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Why Philosophers Should Care About Computational Complexity [article]

Scott Aaronson
2011 arXiv   pre-print
on the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume's problem of induction, Goodman's grue riddle, the foundations of quantum mechanics  ...  In particular, I argue that computational complexity theory---the field that studies the resources (such as time, space, and randomness) needed to solve computational problems---leads to new perspectives  ...  This essay will touch on many problems that philosophers have debated for generations, such as strong AI, the problem of induction, the relation between syntax and semantics, and the interpretation of  ... 
arXiv:1108.1791v3 fatcat:eqvibzsxmjczvgmnbtlv5amyxe

Why Philosophers Should Care about Computational Complexity [chapter]

2013 Computability  
In particular, I argue that computational complexity theory-the field that studies the resources (such as time, space, and randomness) needed to solve computational problems-leads to new perspectives on  ...  the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume's problem of induction and Goodman's grue riddle, the foundations of quantum mechanics  ...  "world" where NP-complete problems turn out to be hard in the worst case but easy on average).  ... 
doi:10.7551/mitpress/8009.003.0011 fatcat:sk6y4k62xbfgdn4nytamdeq6my

The ternary Goldbach problem [article]

Harald Andres Helfgott
2015 arXiv   pre-print
The ternary Goldbach conjecture (or three-prime conjecture) states that every odd number greater than 5 can be written as the sum of three primes.  ...  The purpose of this book is to give the first proof of the conjecture, in full.  ...  As their names indicate, the strong conjecture implies the weak one (easily: subtract 3 from your odd number n, then express n − 3 as the sum of two primes).  ... 
arXiv:1501.05438v2 fatcat:yawwwrsawrehja57kfvt3wb3vm

Interview with John Milnor

Martin Raussen, Christian Skau
2012 Notices of the American Mathematical Society  
It's very easy to make guesses, but it feels very good when they turn out to be correct. R & S: That's only one of the quite famous Milnor conjectures.  ...  Such groups always have either polynomial growth or exponential growth.  ... 
doi:10.1090/noti803 fatcat:ftuuhgdpvvfdpac36cawrj6u24

Genetic Programming III - Darwinian Invention and Problem Solving

Peter Nordin
1999 Evolutionary Computation  
Finally, we thank our families for their patience for yet another project that took Dad away for significant periods of time.  ...  Acknowledgments We would like to acknowledge the help of our editor, Denise Penrose, and that of Edward Wade and Emilia Thiuri, at Morgan Kaufmann Publishers.  ...  The concept of extraterrestrial life, for instance, while hard to imagine, is nonetheless easy to accept. What would we say if there were silicon-based beings on another planet?  ... 
doi:10.1162/evco.1999.7.4.451 fatcat:27732t6mfvgt7mzpbvkrv6wcqm

Additive Combinatorics: A Menu of Research Problems [article]

Bela Bajnok
2017 arXiv   pre-print
While the primary purpose is to provide an ample supply of problems for student research, it is hopefully also useful for a wider audience.  ...  It is the author's intention to keep the material current, thus all feedback and updates are greatly appreciated.  ...  Observe that, if Conjecture F.185 is true, then the set Z 2 k \ {2 k−1 } is one such set. Problem F.191 Prove (or disprove) Conjecture F.190.  ... 
arXiv:1705.07444v2 fatcat:qfuxq3xae5avvjcs5ygfb4vvfi

On the Fine-Grained Complexity of Empirical Risk Minimization: Kernel Methods and Neural Networks [article]

Arturs Backurs, Piotr Indyk, Ludwig Schmidt
2017 arXiv   pre-print
In particular, we give conditional hardness results for these problems based on complexity-theoretic assumptions such as the Strong Exponential Time Hypothesis.  ...  While there has been a large body of work on algorithms for various ERM problems, the exact computational complexity of ERM is still not understood.  ...  Hardness of easy problems: Basing hardness on popular conjectures such as the Strong Exponential Time Hypothesis (invited talk). In LIPIcs-Leibniz International Proceedings in Informatics, volume 43.  ... 
arXiv:1704.02958v1 fatcat:6iiabja7j5bvzjuloy47oguzga

Interview with Endre Szemerédi

Martin Raussen, Christian Skau
2013 Notices of the American Mathematical Society  
I gave a series of lectures; Peter Elliot and Edward Wirsing, both extremely strong mathematicians, wrote a paper based almost entirely on my pictures on the blackboard.  ...  Moreover, the algorithm can efficiently run simultaneously on cn processors such that every number is processed by only one of them at a time.  ...  On the day the game was played, the paper appeared with my-as it turned out-correct prediction.  ... 
doi:10.1090/noti948 fatcat:xt7nxxhunzahllsy3422bcco3y

Remembering Jean Bourgain (1954–2018)

Ingrid Daubechies, Freddy Delbaen, Larry Guth, Svetlana Jitomirskaya, Alex Kontorovich, Elon Lindenstrauss, Vitali Milman, Gilles Pisier, Zeev Rudnick, Peter Sarnak, Wilhelm Schlag, Gigliola Staffilani (+2 others)
2021 Notices of the American Mathematical Society  
Since that first time I interacted with Jean at the IAS my admiration for him grew exponentially.  ...  One of the popular topics was the generalization of the Radon-Nikodym theorem for vector-valued measures. The theorem describes when a measure has a density.  ... 
doi:10.1090/noti2290 fatcat:vrtmo7hbjzdwhkyhu5kr3hsnpm

II. Arithmetic [chapter]

Alexandre Borovik, Tony Gardiner
2019 The Essence of Mathematics Through Elementary Problems  
When we talk about "average speed", we are thinking of speed changing as a function of time; and the total distance covered in any given time interval ra, bs is equal to the area under the graph.  ...  The next problem invites you to devise divisibility tests for integers written in base 2 like those for base 10 (that is, tests which implement some check involving the base 2 digits in place of carrying  ...  Note: In the solution to Problem 241 we included the condition on z as part of the statement Ppnq.  ... 
doi:10.11647/obp.0168.02 fatcat:h4vocilu65eelgp7av4u4vmupu

Liberal Arts Colleges: An Overlooked Opportunity?

David Damiano, Stephan Ramon Garcia, Michele Intermont
2016 Notices of the American Mathematical Society  
The focus of this volume is on recent progress towards complete understanding of the direct problem with high contrast or high frequencies, and unified approaches to the inverse and imaging problems for  ...  The papers in this volume contain results on polynomial approximation, rational approximation, Log-optimal configurations on the sphere, random continued fractions, ratio asymptotics for multiple orthogonal  ...  I've been invited to edit a volume based on talks at that meeting, and a course release this fall would allow me to focus on that responsibility.")  ... 
doi:10.1090/noti1381 fatcat:37qqib56ivhb5p3yrdc2i3g6ke

Crafting Your Research Future: A Guide to Successful Master's and Ph.D. Degrees in Science & Engineering

Charles X. Ling, Qiang Yang
2012 Synthesis Lectures on Engineering  
You then formulate a hypothesis as a (problem, solution) pair. Each hypothesis states that the solution can indeed solve the problem.  ...  When it is time for paper writing, the advisor often acts as an editor, We can also roughly categorize journals and conferences into the same four classes based on many factors (such as the Impact Factor  ... 
doi:10.2200/s00412ed1v01y201203eng018 fatcat:bjgmf76vpnedfifwyqrx6fxb2m

The Science and Legacy of Richard Phillips Feynman [article]

Avinash Dhar, Apoorva D. Patel, Spenta R. Wadia
2019 arXiv   pre-print
This year is the 100th birth anniversary of Richard Philips Feynman. This article commemorates his scientific contributions and lasting legacy.  ...  The images of Feynman that we have used in this article are taken from various internet resources. SRW would like to acknowledge the Infosys Foundation Homi Bhabha Chair at ICTS-TIFR.  ...  Acknowledgments We would like to thank Dipan Ghosh and Swaminathan Kailas for inviting this article for Physics News.  ... 
arXiv:1810.07409v2 fatcat:w3nsvzzcaja6hdjirgq3ptqcre

Collaborative Solving in a Human Computing Game Using a Market, Skills and Challenges

Olivier Tremblay-Savard, Alexander Butyaev, Jérôme Waldispühl
2016 Proceedings of the 2016 Annual Symposium on Computer-Human Interaction in Play - CHI PLAY '16  
In this paper, we design a novel multi-player game-with-a-purpose, and analyze the impact of multiple game mechanisms on the performance of the system.  ...  The second approach could be used to explore larger search spaces while harnessing collective intelligence, but popular crowdsourcing systems making use of the Amazon Mechanical Turk deliberately forbid  ...  advice on the statistical tests.  ... 
doi:10.1145/2967934.2968104 fatcat:xhlwkvpwjng7ha33q2zfh6adpe

Deterministic Dynamics and Chaos: Epistemology and Interdisciplinary Methodology [article]

Eleonora Catsigeras
2011 arXiv   pre-print
On the other hand, we propose the converse relation which consists in the formulation of new abstract mathematical problems appearing from processes and structures under research of psychology.  ...  particular, on the theory of chaos.  ...  the hypothesis of research, to simplify the mathematical problem under investigation as much as needed (and as less as possible).  ... 
arXiv:1106.4087v1 fatcat:x2filrkznnc7naz75hob64ut4y
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