mathematicians-from-israel

"Combinatorics is primarily the mathematics of finite objects, investigating the properties of combinatorial structures. Its areas of study include exact and asymptotic enumeration, graph theory, probabilistic and extremal combinatorics, designs and finite geometries."

"Israel has traditionally always been a strong center of mathematical research. The Hebrew University has been particularly strong in Set Theory, Logic and Ergodic Theory. As mentioned, I used to come to the university only once a week."

"In my research I tried (and still try) to develop effective techniques by tackling interesting problems. Solving such problems, especially ones with a history, is an important goal, but an even more important goal is the introduction of novel ideas and tools that can lead to further progress."

"The core of most of the fundamental questions in theoretical computer science is combinatorial, as the notion of computation is based on manipulations with finite structures. The investigation of the limits of computation leads to basic combinatorial questions, and much of the design and analysis of efficient algorithms is also combinatorial in nature"

"The relations between combinatorics and other mathematical and scientific areas have been crucial in the development of the modern theory. Combinatorial concepts and questions appear naturally in many branches of mathematics, and the area has found applications in other disciplines as well."

"Although a big part of the research on paraconsistent logics has so far been motivated by the paradoxes in naive set theory, and to developing alternative paraconsistent mathematics, I do not think that paraconsistent mathematics has real interest - at least not as long as we deal with truth in pure mathematics."

"For me the value of paraconsistent logics is as a potential instrument, to be used when there is a need to draw practical conclusions from an inconsistent body of "knowledge"."

"The influence on mathematics of its two neighbors, physics and logic, is sometimes opposite or, at least, complementary. Whereas the entropy theorems of probability theory and mathematical physics imply that, in a large universe, disorder is probable, certain combinatorial theorems imply that complete disorder is impossible."

"Programming is much much harder than doing mathematics."

"Mathematics my foot! Algorithms are mathematics too, and often more interesting and definitely more useful."

"Regardless of whether or not God exists, God has no place in mathematics, at least in my book."

"Algorithms existed for at least five thousand years, but people did not know that they were algorithmizing. Then came Turing (and Post and Church and Markov and others) and formalized the notion."

"Conventional wisdom, fooled by our misleading "physical intuition", is that the real world is continuous, and that discrete models are necessary evils for approximating the "real" world, due to the innate discreteness of the digital computer."

"Computer Algebra Systems are NOT the Devil but the new MESSIAH that will take us out of the current utterly trivial phase of human-made mathematics into the much deeper semi-trivial computer-generated phase of future mathematics. Even more important, Computer Algebra Systems will turn out to be much more than just a `tool', since the methodology of computer-assisted and computer-generated research will rule in the future, and will make past mathematics seem like alchemy and astrology, or, at best, theology."

"Math is perfect (in principle), but mathematicians are not (because they are humans), hence the mathematics that (human) mathematicians do is influenced by the weltanschauung of the people around them."

"When a problem seems intractable, it is often a good idea to try to study "toy" versions of it in the hope that as the toys become increasingly larger and more sophisticated, they would metamorphose, in the limit, to the real thing."

"The best way to learn a topic is by teaching it. Similarly the best way to understand a new proof is by writing an expository article about it."

"Let me also remind you that zero, like all of mathematics, is fictional and an idealization. It is impossible to reach absolute zero temperature or to get perfect vacuum. Luckily, mathematics is a fairyland where ideal and fictional objects are possible."

"Many of the successes of `fancy' mathematics are due to sociological and linguistic reasons. They are really high-school-algebra arguments in disguise. Once you strip the fancy verbiage off, what remains is a bare (and much prettier, in my eyes) argument in high-school mathematics, or at most, in Freshman linear-algebra and (formal!) Calculus. For example, I am (almost) sure that Wiles's proof would be expressible in simple language, and if not, there would be a much nicer proof that would."

"Mathematics is so useful because physical scientists and engineers have the good sense to largely ignore the "religious" fanaticism of professional mathematicians, and their insistence on so-called rigor, that in many cases is misplaced and hypocritical, since it is based on "axioms" that are completely fictional, i.e. those that involve the so-called infinity."

"We can trust only ourselves. The president of the United States has to look out for U.S. interests -- that is what he was elected to do. He does not have to look out for Israel's interests, nor do I expect him to. The bottom line is that Obama is president of the United States -- not the world -- so when it comes to Israel's interests I trust the prime minister's discretion."

"“Torah study is an intellectual pursuit, and honoring this ultimate value transfers to other pursuits as well, Jewish homes are full of books while other homes may or may not be. Jewish homes have overflowing bookshelves. Throughout the generations we have given great honor to this intellectual pursuit…Torah study makes the nation and its people of the finest and highest quality.”"

"I think game theory creates ideas that are important in solving and approaching conflict in general."

""Interactive Decision Theory" would perhaps be a more descriptive name for the discipline usually called Game Theory."

"The strong equilibrium point f just described is one of "unrelenting ferocity" against offenders. It exhibits a zeal for meting out justice that is entirely oblivious to the sometimes dire consequences to oneself or to the other faitheful——i.e., those who have not deviated."

"It turns out that the Romans were champs in making peace. Their motto was that if you want to make peace, you need to prepare for war. They knew game theory."

"I would like to suggest that we should perhaps change direction in our efforts to bring about world peace. Up to now all the effort has been put into resolving specific conflicts: India–Pakistan, North–South Ireland, various African wars, Balkan wars, Russia–Chechnya, Israel–Arab, etc., etc. I’d like to suggest that we should shift emphasis and study war in general."

"War has been with us ever since the dawn of civilization. Nothing has been more constant in history than war."

"A person’s behavior is rational if it is in his best interests, given his information."

"The theory of repeated games is able to account for phenomena such as altruism, cooperation, trust, loyalty, revenge, threats (self-destructive or otherwise) – phenomena that may at first seem irrational – in terms of the “selfish” utility-maximizing paradigm of game theory and neoclassical economics."

"The players in a game are said to be in strategic equilibrium (or simply equilibrium) when their play is mutually optimal: when the actions and plans of each player are rational in the given strategic environment – i.e., when each knows the actions and plans of the others."

"Repetition acts as an enforcement mechanism: It makes cooperation achievable when it is not achievable in the one-shot game, even when one replaces strategic equilibrium as the criterion for achievability by the more stringent requirement of perfect equilibrium."

"In many real-world situations, cooperation may be easier to sustain in a long-term relationship than in a single encounter. Analyses of short-run games are, thus, often too restrictive. Robert Aumann was the first to conduct a full-fledged formal analysis of so-called infinitely repeated games. His research identified exactly what outcomes can be upheld over time in long-run relations."

"He advised the audience to remember the Romans, and the fact that as "disagreeable" as they were, the Roman Empire ruled in peace for 400 years."

"Capitulation, sycophancy, and cowardice will only undermine us... Sometimes, you have to courageously follow your own path and not try to curry favor with anyone."

"All these cries for peace we hear in Israel, especially from our side, do not bring peace any closer -- they only push it away. If you chase peace it only eludes you. That's not game theory; that's history."

"The world aligns itself with those who are strong, even if they are the embodiment of evil. That is why [Prime Minister Benjamin] Netanyahu's insistence on addressing Congress in an effort to prevent a deal between the United States and Iran is vital..."