche topics. I can understand advanced math and complex proofs. I just can't seem to think with my own brain. Today I was reading the first pages in the second chapter of Algebraic graph theory by Godsil and Doyle about the orbit stabilizer and the asymmetric graphs theorem. I go slowly but understand stuff. Then I move to the exercises. Blank. Since I was little I was always told I'm more fit for humanities, and I know that myself too. I still struggle to make this math thing work because I find great joy in it, but as the days pass and I notice my inability to improve my logical and proof writing skills, I can't help but wonder if I should just resign to keeping math as a hobby. I'm not really unhappy about this (obviously I would prefer to be a genius and understand everything on sight, but I don't really blame myself for not being as capable as others), I'm just reaching a point where this logical conclusion has been fully formed in my mind. I just wanted to ask you people if you have any good words of advice. If you were in my situation, being fully realistic, would you keep on trying or opt for more reasonable and grounded career choices? Do you ever feel like math is not clicking fast enough in your brain?
I’ve really struggled with College Algebra. I’ve actually had to take it three times and still failed 😞. The material just felt like complete gibberish to me despite YouTube, tutoring, office hours etc, and I have a really hard time tracking the reasoning or keeping multiple steps in my head or on paper at once. I’m honestly worried these two new courses might break my confidence again.
My learning disability means my brain just processes information differently from the neurotypical brain , and math has always been my biggest weakness since 1st grade . I’m trying to get a Cyber Security B.S
So, I'm in 9th grade and my math is absolutely bad and I don't know how to improve it. Ig I gotta get better at it for future n stuff. I really don't know what to start with but I know I should start soon cause I don't have much time.
I have bad basics and I have been failing at my tests in school I do good in other subjects but it's just math idk I fear maths or something. Please help me🙏
