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There are far too many mathematicians for me to name here, you only need to wiki a mathematician of note to find out he is Jewish. Are they taught to think logically and analytically from a young age? What are the possible explanations for this? Have their been any studies on this? Might there be any aspects of Jewish culture or pedagogy that would give rise to their success in mathematics?

P. S. If someone could edit the tags that would be appreciated, as I'm not entirely sure they're the correct ones.

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closed as primarily opinion-based by Mark Fantini, Chris Cunningham, vonbrand, JoeTaxpayer, Benjamin Dickman Jul 27 at 4:11

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise.If this question can be reworded to fit the rules in the help center, please edit the question.

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Jewish does not mean anything uniform, either culturally or genetically. Any meaning it may have may not apply to a number of the mathematicians you can think of. So this question can't be answered, and I'm afraid that all studies attempting to answer it would have been biased at the least. –  Ryan Reich Jul 24 at 14:58
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A possible reason is that there is a strong tradition of almost axiomatic analysis of the Torah and Talmud in (orthodox) jewish culture. Check out judaism.stackexchange.com. If you peruse that site you will find many instances of people teasing apart subtle distinctions between different definitions, arguments by contradiction, ...etc. All of these skills are highly relevant to mathematical thought. It is also considered "fun" to have these types of discussions. This type of reasoning does not stop at the Torah: it spills out into everyday life. –  Steven Gubkin Jul 24 at 16:00
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Speaking as a nonreligious jew, I was still brought up with many of these characteristics, especially by my grandfather: use language carefully, examine everything for logical contradictions. A lot of humor is taking logic to an extreme in my family. I am posting this all as a comment because it is very anecdotal, but I do think these cultural characteristics of Jews could lead to a higher percentage of mathematicians in that population. –  Steven Gubkin Jul 24 at 16:03
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@RyanReich: Jewish does not mean anything uniform, either culturally or genetically. Well, yes and no. Ashkenazi Jews have enough genetic correlations that they have higher incidences of diseases such as Tay-Sachs. Culturally, there are huge differences between groups in the professions they go into. It's not necessary for a culture to be completely homogeneous, or for every member of that culture to go into the same profession. You can still get massive disproportions across groups. E.g., the percentage of Jews who go into medicine is orders of magnitude higher than for Native Americans. –  Ben Crowell Jul 24 at 16:40
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I feel good about closing the question now that we have a good meta-answer from JPBurke; I've voted to close as opinion-based. No offense intended to the original questioner; this was certainly an interesting group of words to read, but I don't think it would be productive to allow many more answers. –  Chris Cunningham Jul 25 at 17:06

4 Answers 4

This question seems like a big opportunity for casual social science conjecturing which may or may not be productive. I hope I can clarify a couple of things in my response.

According to your supporting statement, your question is "what are the possible explanations for why so many mathematicians you look up on Wikipedia are Jewish?" For the purposes of this answer I'm going to assume we are talking about one monolithic group with genetics and culture in common so that I can speak hypothetically (while acknowledging that others have challenges to that aspect of the question, and that they are at least worth thinking about).

One explanation could be that the group is actually better at math. To just ask why this group is better at math, however, would be to assume they are better at math (so I won't do that). It is not actually demonstrated by the wiki search mentioned. If there is more support for this sort of explanation--for instance, a difference in the comparison of means as part of some quantitative study--we could search for an explanation of why those means are different, and look to culture, perhaps. But we are not actually at that point, unless someone provides such evidence.

Another explanation we could conjecture about is that there might be similar means in the Jewish population and other populations, but there might be a greater variance in the data. Meaning that good Jewish mathematicians become more accomplished and thus are among the most famous mathematicians. And, if the means are similar, there would be similarly exceptional low achievers in the same population (or more slightly less accomplished mathematics users-- depending on the shape of the curve). We would look for a different sort of explanation if this is the quantitative difference we noticed in comparison of Jewish and other groups.

There could be cultural reasons that some accomplished Jewish mathematicians are better supported for some reason. Or that they have happened to be in groups at opportune places or times (enough to make really important contributions, but not in great enough numbers to change the mean over a reasonable sample of Jewish people). Yes, smart people "math better" but they do it even betterer in groups.

Conjectures are great starting points for research questions. But outside of using them for that purpose (to propose research) or having actual research and discussing how to extend from that research, I think we enter a realm of imagination rather than scientific enlightenment. One benefit of good social science is that assumptions must be made explicit. In casual conjecturing you will see assumptions pop up like dandelions and participants trample over them toward a possible explanation that catches their eye. I think I would be a lousy research assistant if I didn't point out that outside of scientific research, we often see a compelling conclusion driving whatever justification can connect things. And this is (at the very least) unfair to the groups of people subjected to our conjectures. Discretion and caution are called for. Even if we think we're saying something positive.

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Excellent points. –  Steven Gubkin Jul 24 at 20:56
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Yes, smart people "math better" but they do it even betterer in groups. Ha –  Benjamin Dickman Jul 24 at 21:04
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Interracial differences in intellectual traits are notoriously small and hard to measure because of variables that can't be controlled for. Therefore the cultural reasons referred to in the second-to-last paragraph are the most reasonable null hypothesis. In the U.S., the percentage of people with a given surname who are medical doctors varies from 11% down to 0.02%: opinionator.blogs.nytimes.com/2014/02/21/… This is three orders of magnitude. So it wouldn't be at all surprising if Jews were vastly overrepresented among mathematicians for cultural reasons. –  Ben Crowell Jul 25 at 18:12
    
@BenCrowell - I agree; despite lumping "similar genetics" into my assumptions, my guess is that any significant difference (including ones showing up in the broadly-defined quantitative studies I suggested) would be traced to cultural differences. The OP was much more specific about one aspect of culture. An additional point I could have made would be about how studying very specific (known, identifiable) cultural practices makes it easier to demonstrate real connections to phenomena. A difference of means doesn't answer "what is happening" or "why?" But could tell us "whether or not." –  JPBurke Jul 25 at 18:39
    
Cute way of saying something true "In casual conjecturing you will see assumptions pop up like dandelions and participants trample over them toward a possible explanation that catches their eye." .....+1 –  Tutor Jul 27 at 2:48

My answer is just my educated guess and so it is probably flawed. But I think besides mathematicians, you could also include writers or other scientists, think Freud or Oppenheimer for example. Steven Gubkin in his comments already pointed the major points. I just wanted to add the practice of Judaism is centered on reading and studying the Torah but since the Torah is not clear cut with regard many aspects (oral law) - a great part of studying centers on reading the debates amongst the old rabbis of the Talmud. That is: most of the religious law emerged as result of debates using logical arguments on what is the correct interpretation of some text. The analysis and dissection of the text, creates a culture that gives incentives to debates and arguments based on logic. This culture goes beyond the religious practitioners. Freud, again as an example, was somewhat anti-religious: after his wedding, he forbade his wife to light candles on Friday evenings. Perhaps you could ask the question at Mi Yodeya at Stack Exchange.

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If you're looking up German mathematicians of note of the 1870s to the 1930s, there are some historical reasons for a high fraction of Jews:

1) German academic anti-Semitism may have pushed Jews away from higher-prestige fields like experimental physics. So Jews with physical and mathematical interests may have focused on their mathematical interests or opportunities as a result. (See Jungnickel and McCormmach, Intellectual Mastery of Nature, pp. 286-287: "Among academic fields in Germany, theoretical physics had an unusually high proportion of Jews, who found more opportunity there than in the more desirable field of experimental physics".)

2) Felix Klein believed that Jewish mathematicians tended to have particular habits of thought, and promoted those habits of thought as part of a diverse approach to mathematics. He had enough influence over hiring in German math departments for these views to have an effect. (See David Rowe, "'Jewish mathematics' at Gottingen in the era of Felix Klein".)

3) The German mathematical emigration of the 1930's may have led to German Jewish mathematicians becoming better-known that their non-Jewish counterparts. (See Sanford Segal on Mathematicians Under the Nazis, or his entry on Helmut Hasse in the Dictionary of Scientific Biography.) The Jews who emigrated to the U.S. may have became more integrated into the US-centric mathematical world of the later 20th century than the non-Jews who did not.

Whatever our beliefs about the value of Jews in various fields of math or physics, similar beliefs among various Germans had theirs, and that was enough to cause historical effects.

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This is a really nice question. Although it is discussed by OP, Steven Gubkin and Sergio Parreiras implicitly, I would like to emphasize on cultural root of this phenomena again.

Religion is the most important part of Jewish culture. Some mysterious parts of this special religious culture are Jewish mysticism and Kabbalah which play a vital role in old tradition of Jewish mathematics. In fact one can see numbers all around Torah. A famous example is Book of Numbers which is full of strange numbers.

As a consequence of this Jewish philosophical idea that God created world in the language of numbers (maths) and then coded its secrets somewhere in the Torah, one may think about discovering these secrets using numbers (maths). This idea in Jewish culture gives a divine importance to maths. In this point of view mathematics is a tool to unfold all secrets of the universe and those who believe in this idea analyze every phenomena mathematically to find the signs.

In order to find more on this topic see Pi movie and my question in movies.stackexchange.com

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Interesting....though it should be noted that the "Book of Numbers" isn't exactly about numbers....it is called that because of the large incidence of census-counts taken in the book (ספר פיקודים = Book of Numbers, but possibly more accurately translated as "Book of Countings"); but good pick up! –  Tutor Jul 27 at 2:41
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......Judaism.SE does have a series of questions referred to as "mi-yodeya‌​" for what things are numbered in Judaism [based off of the song "Echad Mi Yodeya," "who knows one?"] if you're interested –  Tutor Jul 27 at 2:46

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