William Cosgrove Creative Portfolio

• Virtual Reality Block/Puzzle Game using Optitrack camera rig – Created at USC’s World Building Media Lab:
  • Merges haptic feedback with virtual reality
    • Uses Oculus Rift. I attached Optitrack sensors to the Rift as well as to a set of wooden blocks. I then used Unity to program the blocks to map to virtual  puzzle pieces that the player works with.  It also features Alex McDowell’s “Chair in VR”, which the play can sit in.
  • Using same set of blocks for multiple games
    • I created multiple game types that could be played with the same set of blocks. One type was a standard puzzle game where you arrange the blocks as you would a puzzle, and it took place in various historical settings (Ancient Greece, Egypt, etc.). Another game was a color matching variant where you needed to observe your surroundings to decipher the right arrangement of the blocks. Lastly, one was based off of the World Building Institute’s renowned project The Leviathan, in which Gerty, a delicate floating jellyfish-like creature, is trapped and you must connect the circuits to free her.

 

• Conway’s Game of Life in 3D – Made for UCSB’s Allosphere (http://www.allosphere.ucsb.edu)
  • The Allosphere is a three story sphere with a metal bridge going through the middle of it. It has 26 projectors that project onto the interior of the sphere. People on the bridge where 3D glasses and get 360 degree immersion. It is meant to be a catalyst for collaboration among scholars.
    • I sat in on a graduate level course taught by the UCSB grad, Karl Yerkes, who was largely responsible for creating the “Allosystem”  coding language (primarily based off C++).  This language is exclusively used for programming for the Allosphere.
    • I created a 3 dimensional version of Conway’s Game of Life, which is the famous example of cellular automation created by mathematician John Horton Conway, the idea of which originated from John von Neumann in the 1940s. It is originally done in two dimensions. It was coded using Allosystem. It works by starting off with a randomized number of cells being “alive”. Then, based on the set of rules, which may be tweaked by the user, the cell colony develops on its own until it peters out, grows out of control, or finds a nice balanced state.                                                           

Regulatory Capture in the Age of COVID-19

By Liam Cosgrove (https://twitter.com/cosgrove_iv)

Our healthcare system is broken, a fact nobody would have disputed in pre-COVID days. Regulatory capture is a reality, and the pharmaceutical industry is fraught with examples. Yet we trusted private-public partnerships to find an optimal solution to a global pandemic, assuming a crisis would bring out the best in historically corrupt institutions.

Here is a brief list of less-than-savory behavior demonstrated by our titans of healthcare: 

• Pfizer and J&J plead guilty to “misbranding with the intent to defraud or mislead” and paying “kickbacks to health care providers to induce them to prescribe [their] drugs”, resulting in fines of $2.3 billion in 2009 and $2.2 billion in 2013, respectively. 
• Pfizer settled another lawsuit for “manipulating studies” and “suppressing negative findings” just a few years later. 
• Moderna has never developed an approved drug yet one of their board members was placed in charge of Operation Warp Speed. This certainly is unrelated to the fact that they received the most federal vaccine R&D funding and have received over $6 billion from our government since the start of the pandemic.
• Gilead Sciences paid $97 million in fines because it “illegally used a non-profit foundation as a conduit to pay the Medicare co-pays for its own drug”.
• In 2005, AstraZeneca’s drug Crestor was shown to be linked to a life-threatening muscle disease while the company withheld evidence of this and two dozen other effects from the public.
• In 2012, GlaxoSmithKline paid $3 billion in fines as it “failed to include certain safety data” relating to their drug, since labeled to be connected to heart failure and attacks.

Thankfully our public health guardians are in place to protect us from the greed and deceit of the private sector, right? Wrong. Enjoy another brief list:

• FDA worked behind the scenes with company Biogen to alter previously conducted trials of their $56,000 per year Alzheimer’s treatment, and “by removing the subset of people for whom the drug didn’t work, they found a slight statistical effect in favor of the drug.” Even after doing this, an advisory committee voted 10-0 against approving the drug. The FDA approved the drug anyways, causing three committee members to resign.
• In that case, the third-party advisors did the right thing. This is not always the case… A study by Science Magazine tracking 107 FDA advisors for four years, found that 62% received money from related drug makers with 25% receiving over $100k and 6% receiving over $1 million. It only takes a few corrupt advisors to fix a panel and feign medical consensus.
• The WHO has come to be dominated by China over the last 17 years by bribing poor nations and altering the organization’s voting structure to ensure their candidates obtain high positions (most notablydirector-general). The WHO parroted false claims made by the CCP in Jan 2020 that COVID-19 had “no clear evidence of human-to-human transmission” (still on Twitter!), despite receiving contrary evidence from Taiwanese health monitors in December 2019 and during which time Chinese hospitals were overrun, requiring mass disinfections across villages: A worker in a protective suit uses a large fogger to disinfect outdoor areas in a village in Qingdao, Shandong province, as the deadly new coronavirus continues to spread in China. Reuters

• If you need more proof that the WHO is in China’s pocket, just watch this clip.
• In 2017, it was revealed that the CDC Director for Heart Disease and Stroke Prevention had been secretly communicating with Coca-Cola, providing guidance on how “to influence world health authorities on sugar and beverage policy matters”.
• As for Fauci and the NIH, I can’t do any better than Dr. Chris Martenson in his video analyzing Fauci’s emails. One thing is clear, the Wuhan research was gain-of-function.

Ok, so now that we’ve thoroughly discredited our public health institutions, let’s move on to why this matters. This article is not concerned with the vaccines. Do your owner research and make your own decisions there.

As mentioned above, the WHO failed to warn the world of the magnitude of the threat, and instead actively advised against a Chinese travel ban when evidence of COVID’s severity was overwhelming. This certainly changed the fate of the world for the worse. How much worse? We can’t know for certain, but it’s interesting to note that Taiwan, who shut down international travel in early January 2020 upon learning of troubling developments in Wuhan, handled the virus exceptionally well, with only 7 deaths in 2020. This is remarkable when compared to other Southeast Asian nations, considering their population size of almost 24 million! It makes you wonder what the fate of the rest of the world could have been, had the WHO done its job.

While the WHO’s corruption and its consequences are upsetting, the solution is simple: disregard their future statements. Taiwan was an early adopter of this policy, and the results speak for themselves. 

Here in the US, our public health systems are mired in good old-fashioned crony capitalism, fascism, corporatism, mercantilism, protectionism…. fancy words for when private companies work with governments to subvert the forces of competition. The suppression of research into off-patent drugs is a nasty symptom of this problem.

While there are countless drugs to which this applies, we will discuss ivermectin. First, addressing the drug’s dismissal by its own manufacturer, Merck, let it be known that ivermectin is no longer under patent. Merck no longer owns exclusive rights to it’s production. The forces of competition have been bestowed upon the drug, thus making it far cheaper. Merck is also currently rolling out an oral COVID treatment, which the US government is funding $1.2 billion to research. This would be under patent and explains their dismissal of ivermectin.

While ivermectin’s effectiveness is still up for debate, a signal that it could be effective against COVID-19 was discovered in early April 2020 through a study at the University of Monash in Australia. The drug is FDA-approved, has existed for 40 years, won a Nobel Prize, and is extremely safe when used at recommended levels. Given the crisis and ivermectin’s safety, it should have been used immediately in hospitals, so it could have been administered safely and its effectiveness been observed. Instead, a week after the Australian study was published, the FDA advised against ivermectin for COVID-19 treatment, forcing desperate people to the black market and causing them to self-prescribe versions of the drug intended for animals. This decision surely had nothing to do with the $615 million in lobbying put forth by the health sector in 2020. Would love to see a FOIA on how that money was spent.

The FDA noted subsequently that “additional testing is needed”. To date, there has not been a single completed, government-funded study on the effectiveness of ivermectin against COVID-19. Meanwhile, they have funneled billions towards research into vaccines and patented treatments. The NIH funded trials for remdesivir, still under patent with Gilead, despite being less effective and having more severe side effects than ivermectin. FDA approved remdesivir under EUA despite published trials later stating “remdesivir was not associated with statistically significant clinical benefits”. As long as a pharmaceutical stands to make a profit, our government will be there to provide funding.

Sadly the solution to the FDA’s corruption is not as simple as Taiwan’s solution for the WHO. Hospitals are open to liability when the FDA does not approve a drug for a specific use, making doctors reluctant to prescribe. Funding randomized clinical trials to convince the FDA is immensely expensive, with the median cost being $19 million to achieve approval. Given ivermectin is off patent, the only way to raise these funds would be through government or crowdfunding. The former option is hopeless as we’ve seen. The latter, while difficult, is possible when people can be educated and persuaded. This brings us to the final culprit, Big Tech.

When cities are locked down and it is forbidden to gather in large groups, public discussion must take place online. Crowdfunding requires the freedom to collaborate. However, discussion of ivermectin has been suppressed across social media:

• Youtube banned a congressional hearing on the topic.
• A member of Australia’s congress was banned from Facebook for discussing it. 
• Twitter banned users for discussing the fact that Twitter was banning users for discussing ivermectin! 
• I was banned from NextDoor for discussing it, which ironically motivated me to write this article. 

People need to be able to work together to solve problems that our government clearly will not.

The timeline is important to keep in mind in order to grasp the consequences brought on from this failure by our institutions. The pandemic was officially announced in March 2020. We have endured a year of lockdowns, over a third of small businesses closing for good, trillions of dollars diverted, an additional 14 million people facing famine due to lockdowns, diminished education from remote learning, mental health issues, rise in crime, the list goes on…

All of this, when we may have had effective treatments as early as April 2020, which our government not only failed to investigate but actively suppressed? Our healthcare system isn’t just broken – it is actively working against public health interests. 

The solution, in my opinion, is privatized healthcare. No private doctor would stay in business if he/she were to withhold safe and likely effective treatments and instead offer expensive and ineffective (remdesivir) or experimental (mRNA vaccines) alternatives. However, this is a discussion for another day.

If you are interested in further investigating ivermectin’s effectiveness against COVID-19, start here.

Last Daily Writing

It feels great to have completed the mock grant proposal. I believe that it was a very valuable experience and will help me in the near future since I plan to apply for graduate school. I feel confident about the tone used throughout the paper. We did not stick to the most rigorous and formal language, but we were technical enough to establish our credibility. This was similar to our examples. There was a hint of personality to each of our example proposals that made them enjoyable to read.

I also feel confident in the content that is included in out grant proposal. We did our research to make sure our equations/facts were correct and up to date. The research process was actually very interesting. Had I not been assigned this project, I would almost surely not have started researching the Riemann Hypothesis. There were many aspects to it that related to my current math class in complex analysis. This assignment was very cool for that reason. While it teaches us to write, it also drives us to learn more about our disciplines.

If I were to revise the assignment again, I would include less generalities like, “This problem is the most infamous problem in the world.” I believe most mathematicians would find a statement like that unnecessary. All in all, I would try to make it more concise and make sure my information is relevant. I personally love learning about math history, and not for the purpose of boosting my ethos, I just enjoy learning about it. I am not sure, however, how commonplace such knowledge is to astute mathematicians. I chose to include multiple historical facts because I like them, but in case I ever write an actual grant proposal, I would first make sure this would not annoy my reader.

This entire process has relaxed my attitude on academic/professional writing. Before this class, academic articles were intimidating. They were these complicated bodies of words that I did not think I could understand. Now, I feel much more at ease about reading them as well as writing them. What helped a lot was finding sources relevant to our topic. I came across many confusing journal articles, most of what was inside I would not understand, but as I read on I found that there was a good amount I actually could understand. This was an exciting realization, that this level of research is right around the corner for me.

URL to RFP

https://nsf.gov/funding/pgm_summ.jsp?pims_id=5431&org=DMS&sel_org=DMS&from=fund

 

Daily Writing #11

Abstract

We are setting out to prove the infamously elusive Riemann Hypothesis. It has been about 150 years since Bernhard Riemann, a professor at University of Gottingen in Germany, proposed the hypothesis. Being the busy man he was, he left it aside for other mathematicians to prove as he continued on with other work. Many have since tried, and while nobody has proved it, there is now a wealth of knowledge on the topic. The central function, Riemann zeta function, is understood much more thoroughly than it once was, especially with the increase in visualization technology. We believe that a proof for this hypothesis is right on the horizon. A proof of this problem could also have very important implications. It would give us an equation to approximate the distribution of prime numbers, a central building block of mathematics. Albert Einstein built his famous theory of general relativity upon some of Riemann’s other work called “Riemann Geometry”. We can never know what will stem from new mathematical discoveries, but history has shown us that, often times, extraordinary scientific discoveries soon emerge. Using graphical representation, multi-dimensional modeling, and number analytics, we believe that we can construct a valid proof of the Riemann Hypothesis.

Methods Draft

I decided to download it as a pdf since the math equations do not transition well into WordPress.

Here it is:

proposedresearch

Daily Writing #10

The math grant proposals we found do not have an explicit methods section. My example has a section titled “Proposed Research” which is similar, in a way. The proposed research section is sort of like a rough sketch of a traditional scientific methods section mixed with a background section. The author describes areas of research that he will be undertaking (just like a background) and then discusses generally what tools he will be using to conduct the research (rough method description. This section is much less rigorous than it would be for a traditional science proposal due to the fact that, in math, it is hard to know exactly what method of research will yield the desired results. For this reason, our methods section will be somewhat vague. Here is an example, “I propose to compute hundreds (or thousands) of such discriminants, and then look for such certificates for their positivity.” (Sottile p.9) Here, the author explicitly states what he will be doing. However, he can’t say exactly what methods he will employ to “look for such certificates for their positivity” or if he will “compute discriminants” in different ways. In math, there are often numerous ways to go about analysis, and it would be a draining task to attempt to describe them all. By stating his plan the way he does, Sottile describes his methods as specifically as is practical. This is what we will attempt to do in our proposal. It is still important to lay out your plans for research because the grant organization needs to see some evidence that you will actually be working. Therefore, we will attempt to be specific in describing our proposed methods, but also include a sensible degree of generality.

The authors do, however, develop credibility with reassuring statements and rhetorical tones. One author mentions how the majority of the grant would go towards students, visitors, and their travel. This establishes a trustworthy quality for him, and shows that he has planned ahead in regards to his spending. In this same paragraph, he emphasizes the importance of training students so that they will become competent and skilled researchers in the future. He also mentions the importance of interdisciplinary work that will arise out of working with other professors and visitors, saying that there are many tools mathematicians use which could greatly benefit scientists. All of these reasons are aimed at reassuring the NSF that their money will be going towards important work, and that the author is responsible enough to follow through with his promises.

Intro/Background Draft

William Cosgrove

Sam Nasreldine

WRIT109ST

Dr. Fancher

Introduction and Background Draft

 

Proposal: Funding for research to prove the Riemann Hypothesis

Introduction

    The Riemann Hypothesis is one of the most famous mathematical problems that is yet to be solved. It is one of the “Millennium Problems”, which are a set of unsolved problems that were chosen by the Clay Mathematics Institute of Cambridge as the most difficult problems facing mathematicians at the turn of the millennium [4]. It has been over 150 years since the hypothesis has been proposed and yet nobody has proved it. This being said, there are countless published articles which conduct mathematical research on the assumption that the Riemann Hypothesis is true. These authors must, of course, state that they are researching under this assumption. Mathematical community members generally believe that the hypothesis is true, but if by some chance it were not, then all of these published works would be invalid, and so on to the “child” published works that stemmed from those ones. It would be a bit of a disaster. Luckily, this is probably not the case. Regardless, it is important that a valid proof is discovered for the Riemann Hypothesis for a couple of reasons. First of all, it is essential that science and math are grounded in proven facts. A proof of the Riemann Hypothesis would ground all the afore mentioned articles in fact. This is the most important reason for proving it. Two other and more general reason are that proving it could result in the discovery of a new method of analysis, which could in turn produce more mathematical breakthroughs, and the research which we will undergo will aid in educating university students to better prepare them for their future research.

    Our research team will use various methods of analysis to construct a proof of the Riemann Hypothesis. We are currently and will continue to undertake extensive research on methods that have been used by other mathematicians, which have shown to have some degree of success. We will be researching past attempts to prove the hypothesis like the Bloch-Kato Conjecture, various manipulations to the Riemann zeta function (which is the main piece of the hypothesis), Leonhard Euler’s related functions, and more. These examples of past work are within fields ranging from number theory, graph theory, geometry, fractals strings, to possibly more. Innovation will also be key, so a main goal of ours will be to pioneer our own analytic methods. Novel techniques in mathematics are often adopted by other mathematicians in hopes that these will assist in their research. Just as we are using equations formulated by Leonhard Euler in the 1700’s, it is possible mathematicians will someday use methods that we invent in their work. This process is integral to the advancement of mathematical knowledge, which is our number one concern.

    Graduate students will assist in research. We will also allow undergraduate students to volunteer if they desire. Training a competent workforce for the future is important across all disciplines. We all want our scientists to be able to excel and we want them to have the world’s best interests at heart. A study conducted by C. Madan and B. Teitge at the University of Alberta concluded that undergraduate students who were part of research teams had a clearer understanding of the publication process in their field and gained a passion for research. Including students in our mathematics research process will ensure that our field continues to advance for generations to come.

 

Background

    Since the Riemann Hypothesis has not been proven, no one knows which techniques will lead to its solution. For this reason, it is important that we examine many different areas of research. The following list is not an exhaustive list of all the fields which relate to the Riemann Hypothesis; they are just a few central ones. Sections “Analytic Number Theory” and “Fractal Geometry” contain only material that is relevant to our research.

Early Work (Pre 1950) and the Riemann Hypothesis Defined:

    Defining the Riemann Hypothesis is not a simple task. First we begin with the equation it is built upon. This equation is called the Basel Problem and was solved about 100 years earlier by Leonhard Euler. The equation is as follows:

1/1^2 + 1/2^2 + 1/3^2 + 1/4^2 + … + 1/n^2   as n increases to infinity.

It was proved by Euler that this series converges to 2/6. There were other problems similar to the Basel Problem where instead of squaring the denominator it was taken to other powers (3, 4, …), so for some number x, these equations would look like:

1.       f(x) = 1/1^x + 1/2^x + 1/3^x + 1/4^x + … + 1/n^x   as n increases to infinity.

    Bernhard Riemann wanted see what happens when you change the domain of this function to include complex numbers. Complex numbers have a real component and imaginary component. The imaginary component has a coefficient i = -1. It does not make sense when working with real numbers to take the square root of a negative number, so, long ago, mathematicians imagined what would happen if you could. Imaginary numbers are of the form iy, where y is a real number. Complex numbers are of the form z = x + iy, so they have a real part and imaginary part (x and iy respectively). Out of this idea arose the complex plane:

Complex numbers are similar to ordered pairs in the commonly used xy-plane since z can also be written as (x,y).

    Now let’s look at Riemann’s famous function which extends the domain of (1) to include complex numbers. It looks exactly the same as (1) but s is a complex number. The function is famously known as the Riemann zeta function:

r(s) = 1/1s + 1/2s + 1/3s + 1/4s + … + 1/ns as n goes to infinity.

This function only has solutions when the real part of the complex number s is greater than 1 (Re(s) > 1). However, Riemann wanted to analyze this function for all complex numbers, so he analytically continued this function so that it converged for all complex numbers s 1(any s that is not equal to one, in complex form: 1+0i). This continuation is as follows, known as the Riemann functional equation:

r(s) = 22s-1sin(s/2)(1-s)(1-s)

Notice that (1-s) is part of the right side of the equation. This is what makes it a functional equation (points in the equation are defined in relation to other points).

    It turns out that this equation always equals zero when s is a negative even real number, and that is simply because sin(2n/2) = sin(n) = 0. These are the “trivial” zeros and are not the concern of the Riemann Hypothesis. When Riemann was working with his function, he proved that the non-trivial zeroes can only be obtained with s where 0 < Re(s) < 1. The hypothesis, which it is our goal to prove, takes this a step further and states, “All non-trivial zeroes are obtained by complex numbers s with Re(s) = 1/2.” The following shows the zeroes of the zeta function plotted on the complex plane (the dots to the left of the imaginary axis are the trivial zeroes):

Analytic Number Theory:

    The Riemann Hypothesis is considered to be one of the most difficult problems in number theory. Riemann specialized in complex analysis, so his hypothesis ended up making a fascinating bridge between the two fields. Moreover, it has implications for prime numbers and how often they occur, a phenomenon which has puzzled mathematicians for thousands of years.

    Researching how the hypothesis and zeta function are related to analytic number theory will help us in our development of a proof. Analytic number theory is a field in which various methods of analysis are employed to discover properties of the whole numbers. Multiplicative number theorists are interested in the Riemann zeta function because of its implications regarding the frequency of prime numbers.

    Let start by describing the Prime Number Theorem. It offers an equation which approximates the number of primes which occur before a given integer N. Here is that equation:

 

r(N) = N/log(N)

    where (N) is the actual number of primes less than the integer N and log is the natural log.

The Theorem claims that:

lim (as N goes to infinity) r(N) / (N/log(N)) = 1

This implies that their approximation equation gets closer and closer to the actual value as you increase the value of N.

    This theorem does not appear to be related to the Riemann zeta function. Actually, this theorem was not proven until after Riemann’s time (there were other approximations, but they were not as accurate). It was Riemann’s Hypothesis and its surprising connections to the distribution of prime numbers which encouraged mathematicians to use complex analysis in their research on the (N) function. It turns out that if it is true that the locations of the non-trivial zeroes in the Riemann zeta function do indeed lie on the line Re(s) = 1/2, then we would know much more precisely how primes numbers are distributed. There are other approximations which, like the above equation, depend on the truth of the Riemann Hypothesis in order to be accurate. Therefore, it is essential that we obtain a solid proof to solidify our knowledge of prime number distribution.

Graph Theory:

    Examining how the Riemann zeta function alters lines in the complex plane provides interesting visual results. Unlike functions in 2, complex functions are not lines. Instead, they alter the entire complex plane. To visualize this, we must add lines to the complex plane, then apply the function to see how the lines are altered after the function is applied. Here is an example of how the Riemann zeta function, before it is analytically continued, alters the complex plane:

          

We see an interesting pattern emerging. Now here is the analytic continuation:

           

Clearly there are benefits to analyzing the zeta function using graphs. It allows us to see patterns that would never be apparent by simply manipulating the function. One important thing to note about analytic continuations is that they are unique, meaning that if a function can be analytically continued, then it only has one analytic continuation. So the above graph represents the only analytic continuation of the zeta function that exists. However, it is possible to transform any line in the complex plane with a function. So the number of lines that can be altered with the zeta function are literally infinite. This will be an important method of research which we will combine with our number analysis.

3 Questions:

• Is introduction understandable?
• Does it fulfill the three rules adequately?
• Is the background too long-winded? (it is less so than our examples)

 

References

1. E. Bombieri, Problems of the millennium: The Riemann Hypothesis, CLAY, 2000.
2. P. Borwein, S. Choi, B. Rooney, and A. Weirathmueller, The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike, Springer, New York, 2008.
3. L. A. Bunimovich and C. P. Dettmann, Open circular billiards and the Riemann Hypothesis, Physical review letters 94.10, 2005.
4. Clay Mathematics Institute, The Millennium Prize Problems, Oxford, United Kingdom, 2017. http://www.claymath.org/millennium-problems/millennium-prize-problems
5. J. Coates, A. Raghuram, A. Saikia, and R. Sujatha, The Bloch-Kato conjecture for the Riemann Zeta Function, Cambridge University Press, Cambridge, 2015.
6. J. Conrey, The Riemann Hypothesis, Notices of the AMS Volume 50, number 3, 2003.
7. H. Iwaniec and E. Kowalski, Analytic Number Theory, American Mathematical Society: Colloquium Publications volume 53, Providence, RI, 2004.
8. M. Lapidus and M. van Frankenhuijsen, Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings, Springer, New York, 2013.
9. C. Madan and B. Teitge, The Benefits of Undergraduate Research: The Student’s Perspective, Alberta, Canada, 2013.
10. B. Mazur and W. Stein, Prime Numbers and the Riemann Hypothesis, Cambridge University Press, New York, 2016.
11. B. Riemann, On the Number of Prime Numbers less than a Given Quantity, University of Dublin, Ireland, Translated 1998 (original 1859).
12. Sanderson, Grant, Visualizing the Riemann zeta function and analytic continuation, Stanford, California 2016. https://www.youtube.com/watch?v=sD0NjbwqlYw
13. A. Terras, Zeta Functions of Graphs: A Stroll Through the Garden, Cambridge University Press, United Kingdom, 2011.
14. B. Wachsmuth, Interactive Complex Analysis, Seton Hall University, South Orange, New Jersey, 2007.

 

Daily Writing #9

Our (Sam and I) plan is to put most of the emphasis on the importance of proving the Riemann Hypothesis. We will start by stating that proving the hypothesis is our sole research goal. It is easy to see that there is a gap in this area of research, hence the unproven hypothesis. We will then go on to describe the important impact this would have on the math community, by pointing out how many other journal articles in mathematics depend on assuming that the hypothesis is true. A proof would mean that all of this other articles are officially valid (currently they are assumed to be valid since most people believe the hypothesis to be true).

Secondly, we will research various organizations that would be willing to fund such research, and word our introduction to express how our research is inline with the organization’s values. This was a tactic used in both of our model grant proposals.

Another tactic that was used in my grant proposal fits in with emphasizing the importance of the research. The author included the fact that he would be working with graduate students and educating them on how to conduct research properly would follow naturally. The author claimed that this was extremely important since these graduate students will likely be the researchers, professors, and doctors of the future. We may include reasoning like this in our proposal (although we will not actually be employing graduate students). This can’t really be used as a central reason, however, because most grant proposals, regardless of the discipline, can make this claim.

Daily Writing #8

There are numerous proofs in mathematics that begin with “Suppose the Riemann Hypothesis is true…”. This is acceptable since most people already assume that the Riemann Hypothesis is true. All of this is well and good, but what if, by some minuscule chance, someone were to prove that the Riemann Hypothesis were false. Then, all of those proofs would be invalid. It would be a minor disaster.

This is why it is important that somebody proves this hypothesis. While it is probably the case that it is true, a valid proof of it would solidify the base from which so many other proofs have been constructed. Proving the Riemann Hypothesis will not only make it concrete knowledge, but also solidify all those proofs that start out by having the reader suppose the hypothesis is true.

There are many methods to analyzing prime numbers and the Riemann Hypothesis. Using binary numbers, matrix construction, etc. Our team will employ many methods to diversify our research and work towards a valid proof.